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The discovery of the 1144-phase, e.g. CaKFe4As4, creates opportunities to build novel intermetallics with alternative stacking of two parent compounds. Here we formalize the idea by defining a class of bulk crystalline solids with A-B stacking (including 1144-phases and beyond), which is a generalization of hetero-structures from few-layer or thin-film semi-conductors to bulk intermetallics. Theoretically, four families of phosphides \textit{AB}(TM)4P4 (TM=Fe, Ru, Co, Ni) are investigated by first-principles calculations, wherein configurational, vibrational and electronic degrees of freedom are considered. It predicts a variety of stable 1144-phases (especially Ru- and Fe-phosphides). Stability rules are found and structural/electronic properties are discussed. Experimentally, we synthesize high-purity CaKRu4P4 as a proof of principle example. The synthetic method is simple and easily applied. Moreover, it alludes to a strategy to explore complex multi-component compounds, facilitated by a phase diagram coordinated by collective descriptors.
Rich functionalities of transition-metal oxides and their interfaces bear an enormous technological potential. Its realization in practical devices requires, however, a significant improvement of yet relatively low electron mobility in oxide materials. Recently, a mobility boost of about two orders of magnitude has been demonstrated at the spinel/perovskite {\gamma}-Al2O3/SrTiO3 interface compared to the paradigm perovskite/perovskite LaAlO3/SrTiO3. We explore the fundamental physics behind this phenomenon from direct measurements of the momentum-resolved electronic structure of this interface using resonant soft-X-ray angle-resolved photoemission. We find an anomaly in orbital ordering of the mobile electrons in {\gamma}-Al2O3/SrTiO3 which depopulates electron states in the top STO layer. This rearrangement of the mobile electron system pushes the electron density away from the interface that reduces its overlap with the interfacial defects and weakens the electron-phonon interaction, both effects contributing to the mobility boost. A crystal-field analysis shows that the band order alters owing to the symmetry breaking between the spinel {\gamma}-Al2O3 and perovskite SrTiO3. The band-order engineering exploiting the fundamental symmetry properties emerges as another route to boost the performance of oxide devices.
In magic angle twisted bilayer graphene, transport, thermodynamic and spectroscopic experiments pinpoint at a competition between distinct low-energy states with and without electronic order, as well as a competition between localized and delocalized charge carriers. In this study, we utilize Dynamical Mean Field Theory (DMFT) on the topological heavy Fermion (THF) model of twisted bilayer graphene to investigate the emergence of electronic correlations and long-range order in the absence of strain. We explain the nature of emergent insulating and correlated metallic states, as well as transitions between them driven by three central phenomena: (i) the formation of local spin and valley isospin moments around 100K, (ii) the ordering of the local isospin moments around 10K, and (iii) a cascadic redistribution of charge between localized and delocalized electronic states upon doping. At integer fillings, we find that low energy spectral weight is depleted in the symmetric phase, while we find insulating states with gaps enhanced by exchange coupling in the zero-strain ordered phases. Doping away from integer filling results in distinct metallic states: a "bad metal" above the ordering temperature, where coherence of the low-energy electronic excitations is suppressed by scattering off the disordered local moments, and a "good metal" in the ordered states with coherence of quasiparticles facilitated by isospin order. Upon doping, there is charge transfer between the localized and delocalized orbitals of the THF model such that they get periodically filled and emptied in between integer fillings. This charge reshuffling manifests itself in cascades of doping-induced Lifshitz transitions, local spectral weight redistributions and periodic variations of the electronic compressibility ranging from nearly incompressible to negative.
Strontium ruthenate Sr2RuO4 is an unconventional superconductor whose pairing symmetry has not been fully clarified, despite more than two decades of intensive research. Recent NMR Knight shift experiments have rekindled the Sr2RuO4 pairing debate by giving strong evidence against all odd-parity pairing states, including chiral p-wave pairing that was for a long time the leading pairing candidate. Here, we exclude additional pairing states by analyzing recent elastocaloric measurements [YS. Li et al., Nature 607, 276--280 (2022)]. To be able to explain the elastocaloric experiment, we find that unconventional even-parity pairings must include either large dx2−y2-wave or large {dxz∣dyz}-wave admixtures, where the latter possibility arises because of the body-centered point group symmetry. These {dxz∣dyz}-wave admixtures take the form of distinctively body-centered-periodic harmonics that have horizontal line nodes. Hence gxy(x2−y2)-wave and dxy-wave pairings are excluded as possible dominant even pairing states.
The existence of bound states induced by local impurities coupled to an insulating host depends decisively on the global topological properties of the host's electronic structure. In this context, we consider magnetic impurities modelled as classical unit-length spins that are exchange-coupled to the spinful Haldane model on the honeycomb lattice. We investigate the spectral flow of bound states with the coupling strength J in both the topologically trivial and Chern-insulating phases. In addition to conventional k-space topology, an additional, spatially local topological feature is available, based on the space of impurity-spin configurations forming, in case of R impurities, an R-fold direct product of two-dimensional spheres. Global k-space and local S-space topology are represented by different topological invariants, the first (k-space) Chern number and the R-th (S-space) spin-Chern number. We demonstrate that there is a local S-space topological transition as a function of J associated with a change in the spin Chern number and work out the implications of this for the J-dependent local electronic structure close to the impurities and, in particular, for in-gap bound states. The critical exchange couplings' dependence on the parameters of the Haldane model, and thus on the k-space topological state, is obtained numerically to construct local topological phase diagrams for systems with R=1 and R=2 impurity spins.
Although iron-based catalysts are regarded as a promising alternative to precious metal catalysts, their precise electronic structures during catalysis still pose challenges for computational descriptions. A particularly urgent question is the influence of the environment on the electronic structure, and how to describe this properly with computational methods. Here, we study an iron porphyrin chloride complex adsorbed on a graphene sheet using density functional theory calculations to detail how much the electronic structure is influenced by the presence of a graphene layer. Our results indicate that weak interactions due to van der Waals forces dominate between the porphyrin complex and graphene, and only a small amount of charge is transferred between the two entities. Furthermore, the interplay of the ligand field environment, strong p − d hybridization, and correlation effects within the complex are strongly involved in determining the spin state of the iron ion. By bridging molecular chemistry and solid state physics, this study provides first steps towards a joint analysis of the properties of iron-based catalysts from first principles.
