Two-dimensional (2D) materials are outstanding platforms for exotic physics and emerging applications by forming interfaces. In order to efficiently take into account the substrate screening in the quasiparticle energies of 2D materials, several theoretical methods have been proposed previously but are only applicable to interfaces of two systems' lattice constants with certain integer proportion, which often requires a few percent of strain. In this work, we analytically showed the equivalence and distinction among different approximate methods for substrate dielectric matrices. We evaluated the accuracy of these methods by applying them to calculate quasiparticle energies of hexagonal boron nitride interface systems (heterojunctions and bilayers) and compared the results with explicit interface calculations. Most importantly, we developed an efficient and accurate interpolation technique for dielectric matrices that made quasiparticle energy calculations possible for arbitrarily mismatched interfaces free of strain, which is extremely valuable for practical applications.

Artificial lattices provide a tunable platform to realize exotic quantum devices. A well-known example is artificial graphene (AG), in which electrons are confined in honeycomb lattices and behave as massless Dirac fermions. Recently, AG systems have been constructed by manipulating molecules using scanning tunneling microscope tips, but the nanoscale sizes typical for these constructed systems are impossible for practical device applications and insufficient for direct investigation of the electronic structures using angle-resolved photoemission spectroscopy (ARPES). Here, we demonstrate the synthesis of macroscopic AG by the self-assembly of ${\mathrm{C}}_{60}$ molecules on metal surfaces. Our theoretical calculations and ARPES measurements directly confirm the existence of Dirac cones at the $K$ ($K^{\prime }$) points of the Brillouin zone, in analogy to natural graphene. These results will stimulate ongoing efforts to explore the exotic properties in artificial lattices and provide an important step forward in the realization of molecular quantum devices.

We report on optical excitations in the magnetically ordered phases of multiferroic ${\mathrm{Fe}}_{1.86}{\mathrm{Zn}}_{0.14}{\mathrm{Mo}}_3{\mathrm{O}}_8$ in the frequency range $10–130 {\mathrm{cm}}^{-1}$ (0.3–3.9 THz). In the collinear easy-axis antiferromagnetic phase below $T_N=50$ K, 11 optically active modes have been observed in finite magnetic fields, assuming that the lowest-lying mode is doubly degenerate. The large number of modes reflects either a more complex magnetic structure than in pure ${\mathrm{Fe}}_2{\mathrm{Mo}}_3{\mathrm{O}}_8$ or that spin-stretching modes become active in addition to the usual spin precessional modes. Their magnetic field dependence, for fields applied along the easy axis, reflects the irreversible magnetic-field-driven phase transition from the antiferromagnetic ground state to a ferrimagnetic state, while the number of modes remains unchanged in the covered frequency region. We determined selection rules for some of the antiferromagnetic modes by investigating all polarization configurations and identified magnetic- and electric-dipole active modes as well. In addition to these sharp resonances, a broad electric-dipole active excitation band, which is not influenced by the external magnetic field, occurs below $T_N$ with an onset at $12 {\mathrm{cm}}^{-1}$. We are able to model this absorption band as a vibronic excitation related to the lowest-lying ${\mathrm{Fe}}^{2+}$ electronic states in a tetrahedral environment.

This paper investigates the temperature dependence of quantum information scrambling in local systems with an energy gap, $m$, above the ground state. We study the speed and shape of growing Heisenberg operators as quantified by out-of-time-order correlators, with particular attention paid to so-called contour dependence, i.e., dependence on the way operators are distributed around the thermal circle. We report large-scale tensor network numerics on a gapped chaotic spin chain down to temperatures comparable to the gap which show that the speed of operator growth is strongly contour-dependent. The numerics also show a characteristic broadening of the operator wavefront at finite temperature $T$. To study the behavior at temperatures much below the gap, we perform a perturbative calculation in the paramagnetic phase of a $2+1\mathrm{D} \mathrm{O}(N$) nonlinear sigma model, which is analytically tractable at large $N$. Using the ladder diagram technique, we find that operators spread at a speed $\sqrt{T/m}$ at low temperatures, $T\ll m$. In contrast to the numerical findings of spin chain, the large $N$ computation is insensitive to the contour dependence and does not show broadening of operator front. We discuss these results in the context of a recently proposed state-dependent bound on scrambling.

