We investigate the electronic band structure of graphene on a series of two-dimensional magnetic transition-metal phosphorus trichalcogenide monolayers, ${M\text{P}X}_3$ with $M=\{\mathrm{Mn},\mathrm{Fe},\mathrm{Ni},\mathrm{Co}\}$ and $X=\{\mathrm{S},\mathrm{Se}\}$, with first-principles calculations. A symmetry-based model Hamiltonian is employed to extract orbital parameters and sublattice resolved proximity-induced exchange couplings (${\lambda }_{\text{ex}}^{\text{A}}$ and ${\lambda }_{\text{ex}}^{\text{B}}$) from the low-energy Dirac bands of the proximitized graphene. Depending on the magnetic phase of the ${M\text{P}X}_3$ layer (ferromagnetic and three antiferromagnetic ones), completely different Dirac dispersions can be realized with exchange splittings ranging from 0 to 10 meV. Remarkably, not only the magnitude of the exchange couplings depends on the magnetic phase, but also the global sign and the type. Important, one can realize uniform $({\lambda }_{\text{ex}}^{\text{A}}\approx {\lambda }_{\text{ex}}^{\text{B}})$ and staggered $({\lambda }_{\text{ex}}^{\text{A}}\approx -{\lambda }_{\text{ex}}^{\text{B}})$ exchange couplings in graphene. From selected cases we find that the interlayer distance, as well as a transverse electric field, are efficient tuning knobs for the exchange splittings of the Dirac bands. More specifically, decreasing the interlayer distance by only about 10%, a giant fivefold enhancement of proximity exchange is found, while applying few V/nm of electric field, provides tunability of proximity exchange by tens of percent. We have also studied the dependence on the Hubbard $U$ parameter and find it to be weak. Moreover, we find that the effect of SOC on the proximitized Dirac dispersion is negligible compared to the exchange coupling.

Recently, great experimental efforts towards designing topological electronic states have been invested in layered incommensurate heterostructures, which form various nano- and mesoscale domains. In particular, it has become clear that a delicate interplay of different spin-orbit terms is induced in graphene on transition metal dichalcogenide substrates. We therefore theoretically study various types of domain walls in spin-orbit coupling in graphene looking for robust one-dimensional propagating electronic states. To do so, we use an interface Chern number and a spectral flow analysis in the low-energy theory and contrast our results to the standard arguments based on valley-Chern numbers or Chern numbers in continuum models. Surprisingly, we find that a sign-changing domain wall in valley-Zeeman spin-orbit coupling binds two robust Kramers pairs, within the bulk gap opened due to a simultaneous presence of Rashba coupling. We also study the robustness to symmetry breaking and lattice backscattering effects in tight-binding models. We show an explicit mapping of our valley-Zeeman domain wall to a domain wall in gated spinless bilayer graphene. We discuss the possible spectroscopic and transport signatures of various types of spin-orbit coupling domain walls in heterostructures.

We study the quantum electrodynamics of Luttinger fermions with quadratic band-crossing dispersion in three dimensions. The model can be viewed as the low-energy effective theory of a putative U(1) quantum spin liquid with fermionic Luttinger spinons, or as an extension of the Luttinger-Abrikosov-Beneslavskii (LAB) model that accounts for transverse gauge fluctuations with finite photon velocity. Aided by a renormalization group analysis below four dimensions, we elucidate the presence and stability of quantum critical phenomena in this model. We find that the non-Fermi liquid LAB phase is stable against gauge fluctuations and can thus also be viewed as a U(1) spin liquid with gapless Luttinger spinons. We discover a multicritical point with Lifshitz scaling that corresponds to a time-reversal symmetry-breaking quantum phase transition from the LAB state to a chiral spin liquid with spinon Landau levels and birefringent emergent photons. This multicritical point is characterized by a finite fermion-photon coupling in the infrared and can be viewed as a fermionic analog of the Rokhsar-Kivelson point in three-dimensional quantum dimer models.