Although iron-based catalysts are regarded as a promising alternative to precious metal catalysts, their precise electronic structures during catalysis still pose challenges for computational descriptions. A particularly urgent question is the influence of the environment on the electronic structure, and how to describe this properly with computational methods. Here, we study an iron porphyrin chloride complex adsorbed on a graphene sheet using density functional theory calculations to detail how much the electronic structure is influenced by the presence of a graphene layer. Our results indicate that weak interactions due to van der Waals forces dominate between the porphyrin complex and graphene, and only a small amount of charge is transferred between the two entities. Furthermore, the interplay of the ligand field environment, strong p − d hybridization, and correlation effects within the complex are strongly involved in determining the spin state of the iron ion. By bridging molecular chemistry and solid state physics, this study provides first steps towards a joint analysis of the properties of iron-based catalysts from first principles.
The discovery of the 1144-phase, e.g. CaKFe4As4, creates opportunities to build novel intermetallics with alternative stacking of two parent compounds. Here we formalize the idea by defining a class of bulk crystalline solids with A-B stacking (including 1144-phases and beyond), which is a generalization of hetero-structures from few-layer or thin-film semi-conductors to bulk intermetallics. Theoretically, four families of phosphides \textit{AB}(TM)4P4 (TM=Fe, Ru, Co, Ni) are investigated by first-principles calculations, wherein configurational, vibrational and electronic degrees of freedom are considered. It predicts a variety of stable 1144-phases (especially Ru- and Fe-phosphides). Stability rules are found and structural/electronic properties are discussed. Experimentally, we synthesize high-purity CaKRu4P4 as a proof of principle example. The synthetic method is simple and easily applied. Moreover, it alludes to a strategy to explore complex multi-component compounds, facilitated by a phase diagram coordinated by collective descriptors.
The discovery of the 1144-phase, e.g. CaKFe4As4, creates opportunities to build novel intermetallics with alternative stacking of two parent compounds. Here we formalize the idea and introduce a concept, namely hetero-crystals (HC), to describe a unique class of bulk crystalline solids with such A-B stacking (including 1144-phases and beyond). HC generalizes hetero-structures from few-layer or thin-film semi-conductors to bulk intermetallics. We illustrate the HC concept with the example of 1144-phases. Theoretically, four families of phosphides \textit{AB}(TM)4P4 (TM=Fe, Ru, Co, Ni) are investigated by first-principles calculations, wherein configurational, vibrational and electronic degrees of freedom are considered. It predicts a variety of stable 1144-phases (especially Ru- and Fe-phosphides). Stability rules are found and structural/electronic properties are discussed. Experimentally, we synthesize high-purity CaKRu4P4 as a proof of principle example of such a HC. The synthetic method is simple and can be applied to other HC. Moreover, HC alludes to a new strategy to explore complex multi-component compounds, facilitated by a new phase diagram coordinated by collective descriptors.
Twisted heterostructures of van der Waals materials have received much attention for their many remarkable properties. Here, we present a comprehensive theory of the long-range ordered magnetic phases of twisted bilayer α-RuCl3 via a combination of first-principles calculations and atomistic simulations. While a monolayer exhibits zigzag antiferromagnetic order with three possible ordering wave vectors, a rich phase diagram is obtained for moiré superlattices as a function of interlayer exchange and twist angle. For large twist angles, each layer spontaneously picks a single zigzag ordering wave vector, whereas, for small twist angles, the ground state involves a combination of all three wave vectors in a complex hexagonal domain structure. This multi-domain order minimizes the interlayer energy while enduring the energy cost due to the domain wall formation. Our results indicate that magnetic frustration due to stacking-dependent interlayer exchange in moiré superlattices can be used to tune the magnetic ground state and enhance quantum fluctuations in α-RuCl3.
Evolution of nematic fluctuations in CaK(Fe1−xNix)4As4 with spin-vortex crystal magnetic order
(2020)
The CaK(Fe1−xNix)4As4 superconductors resemble the archetypal 122-type iron-based materials but have a crystal structure with distinctly lower symmetry. This family hosts one of the few examples of the so-called spin-vortex crystal magnetic order, a non-collinear magnetic configuration that preserves tetragonal symmetry, in contrast to the orthorhombic collinear stripe-type magnetic configuration common to the 122-type systems. Thus, nematic order is completely absent from its phase diagram. To investigate the evolution of nematic fluctuations in such a case, we present elastoresistance and elastic modulus measurements in CaK(Fe1−xNix)4As4 (x=0−0.05) combined with phenomenological modeling and density functional theory. We find clear experimental signatures of considerable nematic fluctuations, including softening of the Young's modulus Y[110] and a Curie-Weiss type divergence of the B2g elastoresistance coefficient in CaK(Fe0.951Ni0.049)4As4. Overall, nematic fluctuations within this series bear strong similarities to the hole-doped Ba1−xKxFe2As2 series, including a substitution-induced sign change. Our theoretical analysis addresses the effect of the specific crystal symmetry of the 1144-type structure in determining its magnetic ground state and on the nematic fluctuations.
We investigate the magnetism of a previously unexplored distorted spin-1/2 kagome model consisting of three symmetry-inequivalent nearest-neighbor antiferromagnetic Heisenberg couplings and uncover a rich ground state phase diagram even at the classical level. Using analytical arguments and numerical techniques we identify a collinear Q⃗ =0 magnetic phase, two unusual non-collinear coplanar Q⃗ =(1/3,1/3) phases and a classical spin liquid phase with a degenerate manifold of non-coplanar ground states, resembling the jammed spin liquid phase found in the context of a bond-disordered kagome antiferromagnet. We further show with density functional theory calculations that the recently synthesized Y-kapellasite Y3Cu9(OH)19Cl8 is a realization of this model and predict its ground state to lie in the region of Q⃗ =(1/3,1/3) order, which remains stable even after inclusion of quantum fluctuation effects within variational Monte Carlo and pseudofermion functional renormalization group. Interestingly, the excitation spectrum of Y-kapellasite lies between that of an underlying triangular lattice of hexagons and a kagome lattice of trimers. The presented model opens a new direction in the study of kagome antiferromagnets.
