Van der Waals (vdW) ferromagnets have enabled the development of heterostructures assembled from exfoliated monolayers with spintronics functionalities, making it important to understand and ultimately tune their magnetic properties at the microscopic level. Information about the magnetic properties of these systems comes, so far, largely from macroscopic techniques, with little being known about the microscopic magnetic properties. Here, we combine spin-polarized scanning tunneling microscopy and quasiparticle interference imaging with neutron scattering to establish the magnetic and electronic properties of the metallic vdW ferromagnet ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$. By imaging domain walls at the atomic scale, we can relate the domain wall width to the exchange interaction and magnetic anisotropy extracted from the magnon dispersion as measured in inelastic neutron scattering, with excellent agreement between the two techniques. From comparison with density functional theory calculations we can assign the quasiparticle interference to be dominated by spin-majority bands. We find a dimensional dichotomy of the bands at the Fermi energy: bands of minority character are predominantly two-dimensional in character, whereas the bands of majority character are three-dimensional. We expect that this will enable new design principles for spintronics devices.

Magnetic skyrmions are topologically distinct particles whose thermally activated motion could be used to implement probabilistic computing paradigms. While solid-liquid phase transitions in skyrmion lattices have been demonstrated, the behavior of a skyrmion liquid and the effects of pinning are largely unknown. Here we demonstrate the formation of a weakly pinned skyrmion liquid in a magnetic heterostructure. By inserting a Ru wedge layer at the ferromagnet/heavy metal interface we evaluate the dependence of skyrmion dynamics on the skyrmion size and density. Our experiments demonstrate that the diffusion of skyrmions is largest in dense liquids with small skyrmions. The thermal motion of skyrmions at room temperature easily overcomes the narrow distribution of pinning site energies in the granular film structure, satisfying a key requirement of probabilistic device architectures. Micromagnetic simulations support the findings and also reveal the existence of a thermally activated high-frequency collective oscillation.

Pontrjagin's seminal topological classification of two-band Hamiltonians in three momentum dimensions is hereby enriched with the inclusion of crystallographic rotational symmetry. The enrichment is attributed to a new topological invariant which quantifies a $2\pi$-quantized change in the Berry-Zak phase between a pair of rotation-invariant lines in the bulk, three-dimensional Brillouin zone; because this change is reversed on the complementary section of the Brillouin zone, we refer to this new invariant as a returning Thouless pump (RTP). We find that the RTP is associated with anomalous values for the angular momentum of surface states, which guarantees metallic in-gap states for open boundary conditions with sharply terminated hoppings; more generally for arbitrarily terminated hoppings, surface states are characterized by Berry-Zak phases that are quantized to a rational multiple of $2\pi$. The RTP adds to the family of topological invariants (the Hopf and Chern numbers) that are known to classify two-band Hamiltonians in Wigner-Dyson symmetry class A. Of these, the RTP and Hopf invariants are delicate, meaning that they can be trivialized by adding a particular trivial band to either the valence or the conduction subspace. Not all trivial band additions will nullify the RTP invariant, which allows its generalization beyond two-band Hamiltonians to arbitrarily many bands; such generalization is a hallmark of symmetry-protected delicate topology.

We present a theoretical framework to describe polarons from first principles within a many-body Green's function formalism. Starting from a general electron-phonon Hamiltonian, we derive a self-consistent Dyson equation in which the phonon-mediated self-energy is composed by two distinct terms. One term is the Fan-Migdal self-energy and describes dynamic electron-phonon processes, the other term is a contribution to the self-energy originating from the static displacements of the atomic nuclei in the polaronic ground state. The lowest-order approximation to the present theory yields the standard many-body perturbation theory approach to electron-phonon interactions in the limit of large polarons, and the ab initio polaron equations introduced [Sio et al., Phys. Rev. B 99, 235139 (2019); Phys. Rev. Lett. 122, 246403 (2019)] in the limit of small polarons. A practical recipe to implement the present unifying formalism in first-principles calculations is outlined. We apply our method to the Fröhlich model, and obtain remarkably accurate polaron energies at all couplings, in line with Feynman's polaron theory and diagrammatic Monte Carlo calculations. We also recover the well-known results of Fröhlich and Pekar at weak and strong coupling, respectively. The present approach enables predictive many-body calculations of polarons in real materials at all couplings.