The Nielsen-Ninomiya theorem set up a ground rule for the minimal number of the topological points in a Brillouin zone. Notably, in the 2D Brillouin zone, chiral symmetry and space-time inversion symmetry can properly define topological invariants as charges characterizing the stability of the nodal points so the nonzero charges protect these points. Due to the charge neutralization, the Nielsen-Ninomiya theorem requires at least two stable topological points in the entire Brillouin zone. However, additional crystalline symmetries might duplicate the points. In this regard, for the wallpaper groups with crystalline symmetries, the minimal number of the nodal points in the Brillouin zone might be more than two. In this paper, we determine the minimal numbers of the nodal points for the wallpaper groups in chiral-symmetric and space-time-inversion-symmetric systems separately and provide examples for topological materials, such as topological nodal time-reversal-symmetric superconductors and Dirac semimetals. This generalized Nielsen-Ninomiya theorem serves as a guide to search for 2D topological nodal materials and platforms for twistronics. Furthermore, we show the Nielsen-Ninomiya theorem can be extended to 2D non-Hermitian systems hosting topologically protected exceptional points and Fermi points for the 17 wallpaper groups and use the violation of the theorem on the surface to classify 3D Hermitian and non-Hermitian topological bulks.

We study bosonic systems on a space-time lattice (with imaginary time) defined by path integrals of commuting fields. We introduce a concept of branch-independent bosonic (BIB) systems, whose path integral is independent of the branch structure of the space-time simplicial complex, even for a space-time with boundaries. In contrast, a generic lattice bosonic (GLB) system's path integral may depend on the branch structure. We find the invertible topological order characterized by the Stiefel-Whitney cocycle [such as $(4+1)\mathrm{d}$ ${\mathrm{w}}_2{\mathrm{w}}_3$] to be nontrivial for branch-independent bosonic systems, but this topological order and a trivial gapped tensor product state belong to the same phase (via a smooth deformation without any phase transition) for generic lattice bosonic systems. This implies that the invertible topological orders in generic lattice bosonic systems on a space-time lattice are not classified by the oriented cobordism. The branch dependence on a lattice may be related to the orthonormal frame of smooth manifolds and the framing anomaly of continuum field theories. In general, the branch structure on a discretized lattice may be related to a frame structure on a smooth manifold that trivializes any Stiefel-Whitney classes. We construct branch-independent bosonic systems to realize the ${\mathrm{w}}_2{\mathrm{w}}_3$ topological order, and its $(3+1)\mathrm{d}$ gapped or gapless boundaries. One of the gapped boundaries is a $(3+1)\mathrm{d}$ ${\mathbb{Z}}_2$ gauge theory with (1) fermionic ${\mathbb{Z}}_2$ gauge charge particle which trivializes ${\mathrm{w}}_2$ and (2) “fermionic” ${\mathbb{Z}}_2$ gauge flux line trivializes ${\mathrm{w}}_3$. In particular, if the flux loop's world sheet is unorientable, then the orientation-reversal one-dimensional world line must correspond to a fermion world line that does not carry the ${\mathbb{Z}}_2$ gauge charge. We also explain why Spin and Spin${}^c$ structures trivialize the ${\mathrm{w}}_2{\mathrm{w}}_3$ nonperturbative global pure gravitational anomaly to zero [which helps to construct the anomalous $(3+1)\mathrm{d}$ gapped ${\mathbb{Z}}_2$ and gapless all-fermion U(1) gauge theories], but the Spin${}^h$ and Spin${\times }_{{\mathbb{Z}}_2}$Spin$(n\ge 3)$ structures modify the ${\mathrm{w}}_2{\mathrm{w}}_3$ into a nonperturbative global mixed gauge-gravitational anomaly, which helps to constrain grand unifications (e.g., $n=10,18$) or construct new models.

Heterostructures composed of different layered materials provide novel opportunities to investigate the electronic correlations between them. Here we investigate frictional drag between graphene and ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ (LAO/STO) heterostructures. The LAO/STO layer underneath the graphene is rendered conductive using conductive atomic force microscope (c-AFM) lithography, creating a two-layer system in which the LAO serves as an ultrathin ($<$2 nm) insulating barrier. By sourcing current in both the STO layer and graphene layer, Coulomb drag is studied in a wide range, from an STO superconducting region to a graphene quantum Hall region. Pronounced fluctuations in the frictional drag resistance are observed when the STO is superconducting. A large enhancement of drag resistance is observed when the STO becomes superconducting. Pronounced stripelike oscillations in the frictional drag appear in the quantum Hall region, both along the main channel and the transverse (Hall) configuration. The behavior is consistent with numerical simulations that model energy and momentum transfer from the STO layer to the graphene layer. These help to create a platform for graphene-based metamaterials using the programmable LAO/STO interface.