Transition-metal dichalcogenide heterostructures exhibit moiré patterns that spatially modulate the electronic structure across the material's plane. For certain material pairs, this modulation acts as a potential landscape with deep, trigonally symmetric wells capable of localizing interlayer excitons, forming periodic arrays of quantum emitters. Here, we study these moiré localized exciton states and their optical properties. By numerically solving the two-body problem for an interacting electron-hole pair confined by a trigonal potential, we compute the localized exciton spectra for different pairs of materials. We derive optical selection rules for the different families of localized states, each belonging to one of the irreducible representations of the potential's symmetry group $C_{3v}$, and numerically estimate their polarization-resolved absorption spectra. We find that the optical response of localized moiré interlayer excitons is dominated by states belonging to the doubly degenerate $E$ irreducible representation. Our results provide insights into the optical properties of artificially confined excitons in two-dimensional semiconductors.

Two-dimensional (2D) materials are usually envisioned as flat, truly 2D layers. However out-of-plane corrugations are inevitably present in these materials. In this paper, we show that graphene flakes encapsulated between insulating crystals (hexagonal boron nitride, ${\mathrm{WSe}}_2$), although having large mobilities, surprisingly contain out-of-plane corrugations. The height fluctuations of these corrugations are revealed using weak-localization measurements in the presence of a static in-plane magnetic field. Due to the random out-of-plane corrugations, the in-plane magnetic field results in a random out-of-plane component to the local graphene plane, which leads to a substantial decrease of the phase coherence time. Atomic force microscope measurements also confirm a long-range height modulation present in these crystals. Our results suggest that phase coherent transport experiments relying on purely in-plane magnetic fields in van der Waals heterostructures have to be taken with serious care.

The thermal Hall conductance $K$ of the fractional quantum Hall state at filling fraction $\nu =5/2$ has recently been measured to be $K=2.5{\pi }^2{k}_B^{2}T/3h$ [M. Banerjee et al. Nature (London) 559, 205 (2018)]. The half-integer value of this result (in units of ${\pi }^2{k}_B^{2}T/3h$) provides strong evidence for the presence of a Majorana edge mode and a corresponding quantum Hall state hosting quasiparticles with non-Abelian statistics. Whether this measurement points to the realization of the PH-Pfaffian or the anti-Pfaffian state has been the subject of debate. Here we consider the implications of this measurement for anti-Pfaffian edge-state transport. We show that in the limit of strong Coulomb interaction and an approximate spin degeneracy in the lowest Landau level, the anti-Pfaffian state admits low-temperature edge phases that are consistent with the Hall conductance measurements. These edge phases can exhibit fully equilibrated electrical transport coexisting with partially equilibrated heat transport over a range of temperatures. Through a study of the kinetic equations describing low-temperature electrical and heat transport of these edge states, we determine regimes of parameter space, controlling the interactions between the different edge modes that agree with experiment.

Rare-earth ions typically exhibit larger magnetic moments than transition-metal ions and thus promise the opening of a wider exchange gap in the Dirac surface states of topological insulators. Yet in a recent photoemission study of Eu-doped ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ films, the spectra remained gapless down to $T=20$ K. Here we scrutinize whether the conditions for a substantial gap formation in this system are present by combining spectroscopic and bulk characterization methods with theoretical calculations. For all studied Eu doping concentrations, our atomic multiplet analysis of the $M_{4,5}$ x-ray absorption and magnetic circular dichroism spectra reveals a ${\mathrm{Eu}}^{2+}$ valence and confirms a large magnetic moment, consistent with a $4f^7{}^{8}S_{7/2}$ ground state. At temperatures below 10 K, bulk magnetometry indicates the onset of antiferromagnetic (AFM) ordering. This is in good agreement with density functional theory, which predicts AFM interactions between the Eu impurities. Our results support the notion that antiferromagnetism can coexist with topological surface states in rare-earth-doped ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and call for spectroscopic studies in the Kelvin range to look for novel quantum phenomena such as the quantum anomalous Hall effect.

