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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.
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.
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.
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.
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.
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.
Using the notion of a root datum of a reductive group G we propose a tropical analogue of a principal G-bundle on a metric graph. We focus on the case G=GLn, i.e. the case of vector bundles. Here we give a characterization of vector bundles in terms of multidivisors and use this description to prove analogues of the Weil--Riemann--Roch theorem and the Narasimhan--Seshadri correspondence. We proceed by studying the process of tropicalization. In particular, we show that the non-Archimedean skeleton of the moduli space of semistable vector bundles on a Tate curve is isomorphic to a certain component of the moduli space of semistable tropical vector bundles on its dual metric graph.
In this article we provide a stack-theoretic framework to study the universal tropical Jacobian over the moduli space of tropical curves. We develop two approaches to the process of tropicalization of the universal compactified Jacobian over the moduli space of curves -- one from a logarithmic and the other from a non-Archimedean analytic point of view. The central result from both points of view is that the tropicalization of the universal compactified Jacobian is the universal tropical Jacobian and that the tropicalization maps in each of the two contexts are compatible with the tautological morphisms. In a sequel we will use the techniques developed here to provide explicit polyhedral models for the logarithmic Picard variety.
We report about the properties of the underlying event measured with ALICE at the LHC in pp and p−Pb collisions at sNN−−−√=5.02 TeV. The event activity, quantified by charged-particle number and summed-pT densities, is measured as a function of the leading-particle transverse momentum (ptrigT). These quantities are studied in three azimuthal-angle regions relative to the leading particle in the event: toward, away, and transverse. Results are presented for three different pT thresholds (0.15, 0.5, and 1 GeV/c) at mid-pseudorapidity (|η|<0.8). The event activity in the transverse region, which is the most sensitive to the underlying event, exhibits similar behaviour in both pp and p−Pb collisions, namely, a steep increase with ptrigT for low ptrigT, followed by a saturation at ptrigT≈5 GeV/c. The results from pp collisions are compared with existing measurements at other centre-of-mass energies. The quantities in the toward and away regions are also analyzed after the subtraction of the contribution measured in the transverse region. The remaining jet-like particle densities are consistent in pp and p−Pb collisions for ptrigT>10 GeV/c, whereas for lower ptrigT values the event activity is slightly higher in p−Pb than in pp collisions. The measurements are compared with predictions from the PYTHIA 8 and EPOS LHC Monte Carlo event generators.
The first measurement of the e+e− pair production at low lepton pair transverse momentum (pT,ee) and low invariant mass (mee) in non-central Pb−Pb collisions at sNN−−−√=5.02 TeV at the LHC is presented. The dielectron production is studied with the ALICE detector at midrapidity (|ηe|<0.8) as a function of invariant mass (0.4≤mee<2.7 GeV/c2) in the 50−70% and 70−90% centrality classes for pT,ee<0.1 GeV/c, and as a function of pT,ee in three mee intervals in the most peripheral Pb−Pb collisions. Below a pT,ee of 0.1 GeV/c, a clear excess of e+e− pairs is found compared to the expectations from known hadronic sources and predictions of thermal radiation from the medium. The mee excess spectra are reproduced, within uncertainties, by different predictions of the photon−photon production of dielectrons, where the photons originate from the extremely strong electromagnetic fields generated by the highly Lorentz-contracted Pb nuclei. Lowest-order quantum electrodynamic (QED) calculations, as well as a model that takes into account the impact-parameter dependence of the average transverse momentum of the photons, also provide a good description of the pT,ee spectra. The measured ⟨p2T,ee⟩−−−−−√ of the excess pT,ee spectrum in peripheral Pb−Pb collisions is found to be comparable to the values observed previously at RHIC in a similar phase-space region.