The structural properties of two Ge-As-Se glass compositions (${\mathrm{Ge}}_{10}{\mathrm{As}}_{10}{\mathrm{Se}}_{80}$ and ${\mathrm{Ge}}_{21}{\mathrm{As}}_{21}{\mathrm{Se}}_{58}$) are investigated from a combination of density-functional-based molecular dynamics simulations and neutron/x-ray scattering experiments. We first focus on structural characteristics, including structure factors, pair distribution functions, angular distributions, coordination numbers, and neighbor distributions, and compare our results with the experimental data. Results leave anticipated coordinations from the octet rule (${\mathrm{Se}}^{\mathrm{II}}, {\mathrm{As}}^{\mathrm{III}}$, and ${\mathrm{Ge}}^{\mathrm{IV}}$) unchanged, and these are contrasted with respect to glasses having the same average coordination number $\overline{r}$ such as binary ${\mathrm{As}}_{30}{\mathrm{Se}}_{70}$ and ${\mathrm{Ge}}_{33}{\mathrm{Se}}_{67}$. The increase of (As,Ge) content induces a growth of ring structures that are dominated by edge-sharing motifs (four-membered rings) having mostly heteropolar bonds, while As-As and As-Ge homopolar bonds are clearly more favored than Ge-Ge. These features signal that both topological (rings) and chemical (bonds) features are different with respect to related binaries. The validity of the so-called vibrational isocoordination rule stating that properties of multicomponent chalcogenides depend solely on $\overline{r}$ is checked, and results from a vibrational analysis indicates that this rule is merely satisfied for the Se-rich composition. An inspection of correlations via the Bhatia-Thornton formalism shows that topological ordering is not only different between ${\mathrm{Ge}}_{10}{\mathrm{As}}_{10}{\mathrm{Se}}_{80}$ and ${\mathrm{Ge}}_{21}{\mathrm{As}}_{21}{\mathrm{Se}}_{58}$ but also radically contrasts with respect to the isocoordinated binary glasses and displays an obvious reduced directional bonding.

Symmetry-protected spectral topology in extended non-Hermitian quantum systems has interesting manifestations such as dynamically anomalous chiral currents and skin effect. In this paper, we study the interplay between symmetries and disorder in a paradigmatic model for spectral topology—the nonreciprocal Su-Schrieffer-Heeger model. We consider the effect of on-site perturbations (both real and purely imaginary) that explicitly break the sublattice symmetry. Such symmetry-breaking terms can retain a nontrivial spectral topology but lead to a different symmetry class. We numerically study the effect of disorder in on-site and nonreciprocal hopping terms. Using a real-space winding number that is self-averaging and quantized, we investigate the impact of disorder on the spectral topology and associated anomalous chiral modes under periodic boundary conditions. We discover a remarkable robustness of chiral current and its self-averaging nature under disorder. The value of the chiral current retains the clean system value, is independent of disorder strength, and is tracked completely by the real-space winding number for class A which has no symmetries, and class AIII, which has a sublattice symmetry. In class ${\mathrm{D}}^{†}$, which has $PT$-symmetric on-site gain and loss terms, we find that the disorder-averaged current is not robust while the winding number is robust. We study the localization physics using the inverse participation ratio and local density of states. As the disorder strength is increased, a mobility-edge phase with a finite winding appears. The abrupt vanishing of the winding number marks a transition from a partially localized to a fully localized phase. Under open boundary conditions, we similarly observe a series of transitions through skin effect–partial skin effect–no skin effect phases. Further, we study the non-Hermitian Anderson skin effect (NHASE) for different symmetry classes, where the system without skin effect develops a disorder-driven skin effect at intermediate disorder values. Remarkably, while NHASE is present for different classes, the real-space winding number shows a direct correspondence with it only when all symmetries are broken.