We study the normal state electronic structure of the recently discovered infinite-layer nickelate superconductor, ${\mathrm{Nd}}_{1-x}{\mathrm{Sr}}_x{\mathrm{NiO}}_2$, using density functional theory plus dynamical mean-field theory calculations. Starting with the multiorbital compound ${\mathrm{SrNiO}}_2$, our calculations show that despite large charge-carrier doping from ${\mathrm{SrNiO}}_2$ to ${\mathrm{LaNiO}}_2$, the $\mathrm{Ni}\text{−}3d$ total occupancy is barely changed due to the decreased hybridization with the occupied oxygen-$2p$ states and increased hybridization with the unoccupied $\mathrm{La}\text{−}5d$ states. Thus, using ${\mathrm{SrNiO}}_2$ as a reference, ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_x{\mathrm{NiO}}_2$ is naturally and conclusively found to be a multiorbital electronic system with characteristic Hund's metal behaviors, such as metallicity, the importance of high-spin configurations, tendency towards orbital differentiation, and the absence of magnetism in regimes which are ordered according to static mean-field theories. Our results are in good agreement with the existing spectroscopic studies and make an essential step towards an understanding of the electronic structures of ${\mathrm{Nd}}_{1-x}{\mathrm{Sr}}_x{\mathrm{NiO}}_2$.

We investigate the thermodynamics and finite-temperature spectral functions of the Holstein polaron using a density-matrix renormalization group method. Our method combines purification and local basis optimization (LBO) as an efficient treatment of phonon modes. LBO is a scheme which relies on finding the optimal local basis by diagonalizing the local reduced density matrix. By transforming the state into this basis, one can truncate the local Hilbert space with a negligible loss of accuracy for a wide range of parameters. In this work, we focus on the crossover regime between large and small polarons of the Holstein model. Here, no analytical solution exists and we show that the thermal expectation values at low temperatures are independent of the phonon Hilbert space truncation provided the basis is chosen large enough. We then demonstrate that we can extract the electron spectral function and establish consistency with results from a finite-temperature Lanczos method. We additionally calculate the electron emission spectrum and the phonon spectral function and show that all the computations are significantly simplified by the local basis optimization. We observe that the electron emission spectrum shifts spectral weight to both lower frequencies and larger momenta as the temperature is increased. The phonon spectral function experiences a large broadening and the polaron peak at large momenta gets significantly flattened and merges almost completely into the free-phonon peak.

We generalize the $\eta$-pairing theory in Hubbard models to the ones with spin-orbit coupling (SOC) and obtain the conditions under which the $\eta$-pairing operator is an eigenoperator of the Hamiltonian. The $\eta$-pairing thus reveals an exact $\text{SU}\left(2\right)$ pseudospin symmetry in our spin-orbit coupled Hubbard model, even though the $\text{SU}\left(2\right)$ spin symmetry is explicitly broken by the SOC. In particular, these exact results can be applied to a variety of Hubbard models with SOC on either bipartite or nonbipartite lattices, whose noninteracting limit can be a Dirac semimetal, a Weyl semimetal, a nodal-line semimetal, and a Chern insulator. The $\eta$-pairing conditions also impose constraints on the band topology of these systems. We then construct and focus on an interacting Dirac-semimetal model, which exhibits an exact pseudospin symmetry with fine-tuned parameters. The stability regions for the exact $\eta$-pairing ground states (with momentum $\mathit{\pi }$ or $\mathit{0}$) and the exact charge-density-wave ground states are established. Between these distinct symmetry-breaking phases, there exists an exactly solvable multicritical line. In the end, we discuss possible experimental realizations of our results.