We investigate the magnetism of a previously unexplored distorted spin-1/2 kagome model consisting of three symmetry-inequivalent nearest-neighbor antiferromagnetic Heisenberg couplings Jhexagon, J and J', and uncover a rich ground state phase diagram even at the classical level. Using analytical arguments and numerical techniques we identify a collinear Q = 0 magnetic phase, two unusual non-collinear coplanar Q = (1/3,1/3) phases and a classical spin liquid phase with a degenerate manifold of non-coplanar ground states, resembling the jammed spin liquid phase found in the context of a bond-disordered kagome antiferromagnet. We further show with density functional theory calculations that the recently synthesized Y-kapellasite Y3Cu9(OH)19Cl8 is a realization of this model and predict its ground state to lie in the region of Q = (1/3,1/3) order, which remains stable even after inclusion of quantum fluctuation effects within variational Monte Carlo and pseudofermion functional renormalization group. The presented model opens a new direction in the study of kagome antiferromagnets.
The discovery of superconductivity in layered vanadium-based kagome metals AV3Sb5 (A: K, Rb, Cs) has added a new family of materials to the growing class of possible unconventional superconductors. However, the nature of the superconducting pairing in these materials remains elusive. We present a microscopic theoretical study of the leading superconducting instabilities on the kagome lattice based on spin- and charge-fluctuation mediated Cooper pairing. The applied methodology includes effects of both on-site and nearest-neighbor repulsive Coulomb interactions. Near the upper van Hove filling -- relevant for the AV3Sb5 materials -- we find a rich phase diagram with several pairing symmetries being nearly degenerate. In particular, while a substantial fraction of the phase diagram is occupied by a spin-singlet order parameter transforming as a two-dimensional irreducible representation of the point group, several nodal spin-triplet pairing states remain competitive. We compute the band and interaction parameter-dependence of the hierarchy of the leading superconducting instabilities, and determine the detailed momentum dependence of the resulting preferred gap structures. Crucially, for moderate values of the interaction parameters, the individual pairing states depend strongly on momentum and exhibit multiple nodes on the Fermi surface. We discuss the properties of these superconducting gap structures in light of recent experimental developments of the AV3Sb5 materials.
The Kitaev material α-RuCl3 is among the most prominent candidates to host a quantum spin-liquid state endowed with fractionalized excitations. Recent experimental and theoretical investigations have separately revealed the importance of both the magnetoelastic coupling and the magnetic anisotropy, in dependence of the applied magnetic field direction. In this combined theoretical and experimental research, we investigate the anisotropic magnetic and magnetoelastic properties for magnetic fields applied along the main crystallographic axes as well as for fields canted out of the honeycomb plane. We found that the magnetostriction anisotropy is unusually large compared to the anisotropy of the magnetization, which is related to the strong magnetoelastic Γ′˜-type coupling in our \textit{ab-initio} derived model. We observed large, non-symmetric magnetic anisotropy for magnetic fields canted out of the honeycomb ab-plane in opposite directions, namely towards the +c∗ or −c∗ axes, respectively. The observed directional anisotropy is explained by considering the relative orientation of the magnetic field with respect to the co-aligned RuCl6 octahedra. Magnetostriction measurements in canted fields support this non-symmetric magnetic anisotropy, however these experiments are affected by magnetic torque effects. Comparison of theoretical predictions with experimental findings allow us to recognize the significant contribution of torque effects in experimental setups where α-RuCl3 is placed in canted magnetic fields.
Layered {\alpha}-RuCl3 is a promising material to potentially realize the long-sought Kitaev quantum spin liquid with fractionalized excitations. While evidence of this exotic state has been reported under a modest in-plane magnetic field, such behavior is largely inconsistent with theoretical expectations of Kitaev phases emerging only in out-of-plane fields. These predicted field-induced states have been mostly out of reach due to the strong easy-plane anisotropy of bulk crystals, however. We use a combination of tunneling spectroscopy, magnetotransport, electron diffraction, and ab initio calculations to study the layer-dependent magnons, anisotropy, structure, and exchange coupling in atomically thin samples. Due to structural distortions, the sign of the average off-diagonal exchange changes in monolayer {\alpha}-RuCl3, leading to a reversal of magnetic anisotropy to easy-axis. Our work provides a new avenue to tune the magnetic interactions in {\alpha}-RuCl3 and allows theoretically predicted quantum spin liquid phases for out-of-plane fields to be more experimentally accessible.
Under temperature or pressure tuning, tetragonal EuPd2Si2 is known to undergo a valence transition from nearly divalent to nearly trivalent Eu accompanied by a volume reduction. Albeit intensive work, its origin is not yet completely understood. Here, we investigate the mechanism of the valence transition under volume compression by density functional theory calculations (DFT). Our analysis suggests that the transition is a consequence of an enhanced c−f hybridization between localized Eu 4f states and itinerant conduction states (Eu 5d, Pd 4d, and Si 3p) where the interplay of the electronic bandwidth, crystal field environment, Coulomb repulsion, Hund's coupling and spin-orbit coupling plays a crucial role for the transition to happen. The change in the electronic structure is intimately related to the volume reduction where Eu-Pd(Si) bond lengths shorten. In a next step we compare our DFT results to surface-sensitive photoemission data in which the mixed-valent properties of EuPd2Si2 are reflected in a simultaneous observation of divalent and trivalent signals from the Eu 4f shell.
We investigate the magnetism of a previously unexplored distorted spin-1/2 kagome model consisting of three symmetry-inequivalent nearest-neighbor antiferromagnetic Heisenberg couplings Jhexagon, J and J', and uncover a rich ground state phase diagram even at the classical level. Using analytical arguments and numerical techniques we identify a collinear Q = 0 magnetic phase, two unusual non-collinear coplanar Q = (1/3,1/3) phases and a classical spin liquid phase with a degenerate manifold of non-coplanar ground states, resembling the jammed spin liquid phase found in the context of a bond-disordered kagome antiferromagnet. We further show with density functional theory calculations that the recently synthesized Y-kapellasite Y3Cu9(OH)19Cl8 is a realization of this model and predict its ground state to lie in the region of Q = (1/3,1/3) order, which remains stable even after inclusion of quantum fluctuation effects within variational Monte Carlo and pseudofermion functional renormalization group. The presented model opens a new direction in the study of kagome antiferromagnets.
Due to the small photon momentum, optical spectroscopy commonly probes magnetic excitations only at the center of the Brillouin zone; however, there are ways to override this restriction. In case of the distorted kagome quantum magnet Y-kapellasite, Y3Cu9(OH)19Cl8, under scrutiny here, the spin (magnon) density of states (SDOS) can be accessed over the entire Brillouin zone through three-center magnon excitations. This mechanism is aided by the three different magnetic sublattices and strong short-range correlations in the distorted kagome lattice. The results of THz time-domain experiments agree remarkably well with linear spin-wave theory (LSWT). Relaxing the conventional zone-center constraint of photons gives a new aspect to probe magnetism in matter.