Linear quench of the transverse field drives the quantum Ising chain across a quantum critical point from the paramagnetic to the ferromagnetic phase. We focus on normal and anomalous quadratic correlators between fermionic kink creation and annihilation operators. They depend not only on the Kibble-Zurek (KZ) correlation length but also on a dephasing length scale, which differs from the KZ length by a logarithmic correction. Additional slowing down of the ramp in the ferromagnetic phase further increases the dephasing length and suppresses the anomalous correlator. The quadratic correlators enter Pfaffians that yield experimentally relevant kink correlation functions, the probability distribution of ferromagnetic domain sizes, and, closely related, emptiness formation probability. The latter takes the form of a Pfaffian of a block Toeplitz matrix that allows for some analytic asymptotes. Finally, we obtain further insight into the structure of the state at the end of the ramp by interpreting it as a paired state of fermionic kinks characterized by its pair wave function. All those quantities are sensitive to quantum coherence between eigenstates with different numbers of kinks, thus making them a convenient probe of the quantumness of a quantum simulator platform.

Noncentrosymmetric ferromagnetic systems with large Dzylochinskii-Moriya interaction (DMI) have gained intensive attention for hosting topologically protected solitons such as skyrmions and bimerons. Recently, a series of two-dimensional (2D) Li- and Na-based chromium chalcogenides has been theoretically predicted to be a new family of intrinsic inversion asymmetric ferromagnets. Here, by combining first-principles calculations and atomistic spin model simulations, we unveil that there is very large DMI in these series of 2D alkali-based chromium chalcogenides, which enables a variety of filed-free topological spin textures in these structures. Furthermore, we find robust hole-doping tunable DMI in the ${\mathrm{LiCrSe}}_2$ and ${\mathrm{NaCrSe}}_2$ monolayers. Our finding opens up further possibilities toward 2D materials in spintronic devices.

We use the constrained random-phase approximation (cRPA) method to calculate the Hubbard $U$ parameter in four one-dimensional magnetic transition metal atom oxides of composition ${\mathrm{XO}}_2$ (X = Mn, Fe, Co, Ni) on Ir(100). In addition to the expected screening of the oxide, i.e., a significant reduction of the $U$ value by the presence of the metal substrate, we find a strong dependence on the electronic configuration (multiplet) of the $\mathrm{X}(d$) orbital. Each particular electronic configuration attained by atom X is dictated by the O ligands, as well as by the charge transfer and hybridization with the Ir(100) substrate. We find that ${\mathrm{MnO}}_2$ and ${\mathrm{NiO}}_2$ chains exhibit two different screening regimes, while the case of ${\mathrm{CoO}}_2$ is somewhere in between. The electronic structure of the ${\mathrm{MnO}}_2$ chain remains almost unchanged upon adsorption. Therefore, in this regime, the additional screening is predominantly generated by the electrons of the neighboring metal surface atoms. The screening strength for ${\mathrm{NiO}}_2$/Ir(100) is found to depend on the $\mathrm{Ni}(d$) configuration in the adsorbed state. The case of ${\mathrm{FeO}}_2$ shows an exceptional behavior, as it is the only insulating system in the absence of the metallic substrate and, thus, it has the largest $U$ value. However, this value is significantly reduced by the two mentioned screening effects after adsorption.

We present a scalable machine learning (ML) model to predict local electronic properties such as on-site electron number and double occupation for disordered correlated electron systems. Our approach is based on the locality principle, or the nearsightedness nature, of many-electron systems, which means local electronic properties depend mainly on the immediate environment. A ML model is developed to encode this complex dependence of local quantities on the neighborhood. We demonstrate our approach using the square-lattice Anderson-Hubbard model, which is a paradigmatic system for studying the interplay between Mott transition and Anderson localization. We develop a lattice descriptor based on the group-theoretical method to represent the on-site random potentials within a finite region. The resultant feature variables are used as input to a multilayer fully connected neural network, which is trained from data sets of variational Monte Carlo (VMC) simulations on small systems. We show that the ML predictions agree reasonably well with the VMC data. Our work underscores the promising potential of ML methods for multiscale modeling of correlated electron systems.

The spin-orbit coupled double perovskite iridate ${\mathrm{Ba}}_2{\mathrm{YIrO}}_6$ with $d^4$ occupancy of Ir is considered as a candidate material for a nonmagnetic $J=0$ ground state. The issue of existence of such a state in ${\mathrm{Ba}}_2{\mathrm{YIrO}}_6$, however, has opened up intense debates both in experimental and theoretical studies. In this study, we revisit the issue using ab initio density functional combined with dynamical mean-field theory to investigate the magnetic properties of ${\mathrm{Ba}}_2{\mathrm{YIrO}}_6$ down to zero temperature. To reach the ground state, a recently developed impurity solver based on tensor-product states working directly at zero temperature is employed. We find that ${\mathrm{Ba}}_2{\mathrm{YIrO}}_6$ has a small instantaneous nonzero magnetic moment, both at $T=0\mathrm{K}$ as well as at room temperature. We did not observe any evidence of magnetic ordering, not even at $T=0\mathrm{K}$. From the calculated local magnetic susceptibility we see that the quantum fluctuations are very strong and effective in screening the instantaneous moments. This dynamical screening, together with frustration effects in the fcc lattice that can lead to almost degenerate magnetic ground states, prevents any long-range ordering.