One of the hallmarks of quantum statistics, tightly entwined with the concept of topological phases of matter, is the prediction of anyons. Although anyons are predicted to be realized in certain fractional quantum Hall systems, they have not yet been unambiguously detected in experiment. Here we introduce a simple quantum impurity model, where bosonic or fermionic impurities turn into anyons as a consequence of their interaction with the surrounding many-particle bath. A cloud of phonons dresses each impurity in such a way that it effectively attaches fluxes or vortices to it and thereby converts it into an Abelian anyon. The corresponding quantum impurity model, first, provides a different approach to the numerical solution of the many-anyon problem, along with a concrete perspective of anyons as emergent quasiparticles built from composite bosons or fermions. More importantly, the model paves the way toward realizing anyons using impurities in crystal lattices as well as ultracold gases. In particular, we consider two heavy electrons interacting with a two-dimensional lattice crystal in a magnetic field, and show that when the impurity-bath system is rotated at the cyclotron frequency, impurities behave as anyons as a consequence of the angular momentum exchange between the impurities and the bath. A possible experimental realization is proposed by identifying the statistics parameter in terms of the mean-square distance of the impurities and the magnetization of the impurity-bath system, both of which are accessible to experiment. Another proposed application is impurities immersed in a two-dimensional weakly interacting Bose gas.

Entanglement-related properties work as a nice fingerprint of the quantum many-body wave function. However, those of fermionic models are hard to evaluate in standard numerical methods because they suffer from finite-size effects. We show that a so-called density embedding theory (DET) can evaluate them without a size scaling analysis, in comparably high quality with those obtained by a large-size density matrix renormalization group analysis. This method projects the large-scale original many-body Hamiltonian to a small number of basis sets defined on a local cluster, and optimizes the choice of these bases by tuning the local density matrix. The DET entanglement spectrum of one-dimensional interacting fermions perfectly reproduces the exact ones and works as a marker of the phase transition point. It is further shown that the phase transitions in two dimensions could be determined by the entanglement entropy and the fidelity that reflects the change of the structure of the wave function.

Strong coupling between two quanta of different excitations leads to the formation of a hybridized state that paves a way for exploiting new degrees of freedom to control phenomena with high efficiency and precision. A magnon polaron is the hybridized state of a phonon and a magnon, the elementary quanta of lattice vibrations and spin waves in a magnetically ordered material. A magnon polaron can be formed at the intersection of the magnon and phonon dispersions, where their frequencies coincide. The observation of magnon polarons in the time domain has remained extremely challenging because the weak interaction of magnons and phonons and their short lifetimes jeopardize the strong coupling required for the formation of a hybridized state. Here, we overcome these limitations by spatial matching of magnons and phonons in a metallic ferromagnet with a nanoscale periodic surface pattern. The spatial overlap of the selected phonon and magnon modes formed in the periodic ferromagnetic structure results in a high coupling strength which, in combination with their long lifetimes, allows us to find clear evidence of an optically excited magnon polaron. We show that the symmetries of the localized magnon and phonon states play a crucial role in the magnon polaron formation and its manifestation in the optically excited magnetic transients.

We investigate a quantum well that consists of a thin topological insulator sandwiched between two trivial insulators. More specifically, we consider smooth interfaces between these different types of materials such that the interfaces host not only the chiral interface states, whose existence is dictated by the bulk-edge correspondence, but also massive Volkov-Pankratov states. We investigate possible hybridization between these interface states as a function of the width of the topological material and of the characteristic interface size. Most saliently, we find a strong qualitative difference between an extremely weak effect on the chiral interface states and a more common hybridization of the massive Volkov-Pankratov states that can be easily understood in terms of quantum tunneling in the framework of the model of a (Dirac) quantum well we introduce here.

Chern-Simons theories have been very successful in explaining integer and fractional quantum Hall phases of matter, topological insulators, and Weyl semimetals. However, it remains an open question as to whether Chern-Simons theories can be adapted to topological photonics. We develop a viscous Maxwell-Chern-Simons theory to capture the fundamental physics of a topological electromagnetic phase of matter. We show the existence of a unique spin-1 skyrmion in the viscous Hall fluid arising from a photonic Zeeman interaction in momentum space. Our work bridges the gap between electromagnetic and condensed matter topological physics while also demonstrating the central role of photon spin-1 quantization in identifying new phases of matter.

