When one of the graphene layers of magic-angle twisted bilayer graphene is nearly aligned with its hexagonal boron nitride substrate (a configuration dubbed TBG/hBN), the active electronic bands are nearly flat and have a Chern number $C=\pm 1$. Recent experiments demonstrated a quantum anomalous Hall effect and spontaneous valley polarization at integer filling ${\nu }_T=3$ of the conduction band in this system. Motivated by this discovery, we ask whether fractional quantum anomalous Hall states (FQAHs) could also emerge in TBG/hBN. We focus on the range of filling fractions where valley ferromagnetism was observed experimentally. Using exact diagonalization, we find that the ground states at ${\nu }_T=\frac{10}{3}$ and ${\nu }_T=\frac{17}{5}$ are fractional Chern insulator states in the flatband limit (in the hole picture, these are the FQH fractions $\frac{2}{3}$ and $\frac{3}{5}$). The ground state is either spin polarized or a spin singlet, depending sensitively on band parameters. For nominally realistic band parameters, spin polarization is favored. Flattening the Berry curvature by changing a band parameter gives way to the spin singlet phase. Our estimation of the charge gap in the flatband limit shows that the FQAH state may be seen at accessible temperatures in experiments. We also study the effect of a nonzero bandwidth and show that there is a reasonable range of parameters in which the FQAH state is the ground state.

Recent experiments on bilayer graphene twisted near the magic angle have observed spontaneous integer quantum Hall states in the presence of an aligned hexagonal boron nitride substrate. These states arise from the complete filling of Chern bands. A natural question is whether fractional filling of the same bands would lead to fractional Chern insulators (FCIs), i.e., fractional quantum Hall states realized in the absence of a magnetic field. Here, we argue that the magic angle graphene bands have favorable quantum geometry for realizing FCIs. We show that in the tractable “chiral” limit, the flatbands wave functions are an analytic function of the crystal momentum. This remarkable property fixes the quantum metric up to an overall momentum-dependent scale factor, the local Berry curvature, whose variation is itself small. Thus the three conditions associated with FCI stability—(i) narrow bands, (ii) “ideal” quantum metric, and (iii) relatively uniform Berry curvature—are all satisfied. Our work emphasizes continuum real-space approaches to FCIs, in contrast to earlier works, which mostly focused on tight-binding models. This enables us to construct a Laughlin wave function on a real-space torus that is a zero-energy ground state of the Coulomb interaction in the limit of very short screening length. Finally, we discuss the evolution of the band geometry on tuning away from the chiral limit and show numerically that some of the desirable properties continue to hold at a quantitative level for realistic parameter values.

Nonlocality is an interesting topic in quantum physics and is usually mediated by some unique quantum states. Here we investigate a Weyl semimetal slab and find an exotic nonlocal correlation effect when placing two potential wells merely on the top and bottom surfaces. This correlation arises from the peculiar Weyl orbit in Weyl semimetals and is a consequence of the bulk-boundary correspondence in topological band theory. A giant nonlocal transport signal and a body breakdown by Weyl fermions are further uncovered, which can serve as signatures for verifying this nonlocal correlation effect experimentally. Our results extend another member in the nonlocality family and have potential applications for designing unique electric devices with fancy functions.

We show that non-Hermiticity enables topological phases with unidirectional transport in one-dimensional Floquet chains. The topological signatures of these phases are noncontractible loops in the spectrum of the Floquet propagator that are separated by an imaginary gap. Such loops occur exclusively in non-Hermitian Floquet systems. We define the corresponding topological invariant as the winding number of the Floquet propagator relative to the imaginary gap. To relate topology to transport, we introduce the concept of regularized dynamics of non-Hermitian chains. We establish that, under the conditions of regularized dynamics, transport is quantized insofar as the charge transferred over one period equals the topological winding number. We illustrate these theoretical findings with the example of a Floquet chain that features a topological phase transition and acts as a charge pump in the nontrivial topological phase. We finally discuss whether these findings justify the notion that non-Hermitian Floquet chains support topological transport.