The rich functionalities of transition-metal oxides and their interfaces bear an enormous technological potential. Its realization in practical devices requires, however, a significant improvement of yet relatively low electron mobility in oxide materials. Recently, a mobility boost of about 2 orders of magnitude has been demonstrated at the spinel–perovskite γ-Al2O3/SrTiO3 interface compared to the paradigm perovskite–perovskite LaAlO3/SrTiO3 interface. We explore the fundamental physics behind this phenomenon from direct measurements of the momentum-resolved electronic structure of this interface using resonant soft-X-ray angle-resolved photoemission. We find an anomaly in orbital ordering of the mobile electrons in γ-Al2O3/SrTiO3 which depopulates electron states in the top SrTiO3 layer. This rearrangement of the mobile electron system pushes the electron density away from the interface, which reduces its overlap with the interfacial defects and weakens the electron–phonon interaction, both effects contributing to the mobility boost. A crystal-field analysis shows that the band order alters owing to the symmetry breaking between the spinel γ-Al2O3 and perovskite SrTiO3. Band-order engineering, exploiting the fundamental symmetry properties, emerges as another route to boost the performance of oxide devices.
The families of organic charge-transfer salts 𝜅-(BEDT-TTF)2𝑋 and 𝜅-(BETS)2𝑋, where BEDT-TTF and BETS stand for the organic donor molecules C10H8S8 and C10H8S4Se4, respectively, and X for an inorganic electron acceptor, have been proven to serve as a powerful playground for the investigation of the physics of frustrated Mott insulators. These materials have been ascribed a model character, since the dimerization of the organic molecules allows to map these materials onto a single band Hubbard model, in which the dimers reside on an anisotropic triangular lattice. By changing the inorganic unit X or applying physical pressure, the correlation strength and anisotropy of the triangular lattice can be varied. This has led to the discovery of a variety of exotic phenomena, including quantum-spin liquid states, a plethora of long-range magnetic orders in proximity to a Mott metal-insulator transition, and unconventional superconductivity. While many of these phenomena can be described within this effective one-band Hubbard model on a triangular lattice, it has become evident in recent years that this simplified description is insufficient to capture all observed magnetic and electronic properties. The ingredients for generalized models that are relevant include, but are not limited to, spin-orbit coupling, intra-dimer charge and spin degrees of freedom, electron-lattice coupling, as well as disorder effects. Here, we review selected theoretical and experimental discoveries that clearly demonstrate the relevance thereof. At the same time, we outline that these aspects are not only relevant to this class of organic charge-transfer salts, but are also receiving increasing attention in other classes of inorganic strongly correlated electron systems. This reinforces the model character that the 𝜅-phase organic charge-transfer salts have for understanding and discovering novel phenomena in strongly correlated electron systems from a theoretical and experimental point of view.
The search for materials with topological properties is an ongoing effort. In this article we propose a systematic statistical method, supported by machine learning techniques, that is capable of constructing topological models for a generic lattice without prior knowledge of the phase diagram. By sampling tight-binding parameter vectors from a random distribution, we obtain data sets that we label with the corresponding topological index. This labeled data is then analyzed to extract those parameters most relevant for the topological classification and to find their most likely values. We find that the marginal distributions of the parameters already define a topological model. Additional information is hidden in correlations between parameters. Here we present as a proof of concept the prediction of the Haldane model as the prototypical topological insulator for the honeycomb lattice in Altland-Zirnbauer (AZ) class A. The algorithm is straightforwardly applicable to any other AZ class or lattice, and could be generalized to interacting systems.
Recent density functional theory (DFT) calculations for KFe2As2 have been shown to be insufficient to satisfactorily describe angle-resolved photoemission (ARPES) measurements as well as observed de Haas–van Alphen (dHvA) frequencies. In the present work, we extend DFT calculations based on the full-potential linear augmented plane-wave method by dynamical mean field theory (DFT+DMFT) to include correlation effects beyond the local density approximation. We present results for two sets of reported crystal structures. Our calculations indicate that KFe2As2 is a moderately correlated metal with a mass renormalization factor of the Fe $3{\rm d}$ orbitals between 1.6 and 2.7. Furthermore, the obtained shape and size of the Fermi surface are in good agreement with ARPES measurements and we observe some topological changes with respect to DFT calculations such as the opening of an inner hole cylinder at the Z point. As a result, our calculated dHvA frequencies differ greatly from existing DFT results and qualitatively agree with experimental data. On this basis, we argue that correlation effects are important to understand the -presently under debate- nature of the superconducting state in KFe2As2.
We demonstrate ultra-sharp (≲10 nm) lateral p-n junctions in graphene using electronic transport, scanning tunneling microscopy, and first principles calculations. The p-n junction lies at the boundary between differentially-doped regions of a graphene sheet, where one side is intrinsic and the other is charge-doped by proximity to a flake of α-RuCl3 across a thin insulating barrier. We extract the p-n junction contribution to the device resistance to place bounds on the junction width. We achieve an ultra-sharp junction when the boundary between the intrinsic and doped regions is defined by a cleaved crystalline edge of α-RuCl3 located 2 nm from the graphene. Scanning tunneling spectroscopy in heterostructures of graphene, hexagonal boron nitride, and α-RuCl3 shows potential variations on a sub-10 nm length scale. First principles calculations reveal the charge-doping of graphene decays sharply over just nanometers from the edge of the α-RuCl3 flake.
Strontium ruthenate Sr2RuO4 is an unconventional superconductor whose pairing symmetry has not been fully clarified, despite more than two decades of intensive research. Recent NMR Knight shift experiments have rekindled the Sr2RuO4 pairing debate by giving strong evidence against all odd-parity pairing states, including chiral p-wave pairing that was for a long time the leading pairing candidate. Here, we exclude additional pairing states by analyzing recent elastocaloric measurements [YS. Li et al., Nature 607, 276--280 (2022)]. To be able to explain the elastocaloric experiment, we find that unconventional even-parity pairings must include either large dx2−y2-wave or large {dxz∣dyz}-wave admixtures, where the latter possibility arises because of the body-centered point group symmetry. These {dxz∣dyz}-wave admixtures take the form of distinctively body-centered-periodic harmonics that have horizontal line nodes. Hence gxy(x2−y2)-wave and dxy-wave pairings are excluded as possible dominant even pairing states.