We propose and investigate a simple one-dimensional model for a single-channel quantum wire hosting electrons that interact repulsively and are subject to a significant spin-orbit interaction. We show that an external Zeeman magnetic field, applied at the right angle to the Rashba spin-orbit axis, drives the wire into a correlated spin-density wave state with gapped spin and gapless charge excitations. By computing the ground-state degeneracies of the model with either (anti)periodic or open boundary conditions, we conclude that the correlated spin-density state realizes a gapless symmetry-protected topological phase, as the ground state is unique in the ring geometry while it is twofold degenerate in the wire with open boundaries. Microscopically the twofold degeneracy is found to be protected by the conservation of the magnetization parity. Open boundaries induce localized zero-energy (midgap) states which are described, at the special Luther-Emery point of the model, by Majorana fermions. We find that spin densities at the open ends of the wire exhibit unusual long-ranged correlations despite the fact that all correlations in the bulk of the wire decay in a power-law or exponential fashion. Our study exposes the crucial importance of the long-ranged string operator needed to implement the correct commutation relations between spin densities at different points in the wire. Along the way we rederive the low-energy theory of Galilean-invariant electron systems in terms of current operators.

Combined experimental and modeling studies of the magnetocaloric effect, ultrasound, and magnetostriction were performed on single-crystal samples of the spin-dimer system ${\mathrm{Sr}}_3{\mathrm{Cr}}_2{\mathrm{O}}_8$ in large magnetic fields to probe the spin-correlated regime in the proximity of the field-induced $XY$-type antiferromagnetic order also referred to as a Bose-Einstein condensate of magnons. The magnetocaloric effect, measured under adiabatic conditions, reveals details of the field-temperature $(H,T)$ phase diagram, a dome characterized by critical magnetic-fields $H_{c1}=30.4,H_{c2}=62\mathrm{T}$, and a single maximum ordering temperature $T_{\max }\left(45\mathrm{T}\right)\simeq 8\mathrm{K}$. The sample temperature was observed to drop significantly as the magnetic field is increased, even for initial temperatures above $T_{\max }$, indicating a significant magnetic entropy associated with the field-induced closure of the spin gap. The ultrasound and magnetostriction experiments probe the coupling between the lattice degrees of freedom and the magnetism in ${\mathrm{Sr}}_3{\mathrm{Cr}}_2{\mathrm{O}}_8$. Our experimental results are qualitatively reproduced by a minimalistic phenomenological model of the exchange striction by which sound waves renormalize the effective exchange couplings.

Topological materials are of interest to both fundamental science and advanced technologies because topological states are robust with respect to perturbations and dissipation. Experimental detection of topological invariants is thus in great demand but remains extremely challenging. Ultrafast laser-matter interactions, and in particular high-harmonic generation, meanwhile, were proposed several years ago as tools to explore the structural and dynamical properties of various matter targets. Here we show that the high-harmonic emission signal produced by a circularly polarized laser contains signatures of topological phases and transitions in the paradigmatic Haldane model. In addition to clear shifts of the overall emissivity and harmonic cutoff, the high-harmonic emission shows a unique circular dichroism, which exhibits clear changes in behavior at the topological phase boundary. Our findings pave the way to understand fundamental questions about the ultrafast electron-hole pair dynamics in topological materials via nonlinear high-harmonic generation spectroscopy.

Stoichiometric SnTe is theoretically a small gap semiconductor that undergoes a ferroelectric distortion on cooling. In reality however, crystals are always nonstoichiometric and metallic; the ferroelectric transition is therefore, more accurately described as a polar structural transition. Here, we study the Fermi surface using quantum oscillations as a function of pressure. We find the oscillation spectrum changes at high pressure due to the suppression of the polar transition and less than 10 kbars is sufficient to stabilize the undistorted cubic lattice, this is accompanied by a large decrease in the Hall and electrical resistivities. Combined with our density functional theory calculations and angle-resolved photoemission spectroscopy measurements, this suggests the Fermi surface $L$ pockets have lower mobility than the tubular Fermi surfaces that connect them. Additionally, we find the unusual phenomenon of a linear magnetoresistance that exists irrespective of the distortion that we attribute to regions of the Fermi surface with high curvature.