The coupling between lattice vibration quanta and valence electrons can induce charge-density modulations and decisively influence the transport properties of materials, e.g., leading to conventional superconductivity. In high-critical-temperature superconductors, where electronic correlation is the main actor, the actual role of electron-phonon coupling (EPC) is being intensely debated theoretically and investigated experimentally. We present an in-depth study of how the EPC strength can be obtained directly from resonant inelastic x-ray scattering (RIXS) data through the theoretical approach derived by Ament et al. [Europhys. Lett. 95, 27008 (2011)]. The role of the model parameters (e.g., phonon energy ${\omega }_0$, intermediate state lifetime $1/\mathrm{\Gamma }$, EPC matrix element $M$, and detuning energy $\mathrm{\Omega }$) is thoroughly analyzed, providing general relations among them that can be used to make quantitative estimates of the dimensionless EPC $g={(M/{\omega }_0)}^2$ without detailed microscopic modeling. We then apply these methods to very high-resolution Cu $L_3$-edge RIXS spectra of three ${\mathrm{Nd}}_{1+x}{\mathrm{Ba}}_{2-x}{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ films. For the insulating antiferromagnetic parent compound, the value of $M$ as a function of the in-plane momentum transfer is obtained for Cu-O bond-stretching (breathing) and bond-bending (buckling) phonon branches. For the underdoped and the nearly optimally doped samples, the effects of Coulomb screening and of charge-density-wave correlations on $M$ are assessed. In light of the anticipated further improvements of the RIXS experimental resolution, this work provides a solid framework for an exhaustive investigation of the EPC in cuprates and other quantum materials.

The emergence of photoinduced topological phases and their phase transitions is theoretically predicted in organic salt $\alpha$-(BEDT-TTF)${}_2{\mathrm{I}}_3$, which possesses inclined Dirac cones in its band structure. By analyzing a photodriven tight-binding model describing conduction electrons in the BEDT-TTF layer using the Floquet theorem, we demonstrate that irradiation with circularly polarized light opens a gap at the Dirac points, and the system eventually becomes a Chern insulator characterized by a quantized topological invariant. A rich phase diagram is obtained in the plane of amplitude and frequency of light, which contains Chern insulator, semimetal, and normal insulator phases. We find that the photoinduced Hall conductivity provides a sensitive means to detect the predicted phase evolutions experimentally. This work contributes towards developing the optical manipulation of electronic states in matter through broadening the range of target materials that manifest photoinduced topological phase transitions.

An Alice string is a topological defect with a very peculiar feature. When a defect with a monopole charge encircles an Alice string, the monopole charge changes sign. In this paper, we generalize this notion to the momentum space of periodic media with loss and gain. In particular, we find that the generic band-structure node for a three-dimensional non-Hermitian crystalline system acts as an Alice string, which can flip the Chern number charge carried by Weyl points and by exceptional-line rings. We discuss signatures of this topological structure for a lattice model with one tuning parameter, including nontrivial braiding of bulk band nodes, and the spectroscopic features of both the bulk and the surface states. We also explore how an Alice string affects the validity of the Nielsen-Ninomiya theorem, and present a mathematical description of the braiding phenomenon.

Motivated by recent developments in twisted bilayer graphene moiré superlattices, we investigate the effects of electron-electron interactions in a honeycomb lattice with an applied periodic potential using a finite-temperature Wilson-Fisher momentum shell renormalization group (RG) approach. We start with a low-energy effective theory for such a system, at first giving a discussion of the most general case in which no point group symmetry is preserved by the applied potential, and then focusing on the special case in which the potential preserves a $D_3$ point group symmetry. As in similar studies of bilayer graphene, we find that, while the coupling constants describing the interactions diverge at or below a certain critical temperature $T=T_c$, it turns out that ratios of these constants remain finite and in fact provide information about what types of orders the system is becoming unstable to. However, in contrast to these previous studies, we only find isolated fixed rays, indicating that these orders are likely unstable to perturbations to the coupling constants. Our RG analysis leads to the qualitative conclusion that the emergent interaction-induced symmetry-breaking phases in this model system, and perhaps therefore by extension in twisted bilayer graphene, are generically unstable and fragile, and may thus manifest strong sample dependence.

The thermal Hall conductivities (THCs) ${\kappa }_{ij}$ have extensively been studied in recent condensed matter experiments. THCs can spontaneously become nonzero for a time-reversal-symmetry-broken system, and have a contribution from topologically protected edge states. Here, we focus on an additional bulk effect, the impurity mechanism in superconductors (SCs). Previously, the THCs were calculated for the chiral $p$-wave [S. K. Yip, Supercond. Sci. Technol. 29, 085006 (2016); B. Arfi et al., Phys. Rev. B 39, 8959 (1989)] SCs for point impurities. Generalizing this finding to even-pairing states, we calculate thermal transport coefficients for finite-size impurities using Keldysh quasiclassical Green's functions. We find that for $d$-wave pairing, the impurity mechanism is dominant in ${\kappa }_{yx}$ when compared to the topological contribution except at very low temperatures. This finding is shown to be valid irrespective of the impurity density of the bulk. There are two experimental signatures of the impurity mechanism on ${\kappa }_{yx}$: a nonmonotonic temperature dependence and a possible sign change as a function of temperature depending on the scattering phase shifts and the corresponding $d$-wave representation.