Electronic systems living on Archimedean lattices such as kagome and square–octagon networks are presently being intensively discussed for the possible realization of topological insulating phases. Coining the most interesting electronic topological states in an unbiased way is however not straightforward due to the large parameter space of possible Hamiltonians. A possible approach to tackle this problem is provided by a recently developed statistical learning method (Mertz and Valentí in Phys Rev Res 3:013132, 2021. https://doi.org/10.1103/PhysRevResearch.3.013132), based on the analysis of a large data sets of randomized tight-binding Hamiltonians labeled with a topological index. In this work, we complement this technique by introducing a feature engineering approach which helps identifying polynomial combinations of Hamiltonian parameters that are associated with non-trivial topological states. As a showcase, we employ this method to investigate the possible topological phases that can manifest on the square–octagon lattice, focusing on the case in which the Fermi level of the system lies at a high-order van Hove singularity, in analogy to recent studies of topological phases on the kagome lattice at the van Hove filling.
Continued advances in quantum technologies rely on producing nanometer-scale wires. Although several state-of-the-art nanolithographic technologies and bottom-up synthesis processes have been used to engineer these wires, critical challenges remain in growing uniform atomic-scale crystalline wires and constructing their network structures. Here, we discover a simple method to fabricate atomic-scale wires with various arrangements, including stripes, X-junctions, Y-junctions, and nanorings. Single-crystalline atomic-scale wires of a Mott insulator, whose bandgap is comparable to those of wide-gap semiconductors, are spontaneously grown on graphite substrates by pulsed-laser deposition. These wires are one unit cell thick and have an exact width of two and four unit cells (1.4 and 2.8 nm) and lengths up to a few micrometers. We show that the nonequilibrium reaction-diffusion processes may play an essential role in atomic pattern formation. Our findings offer a previously unknown perspective on the nonequilibrium self-organization phenomena on an atomic scale, paving a unique way for the quantum architecture of nano-network.
In the search for novel organic charge transfer salts with variable degrees of charge transfer we have studied the effects of two modifications of the recently synthesized donor–acceptor system [tetramethoxypyrene (TMP)]–[tetracyanoquinodimethane (TCNQ)]. One is of chemical nature by substituting the acceptor TCNQ molecules by F4TCNQ molecules. The second consists in simulating the application of uniaxial pressure along the stacking axis of the system. In order to test the chemical substitution, we have grown single crystals of the TMP–F4TCNQ complex and analyzed its electronic structure via electronic transport measurements, ab initio density functional theory (DFT) calculations and UV/VIS/IR absorption spectroscopy. This system shows an almost ideal geometrical overlap of nearly planar molecules stacked alternately (mixed stack) and this arrangement is echoed by a semiconductor-like transport behavior with an increased conductivity along the stacking direction. This is in contrast to TMP–TCNQ which shows a less pronounced anisotropy and a smaller conductivity response. Our band structure calculations confirm the one-dimensional behavior of TMP–F4TCNQ with pronounced dispersion only along the stacking axis. Infrared measurements illustrating the C[triple bond, length as m-dash]N vibration frequency shift in F4TCNQ suggest however no improvement in the degree of charge transfer in TMP–F4TCNQ with respect to TMP–TCNQ. In both complexes about 0.1e is transferred from TMP to the acceptor. Concerning the pressure effect, our DFT calculations on the designed TMP–TCNQ and TMP–F4TCNQ structures under different pressure conditions show that application of uniaxial pressure along the stacking axis of TMP–TCNQ may be the route to follow in order to obtain a much more pronounced charge transfer.
RuO₂: a puzzle to be solved
(2023)
Altermagnetism is a topic that has lately been gaining attention and the RuO2 compound is among one of the most studied altermagnetic candidates. However, the survey of available literature on RuO2 properties suggests that there is no consensus about the magnetism of this material. By performing density functional theory calculations, we show that the electronic properties of stoichiometric RuO2 are described in terms of a smaller Hubbard U within DFT+U than the value required to have magnetism. We further argue that Ru vacancies can actually aid the formation of a magnetic state in RuO2. This in turn suggests that a characterization of the amount of Ru vacancies in experimental samples might help the resolution of the controversy between the different experimental results.
Topological semimetal antiferromagnets provide a rich source of exotic topological states which can be controlled by manipulating the orientation of the Néel vector, or by modulating the lattice parameters through strain. We investigate via ab initio density functional theory calculations, the effects of shear strain on the bulk and surface states n two antiferromagnetic EuCd2As2 phases with out-of-plane and in-plane spin configurations. When magnetic moments are along the c-axis, a 3% longitudinal or diagonal shear strain can tune the Dirac semimetal phase to an axion insulator phase, characterized by the parity-based invariant η4I=2. For an in-plane magnetic order, the axion insulator phase remains robust under all shear strains. We further find that for both magnetic orders, the bulk gap increases and a surface gap opens on the (001) surface up to 16 meV. Because of a nonzero η4I index and gapped states on the (001) surface, hinge modes are expected to happen on the side surface states between those gapped surface states. This result can provide a valuable insight in the realization of the long-sought axion states.
The antiferromagnet and semimetal EuCd2As2 has recently attracted a lot of attention due to a wealth of topological phases arising from the interplay of topology and magnetism. In particular, the presence of a single pair of Weyl points is predicted for a ferromagnetic configuration of Eu spins along the c-axis in EuCd2As2. In the search for such phases, we investigate here the effects of hydrostatic pressure in EuCd2As2. For that, we present specific heat, transport and μSR measurements under hydrostatic pressure up to ∼2.5GPa, combined with {\it ab initio} density functional theory (DFT) calculations. Experimentally, we establish that the ground state of EuCd2As2 changes from in-plane antiferromagnetic (AFMab) to ferromagnetic at a critical pressure of ≈2\,GPa, which is likely characterized by the moments dominantly lying within the ab plane (FMab). The AFMab-FMab transition at such a relatively low pressure is supported by our DFT calculations. Furthermore, our experimental and theoretical results indicate that EuCd2As2 moves closer to the sought-for FMc state (moments ∥ c) with increasing pressure further. We predict that a pressure of ≈\,23\,GPa will stabilize the FMc state, if Eu remains in a 2+ valence state. Thus, our work establishes hydrostatic pressure as a key tuning parameter that (i) allows for a continuous tuning between magnetic ground states in a single sample of EuCd2As2 and (ii) enables the exploration of the interplay between magnetism and topology and thereby motivates a series of future experiments on this magnetic Weyl semimetal.