We investigate the two-dimensional Kondo lattice, the minimal model of a heavy fermion compound. Despite its apparent simplicity, its dynamics are both complex and controversial. In the moderate-to-strong coupling regime, the bond fermion theory provides an approximate mapping to an easily solvable fermionic system. This works surprisingly well from a qualitative standpoint, but there are some shortcomings as the method has no precise mathematical foundation. We here try to address this and improve on the method by making an explicit connection to wave function based variational methods and the Gutzwiller approximation. We apply the improved method to both the previously studied Néel magnetic phases, as well as incommensurately and ferromagnetically ordered phase.

We studied the slow dynamics of phase transitions in ${\mathrm{Ba}}_{1-x}{\mathrm{Sr}}_x{\mathrm{V}}_{13}{\mathrm{O}}_{18}$, which is composed of quasitriangular lattices of V ions and exhibits a phase transition into a V orbital ordered state with V trimerization. We found a clear time dependence of magnetic susceptibility and strain on a phase transition, and the transformation time estimated from the time dependence exhibits a peculiar temperature dependence, consistent with nucleation-growth behavior. Detailed analysis indicates that there is a distribution of the transformation time in ${\mathrm{Ba}}_{1-x}{\mathrm{Sr}}_x{\mathrm{V}}_{13}{\mathrm{O}}_{18}$, and the formation of twin structures associated with the phase transition may affect the nucleation-growth dynamics and causes such a distribution of the transformation time.

We propose a geometric approach to the Lieb-Schultz-Mattis theorem for quantum many-body systems with discrete spin-rotation symmetries and lattice inversion or rotation symmetry, but without translation symmetry assumed. Under symmetry twisting on a $(d-1)$-dimensional plane, we find that any $d$-dimensional inversion-symmetric spin system possesses a doubly degenerate spectrum when it hosts a half-integer spin at the inversion-symmetric point. We also show that any rotation-symmetric generalized spin model with a projective representation at the rotation center has a similar degeneracy under symmetry twisting. We argue that these degeneracies imply that a unique symmetric gapped ground state that is smoothly connected to product states is forbidden in the original untwisted systems—generalized inversional or rotational Lieb-Schultz-Mattis theorems without lattice translation symmetry imposed. The traditional Lieb-Schultz-Mattis theorems with translations also fit in the proposed framework.

The interaction between acoustic phonons and electrons in diamond has been investigated by comparing state-of-the-art time-of-flight drift velocity measurements with Monte Carlo simulations. We use a multivariable anisotropic description of acoustic deformation potential scattering. The phonon-electron interaction is the limiting factor for the carrier mobility in ultrapure single crystal diamond. Hence, having a correct description is necessary for both device simulations and for predicting the maximum device performance. The experiments were performed at low temperature and using ultrapure diamond to minimize the influence of other scattering sources. The electronic valley polarization in diamond at low temperatures enables determination of both uniaxial and dilatation deformation potentials in the same experiment. The uniaxial and dilatation deformation potentials are found to be $18.5\pm 0.2$ and $-5.7\pm 0.3$ eV, respectively.

Intrinsic ripples with various configurations and sizes were reported to affect the physical and chemical properties of two-dimensional (2D) materials. By performing molecular dynamics simulations and theoretical analysis, we use two geometric models of the ripple shape to explore numerically the distribution of ripples in the graphene membrane. We focus on the ratio of the ripple height to its diameter ($t/D$) which was recently shown to be the most relevant for chemical activity of graphene membranes. Our result demonstrates that the ripple density decreases as the coefficient $t/D$ increases, in qualitative agreement with the Boltzmann distribution derived analytically from the bending energy of the membrane. Our theoretical paper provides also specific quantitative information on the ripple distribution in graphene and gives new insights applicable to other 2D materials.