We consider a nonequilibrium cross-response phenomenon, where a driven magnetization gives rise to electric shot noise (but no d.c. current). This effect is realized on a nanoscale, with a small metallic ferromagnet which is tunnel coupled to two normal metal leads. The driving gives rise to a precessing magnetization. The geometrically generated noise is related to a nonequilibrium electron distribution in the ferromagnet. Our protocol provides a channel for detecting and characterizing ferromagnetic resonance.

Unambiguous and complete determination of the Fermi surface is a primary step in understanding the electronic properties of topical metals and semimetals, but only in a relatively few cases has this goal been realized. In this work, we present a systematic high-field quantum oscillation study up to 35 T on ZrSiS, a textbook example of a nodal-line semimetal with only linearly dispersive bands crossing the Fermi energy. The topology of the Fermi surface is determined with unprecedented precision and all pockets are identified by comparing the measured angle dependence of the quantum oscillations to density-functional-theory calculations. Comparison of the Shubnikov-de Haas and de Haas-van Alphen oscillations at low temperatures and analysis of the respective Dingle plots reveal the presence of significantly enhanced scattering on the electron pocket. Above a threshold field that is aligned along the $c$ axis of the crystal, the specific cage like Fermi surface of ZrSiS allows for electron-hole tunneling to occur across finite gaps in momentum space, leading to quantum oscillations with a complex frequency spectrum. Additional high-frequency quantum oscillations signify magnetic breakdown orbits that encircle the entire Dirac nodal loop. We suggest that the persistence of quantum oscillations in the resistivity to high temperatures is caused by Stark interference between orbits of nearly equal masses.

We consider quantum many-body systems evolving under a time-independent Hamiltonian $H$ from a nonequilibrium initial state at time $t=0$ towards a close-to-equilibrium state at time $t=\tau$. Subsequently, this state is slightly perturbed and finally propagated for another time period $\tau$ under the inverted Hamiltonian $-H$. The entire procedure may also be viewed as an imperfect time inversion or “echo dynamics.” We unravel a remarkable persistence of such dynamics with respect to the observable deviations of the time-dependent expectation values from the equilibrium expectation value: For most perturbations, the deviations in the final state are essentially independent of the inversion time point $\tau$. Our quantitative analytical predictions compare very well with exact numerical results.

We develop a scheme for engineering genuine thermal states in analog quantum simulation platforms by coupling local degrees of freedom to driven, dissipative ancilla pseudospins. We demonstrate the scheme in a many-body quantum spin lattice simulation setting. A Born-Markov master equation describing the dynamics of the many-body system is developed, and we show that if the ancilla energies are periodically modulated, with a carefully chosen hierarchy of timescales, one can effectively thermalize the many-body system. Through analysis of the time-dependent dynamical generator, we determine the conditions under which the true thermal state is an approximate dynamical fixed point for general system Hamiltonians. Finally, we evaluate the thermalization protocol through numerical simulation and discuss prospects for implementation on current quantum simulation hardware.

The Kitaev model is a beautiful example of frustrated interactions giving rise to deep and unexpected phenomena. In particular, its classical version has remarkable properties stemming from exponentially large ground-state degeneracy. Here, we present a study of magnetic clusters with spin-$S$ moments coupled by Kitaev interactions. We focus on two cluster geometries, the Kitaev square and the Kitaev tetrahedron, that allow us to explicitly enumerate all classical ground states. In both cases, the classical ground-state space (CGSS) is large and self-intersecting, with nonmanifold character. The Kitaev square has a CGSS of four intersecting circles that can be embedded in four dimensions. The tetrahedron CGSS consists of eight spheres embedded in six dimensions. In the semiclassical large-$S$ limit, we argue for effective low-energy descriptions in terms of a single particle moving on these nonmanifold spaces. Remarkably, at low energies, the particle is tied down in bound states formed around singularities at self-intersection points. In the language of spins, the low-energy physics is determined by a distinct set of states that lies well below other eigenstates. These correspond to “Cartesian” states, a special class of classical ground states that are constructed from dimer covers of the underlying lattice. They completely determine the low-energy physics despite being a small subset of the classical ground-state space. This provides an example of order by singularity, where state selection becomes stronger upon approaching the classical limit.