The antiferromagnet and semimetal EuCd2As2 has recently attracted a lot of attention due to a wealth of topological phases arising from the interplay of topology and magnetism. In particular, the presence of a single pair of Weyl points is predicted for a ferromagnetic configuration of Eu spins along the c-axis in EuCd2As2. In the search for such phases, we investigate here the effects of hydrostatic pressure in EuCd2As2. For that, we present specific heat, transport and μSR measurements under hydrostatic pressure up to ∼2.5GPa, combined with {\it ab initio} density functional theory (DFT) calculations. Experimentally, we establish that the ground state of EuCd2As2 changes from in-plane antiferromagnetic (AFMab) to ferromagnetic at a critical pressure of ≈2\,GPa, which is likely characterized by the moments dominantly lying within the ab plane (FMab). The AFMab-FMab transition at such a relatively low pressure is supported by our DFT calculations. Furthermore, our experimental and theoretical results indicate that EuCd2As2 moves closer to the sought-for FMc state (moments ∥ c) with increasing pressure further. We predict that a pressure of ≈\,23\,GPa will stabilize the FMc state, if Eu remains in a 2+ valence state. Thus, our work establishes hydrostatic pressure as a key tuning parameter that (i) allows for a continuous tuning between magnetic ground states in a single sample of EuCd2As2 and (ii) enables the exploration of the interplay between magnetism and topology and thereby motivates a series of future experiments on this magnetic Weyl semimetal.
Motivated by the wealth of proposals and realizations of nontrivial topological phases in EuCd2As2, such as a Weyl semimetallic state and the recently discussed semimetallic versus semiconductor behavior in this system, we analyze in this work the role of the delicate interplay of Eu magnetism, strain and pressure on the realization of such phases. For that we invoke a combination of a group theoretical analysis with ab initio density functional theory calculations and uncover a rich phase diagram with various non-trivial topological phases beyond a Weyl semimetallic state, such as axion and topological crystalline insulating phases, and discuss their realization.
Motivated by the wealth of proposals and realizations of nontrivial topological phases in EuCd2As2, such as a Weyl semimetallic state and the recently discussed semimetallic versus semiconductor behavior in this system, we analyze in this work the role of the delicate interplay of Eu magnetism, strain and pressure on the realization of such phases. For that we invoke a combination of a group theoretical analysis with ab initio density functional theory calculations and uncover a rich phase diagram with various non-trivial topological phases beyond a Weyl semimetallic state, such as axion and topological crystalline insulating phases, and discuss their realization.
Motivated by the wealth of proposals and realizations of nontrivial topological phases in EuCd2As2, such as a Weyl semimetallic state and the recently discussed semimetallic versus semiconductor behavior in this system, we analyze in this work the role of the delicate interplay of Eu magnetism, strain and pressure on the realization of such phases. For that we invoke a combination of a group theoretical analysis with ab initio density functional theory calculations and uncover a rich phase diagram with various non-trivial topological phases beyond a Weyl semimetallic state, such as axion and topological crystalline insulating phases, and discuss their realization.
Lattice strains of appropriate symmetry have served as an excellent tool to explore the interaction of superconductivity in the iron-based superconductors with nematic and stripe spin-density wave (SSDW) order, which are both closely tied to an orthorhombic distortion. In this work, we contribute to a broader understanding of the coupling of strain to superconductivity and competing normal-state orders by studying CaKFe4As4 under large, in-plane strains of B1g and B2g symmetry. In contrast to the majority of iron-based superconductors, pure CaKFe4As4 exhibits superconductivity with relatively high transition temperature of Tc∼35 K in proximity of a non-collinear, tetragonal, hedgehog spin-vortex crystal (SVC) order. Through experiments, we demonstrate an anisotropic in-plane strain response of Tc, which is reminiscent of the behavior of other pnictides with nematicity. However, our calculations suggest that in CaKFe4As4, this anisotropic response correlates with the one of the SVC fluctuations, highlighting the close interrelation of magnetism and high-Tc superconductivity. By suggesting moderate B2g strains as an effective parameter to change the stability of SVC and SSDW, we outline a pathway to a unified phase diagram of iron-based superconductivity.
We present experimental results and theoretical simulations of the adsorption behavior of the metal–organic precursor Co2(CO)8 on SiO2 surfaces after application of two different pretreatment steps, namely by air plasma cleaning or a focused electron beam pre-irradiation. We observe a spontaneous dissociation of the precursor molecules as well as autodeposition of cobalt on the pretreated SiO2 surfaces. We also find that the differences in metal content and relative stability of these deposits depend on the pretreatment conditions of the substrate. Transport measurements of these deposits are also presented. We are led to assume that the degree of passivation of the SiO2 surface by hydroxyl groups is an important controlling factor in the dissociation process. Our calculations of various slab settings, using dispersion-corrected density functional theory, support this assumption. We observe physisorption of the precursor molecule on a fully hydroxylated SiO2 surface (untreated surface) and chemisorption on a partially hydroxylated SiO2 surface (pretreated surface) with a spontaneous dissociation of the precursor molecule. In view of these calculations, we discuss the origin of this dissociation and the subsequent autocatalysis.
Oxygen vacancies in strontium titanate surfaces (SrTiO3) have been linked to the presence of a two-dimensional electron gas with unique behavior. We perform a detailed density functional theory study of the lattice and electronic structure of SrTiO3 slabs with multiple oxygen vacancies, with a main focus on two vacancies near a titanium dioxide terminated SrTiO3 surface. We conclude based on total energies that the two vacancies preferably inhabit the first two layers, i.e. they cluster vertically, while in the direction parallel to the surface, the vacancies show a weak tendency towards equal spacing. Analysis of the nonmagnetic electronic structure indicates that oxygen defects in the surface TiO2 layer lead to population of Ti ${{t}_{2g}}$ states and thus itinerancy of the electrons donated by the oxygen vacancy. In contrast, electrons from subsurface oxygen vacancies populate Ti eg states and remain localized on the two Ti ions neighboring the vacancy. We find that both the formation of a bound oxygen-vacancy state composed of hybridized Ti 3eg and 4p states neighboring the oxygen vacancy as well as the elastic deformation after extracting oxygen contribute to the stabilization of the in-gap state.
In recent years, the notion of 'Quantum Materials' has emerged as a powerful unifying concept across diverse fields of science and engineering, from condensed-matter and coldatom physics to materials science and quantum computing. Beyond traditional quantum materials such as unconventional superconductors, heavy fermions, and multiferroics, the field has significantly expanded to encompass topological quantum matter, two-dimensional materials and their van der Waals heterostructures, Moiré materials, Floquet time crystals, as well as materials and devices for quantum computation with Majorana fermions. In this Roadmap collection we aim to capture a snapshot of the most recent developments in the field, and to identify outstanding challenges and emerging opportunities. The format of the Roadmap, whereby experts in each discipline share their viewpoint and articulate their vision for quantum materials, reflects the dynamic and multifaceted nature of this research area, and is meant to encourage exchanges and discussions across traditional disciplinary boundaries. It is our hope that this collective vision will contribute to sparking new fascinating questions and activities at the intersection of materials science, condensed matter physics, device engineering, and quantum information, and to shaping a clearer landscape of quantum materials science as a new frontier of interdisciplinary scientific inquiry. We stress that this article is not meant to be a fully comprehensive review but rather an up-to-date snapshot of different areas of research on quantum materials with a minimal number of references focusing on the latest developments.
We present a numerical investigation of energy and charge distributions during electron-beam-induced growth of tungsten nanostructures on SiO2 substrates by using a Monte Carlo simulation of the electron transport. This study gives a quantitative insight into the deposition of energy and charge in the substrate and in the already existing metallic nanostructures in the presence of the electron beam. We analyze electron trajectories, inelastic mean free paths, and the distribution of backscattered electrons in different compositions and at different depths of the deposit. We find that, while in the early stages of the nanostructure growth a significant fraction of electron trajectories still interacts with the substrate, when the nanostructure becomes thicker the transport takes place almost exclusively in the nanostructure. In particular, a larger deposit density leads to enhanced electron backscattering. This work shows how mesoscopic radiation-transport techniques can contribute to a model that addresses the multi-scale nature of the electron-beam-induced deposition (EBID) process. Furthermore, similar simulations can help to understand the role that is played by backscattered electrons and emitted secondary electrons in the change of structural properties of nanostructured materials during post-growth electron-beam treatments.
The aim of the present overview article is to raise awareness of an essential aspect that is usually not accounted for in the modelling of electron transport for focused-electron-beam-induced deposition (FEBID) of nanostructures: Surface excitations are on the one hand responsible for a sizeable fraction of the intensity in reflection-electron-energy-loss spectra for primary electron energies of up to a few kiloelectronvolts and, on the other hand, they play a key role in the emission of secondary electrons from solids, regardless of the primary energy. In this overview work we present a general perspective of recent works on the subject of surface excitations and on low-energy electron transport, highlighting the most relevant aspects for the modelling of electron transport in FEBID simulations.
The interaction of trimethyl(methylcyclopentadienyl)platinum(IV) ((C5H4CH3)Pt(CH3)3) molecules on fully and partially hydroxylated SiO2 surfaces, as well as the dynamics of this interaction were investigated using density functional theory (DFT) and finite temperature DFT-based molecular dynamics simulations. Fully and partially hydroxylated surfaces represent substrates before and after electron beam treatment and this study examines the role of electron beam pretreatment on the substrates in the initial stages of precursor dissociation and formation of Pt deposits. Our simulations show that on fully hydroxylated surfaces or untreated surfaces, the precursor molecules remain inactivated while we observe fragmentation of (C5H4CH3)Pt(CH3)3 on partially hydroxylated surfaces. The behavior of precursor molecules on the partially hydroxylated surfaces has been found to depend on the initial orientation of the molecule and the distribution of surface active sites. Based on the observations from the simulations and available experiments, we discuss possible dissociation channels of the precursor.
he family of cubic noncentrosymmetric 3-4-3 compounds has become a fertile ground for the discovery of novel correlated metallic and insulating phases. Here, we report the synthesis of a new heavy fermion compound, Ce3Bi4Ni3. It is an isoelectronic analog of the prototypical Kondo insulator Ce3Bi4Pt3 and of the recently discovered Weyl-Kondo semimetal Ce3Bi4Pd3. In contrast to the volume-preserving Pt-Pd substitution, structural and chemical analyses reveal a positive chemical pressure effect in Ce3Bi4Ni3 relative to its heavier counterparts. Based on the results of electrical resistivity, Hall effect, magnetic susceptibility, and specific heat measurements, we identify an energy gap of 65–70 meV, about eight times larger than that in Ce3Bi4Pt3 and about 45 times larger than that of the Kondo-insulating background hosting the Weyl nodes in Ce3Bi4Pd3. We show that this gap as well as other physical properties do not evolve monotonically with increasing atomic number, i.e., in the sequence Ce3Bi4Ni3−Ce3Bi4Pd3−Ce3Bi4Pt3, but instead with increasing partial electronic density of states of the 𝑑 orbitals at the Fermi energy. This work opens the possibility to investigate the conditions under which topological states develop in this series of strongly correlated 3-4-3 materials.
Heterostructures of graphene in proximity to magnetic insulators open the possibility to investigate exotic states emerging from the interplay of magnetism, strain and charge transfer between the layers. Recent reports on the growth of self-integrated atomic wires of β-RuCl3 on graphite suggest these materials as versatile candidates to investigate these effects. Here we present detailed first principles calculations on the charge transfer and electronic structure of β-RuCl3/heterostructures and provide a comparison with the work function analysis of the related honeycomb family members α-RuX3 (X = Cl,Br,I). We find that proximity of the two layers leads to a hole-doped graphene and electron-doped RuX3 in all cases, which is sensitively dependent on the distance between the two layers. Furthermore, strain effects due to lattice mismatch control the magnetization which itself has a strong effect on the charge transfer. Charge accumulation in β-RuCl3 strongly drops away from the chain making such heterostructures suitable candidates for sharp interfacial junctions in graphene-based devices.