The mechanism of fermionic pairing is the key to understanding various phenomena such as high-temperature superconductivity and the pseudogap phase in cuprate materials. We study the pair correlations in the attractive Hubbard model using ultracold fermions in a two-dimensional optical lattice. By combining the fluctuation-dissipation theorem and the compressibility equation of state, we extract the interacting pair-correlation functions and deduce a characteristic length scale of pairs as a function of interaction and density filling. At sufficiently low filling and weak onsite interaction, we observe that the pair correlations extend over a few lattice sites even at temperatures above the superfluid transition temperature.

Abrikosov vortices in Fe-based superconductors are a promising platform for hosting Majorana zero-energy modes. Their adiabatic exchange is a key ingredient for Majorana-based quantum computing. However, the adiabatic braiding process cannot be realized in state-of-the-art experiments. We propose to replace the infinitely slow, long-path braiding by a procedure that only slightly moves vortices in a special geometry without actually physically exchanging the Majoranas, like a Majorana carousel. Although the resulting finite-time gate is not topologically protected, it is robust against variations in material-specific parameters and in the braiding speed. We prove this analytically. Our results carry over to Y junctions of Majorana wires.

We numerically study yielding in two-dimensional glasses which are generated with a very wide range of stabilities by swap Monte Carlo simulations and then slowly deformed at zero temperature. We provide strong numerical evidence that stable glasses yield via a nonequilibrium discontinuous transition in the thermodynamic limit. A critical point separates this brittle yielding from the ductile one observed in less stable glasses. We find that two-dimensional glasses yield similarly to their three-dimensional counterparts but display larger sample-to-sample disorder-induced fluctuations, stronger finite-size effects, and rougher spatial wandering of the observed shear bands. These findings strongly constrain effective theories of yielding.

Optically induced spin transfer (OISTR) is a pathway to control magnetization dynamics in complex materials on femto- to attosecond timescales. The direct interaction of the laser field with the material creates transient nonequilibrium states, which can exhibit an efficient spin transfer between different magnetic subsystems. How far this spin manipulation via OISTR is a general phenomenon or restricted to a subset of materials with specific properties is an open experimental and theoretical question. Using time-resolved magneto-optical Kerr measurements and time-dependent density functional theory we investigate OISTR in Heusler compounds. We show that the half-Heusler materials NiMnSb and CoMnSb exhibit strong signatures of OISTR, whereas this is less pronounced in the full-Heusler compounds ${\mathrm{Co}}_2\mathrm{MnSi}$, ${\mathrm{Co}}_2\mathrm{FeSi}$, and ${\mathrm{Co}}_2\mathrm{FeAl}$ in agreement with ab initio calculations. Our work opens up a systematic path for coherent manipulation of spin dynamics by direct light-matter interaction.

We theoretically show that the edge of a quantum spin Hall insulator (QSHI), attached to an insulating ferromagnet (FM), can realize a highly efficient spin-to-charge conversion. Based on a one-dimensional QSHI-FM junction, the electron dynamics on the QSHI edge is analyzed, driven by a magnetization dynamics in the FM. Under a large gap opening on the edge from the magnetic exchange coupling, we find that the spin injection into the QSHI edge gets suppressed while the charge current driven on the edge gets maximized, demanded by the band topology of the one-dimensional helical edge states.

The recently discovered material ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ shows an impressive behavior of the quantum anomalous Hall (QAH) conductivity driven by the interplay between ferromagnetism in the $z$ direction and antiferromagnetism in the $xy$ plane. Motivated by these facts, first we build and study a spin-1/2 model to describe the magnetism of Co atoms on the kagome planes. Then, we include conduction electrons which are coupled to the spin-1/2's through a strong Hund's coupling. The spin-orbit coupling results in topological low-energy bands. For 2/3 on-site occupancy, we find a topological transition from a QAH ferromagnetic insulating phase with Chern number one to a quantum spin Hall (QSH) antiferromagnetic phase. The QAH phase is metallic when slightly changing the on-site occupancy. To account for temperature effects, we include fluctuations in the direction of the Hund's coupling. We show how the Hall conductivity can now smoothly evolve when spins develop a ${120}^{\text{o}}$ antiferromagnetism in the $xy$ plane and can synchronize with the ferromagnetic fraction.