Understanding the physics of strongly correlated electronic systems has been a central issue in condensed matter physics for decades. In transition metal oxides, strong correlations characteristic of narrow d bands are at the origin of remarkable properties such as the opening of Mott gap, enhanced effective mass, and anomalous vibronic coupling, to mention a few. SrVO3 with V4+ in a 3d1 electronic configuration is the simplest example of a 3D correlated metallic electronic system. Here, the authors' focus on the observation of a (roughly) quadratic temperature dependence of the inverse electron mobility of this seemingly simple system, which is an intriguing property shared by other metallic oxides. The systematic analysis of electronic transport in SrVO3 thin films discloses the limitations of the simplest picture of e–e correlations in a Fermi liquid (FL); instead, it is shown show that the quasi-2D topology of the Fermi surface (FS) and a strong electron–phonon coupling, contributing to dress carriers with a phonon cloud, play a pivotal role on the reported electron spectroscopic, optical, thermodynamic, and transport data. The picture that emerges is not restricted to SrVO3 but can be shared with other 3d and 4d metallic oxides.
Electronic and magnetic properties of the RuX3 (X=Cl, Br, I) family: two siblings - and a cousin?
(2022)
Motivated by reports of metallic behavior in the recently synthesized RuI3, in contrast to the Mott-insulating nature of the actively discussed α-RuCl3, as well as RuBr3, we present a detailed comparative analysis of the electronic and magnetic properties of this family of trihalides. Using a combination of first-principles calculations and effective-model considerations, we conclude that RuI3, similarly to the other two members, is most probably on the verge of a Mott insulator, but with much smaller magnetic moments and strong magnetic frustration. We predict the ideal pristine crystal of RuI3 to have a nearly vanishing conventional nearest-neighbor Heisenberg interaction and to be a quantum spin liquid candidate of a possibly different kind than the Kitaev spin liquid. In order to understand the apparent contradiction to the reported resistivity ρ, we analyze the experimental evidence for all three compounds and propose a scenario for the observed metallicity in existing samples of RuI3. Furthermore, for the Mott insulator RuBr3, we obtain a magnetic Hamiltonian of a similar form to that in the much-discussed α-RuCl3 and show that this Hamiltonian is in agreement with experimental evidence in RuBr3.
Motivated by recent reports of a quantum-disordered ground state in the triangular lattice compound NaRuO2, we derive a jeff = 1/2 magnetic model for this system by means of first-principles calculations. The pseudospin Hamiltonian is dominated by bond-dependent off-diagonal Γ interactions, complemented by a ferromagnetic Heisenberg exchange and a notably antiferromagnetic Kitaev term. In addition to bilinear interactions, we find a sizable four-spin ring exchange contribution with a strongly anisotropic character, which has been so far overlooked when modeling Kitaev materials. The analysis of the magnetic model, based on the minimization of the classical energy and exact diagonalization of the quantum Hamiltonian, points toward the existence of a rather robust easy-plane ferromagnetic order, which cannot be easily destabilized by physically relevant perturbations.
Deconfinement of Mott localized electrons into topological and spin–orbit-coupled Dirac fermions
(2020)
The interplay of electronic correlations, spin–orbit coupling and topology holds promise for the realization of exotic states of quantum matter. Models of strongly interacting electrons on honeycomb lattices have revealed rich phase diagrams featuring unconventional quantum states including chiral superconductivity and correlated quantum spin Hall insulators intertwining with complex magnetic order. Material realizations of these electronic states are, however, scarce or inexistent. In this work, we propose and show that stacking 1T-TaSe2 into bilayers can deconfine electrons from a deep Mott insulating state in the monolayer to a system of correlated Dirac fermions subject to sizable spin–orbit coupling in the bilayer. 1T-TaSe2 develops a Star-of-David charge density wave pattern in each layer. When the Star-of-David centers belonging to two adyacent layers are stacked in a honeycomb pattern, the system realizes a generalized Kane–Mele–Hubbard model in a regime where Dirac semimetallic states are subject to significant Mott–Hubbard interactions and spin–orbit coupling. At charge neutrality, the system is close to a quantum phase transition between a quantum spin Hall and an antiferromagnetic insulator. We identify a perpendicular electric field and the twisting angle as two knobs to control topology and spin–orbit coupling in the system. Their combination can drive it across hitherto unexplored grounds of correlated electron physics, including a quantum tricritical point and an exotic first-order topological phase transition.
Motivated by the on-going discussion on the nature of magnetism in the quantum Ising chain CoNb2O6, we present a first-principles-based analysis of its exchange interactions by applying an \textit{ab initio} approach with additional modelling that accounts for various drawbacks of a purely density functional theory ansatz. With this method we are able to extract and understand the origin of the magnetic couplings under inclusion of all symmetry-allowed terms, and to resolve the conflicting model descriptions in CoNb2O6. We find that the twisted Kitaev chain and the transverse-field ferromagnetic Ising chain views are mutually compatible, although additional off-diagonal exchanges are necessary to provide a complete picture. We show that the dominant exchange interaction is a ligand-centered exchange process - involving the eg electrons -, which is rendered anisotropic by the low-symmetry crystal fields environments in CoNb2O6, giving rise to the dominant Ising exchange, while the smaller bond-dependent anisotropies are found to originate from d−d kinetic exchange processes involving the t2g electrons. We demonstrate the validity of our approach by comparing the predictions of the obtained low-energy model to measured THz and inelastic neutron scattering spectra.
The family of cubic noncentrosymmetric 3-4-3 compounds has become a fertile ground for the discovery of novel correlated metallic and insulating phases. Here, we report the synthesis of a new heavy fermion compound, Ce3Bi4Ni3. It is an isoelectronic analog of the prototypical Kondo insulator Ce3Bi4Pt3 and of the recently discovered Weyl-Kondo semimetal Ce3Bi4Pd3. In contrast to the volume-preserving Pt-Pd substitution, structural and chemical analyses reveal a positive chemical pressure effect in Ce3Bi4Ni3 relative to its heavier counterparts. Based on the results of electrical resistivity, Hall effect, magnetic susceptibility, and specific heat measurements, we identify an energy gap of 65-70 meV, about eight times larger than that in Ce3Bi4Pt3 and about 45 times larger than that of the Kondo-insulating background hosting the Weyl nodes in Ce3Bi4Pd3. We show that this gap as well as other physical properties do not evolve monotonically with increasing atomic number, i.e., in the sequence Ce3Bi4Ni3-Ce3Bi4Pd3-Ce3Bi4Pt3, but instead with increasing partial electronic density of states of the d orbitals at the Fermi energy. To understand under which condition topological states form in these materials is a topic for future studies.