${\text{La}}_2{\text{Ni}}_7$ is an intermetallic compound that is thought to have itinerant magnetism with small moment $(\sim 0.15{\mu }_{\text{B}}/\text{Ni})$ ordering below 65 K. A recent study of single crystal samples by Ribeiro et al. [Phys. Rev. B 105, 014412 (2022)] determined detailed anisotropic $H-T$ phase diagrams and revealed three zero-field magnetic phase transitions at $T_1\sim 61.0$ K, $T_2\sim 56.5$ K, and $T_3\sim 42$ K. In that study only the highest temperature phase is shown to have a clear ferromagnetic component. Here we present a single crystal neutron diffraction study determining the propagation vector and magnetic moment direction of the three magnetically ordered phases, two incommensurate and one commensurate, as a function of temperature. The higher temperature phases have similar, incommensurate propagation vectors, but with different ordered moment directions. At lower temperatures, the magnetic order becomes commensurate with magnetic moments along the $\mathit{c}$ direction as part of a first-order magnetic phase transition. We find that the low-temperature commensurate magnetic order is consistent with a proposal from earlier DFT calculations.

The late-time dynamics of quantum many-body systems is organized in distinct dynamical universality classes, characterized by their conservation laws and thus by their emergent hydrodynamic transport. Here, we study transport in the one-dimensional Hubbard model with different masses of the two fermionic species. To this end, we develop a quantum Boltzmann approach valid in the limit of weak interactions. We explore the crossover from ballistic to diffusive transport, whose timescale strongly depends on the mass ratio of the two species. For timescales accessible with matrix product operators, we find excellent agreement between these numerically exact results and the quantum Boltzmann equation, even for intermediate interactions. We investigate two scenarios which have been recently studied with ultracold-atom experiments. First, in the presence of a tilt, the quantum Boltzmann equation predicts that transport is significantly slowed down and becomes subdiffusive, consistent with previous studies. Second, we study transport probed by displacing a harmonic confinement potential and find good quantitative agreement with recent experimental data [N. D. Oppong et al., arXiv:2011.12411]. Our results demonstrate that the quantum Boltzmann equation is a useful tool to study complex nonequilibrium states in inhomogeneous potentials, as often probed with synthetic quantum systems.

The lowest-energy excitations of superconductors do not carry an electric charge, as their wave function is equally electron-like and hole-like. This fundamental property is not easy to study in electrical measurements that rely on the charge to generate an observable signal. The ability of a quantum dot to act as a charge filter enables us to solve this problem and measure the quasiparticle charge in superconducting-semiconducting hybrid nanowire heterostructures. We report measurements on a three-terminal circuit, in which an injection lead excites a nonequilibrium quasiparticle distribution in the hybrid system, and the electron or hole component of the resulting quasiparticles is detected using a quantum dot as a tunable charge and energy filter. The results verify the chargeless nature of the quasiparticles at the gap edge and reveal the complete relaxation of injected charge and energy in a proximitized nanowire, resolving open questions in previous three-terminal experiments.

The intertwining of charge order, superconductivity, and band topology has promoted the $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K}$, Rb, Cs) family of materials to the center of attention in condensed matter physics. Underlying those mysterious macroscopic properties such as giant anomalous Hall conductivity (AHC) and chiral charge density wave is their nontrivial band topology. While there have been numerous experimental and theoretical works investigating the nontrivial band structure and especially the van Hove singularities, the exact topological phase of this family remains to be clarified. In this work, we identify ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ as a Dirac nodal line semimetal based on the observation of multiple Dirac nodal lines and loops close to the Fermi level. Combining photoemission spectroscopy and density functional theory, we identify two groups of Dirac nodal lines along the $k_z$ direction and one group of Dirac nodal loops in the $A-H-L$ plane. These nodal loops are located at the Fermi level within the instrumental resolution limit. Importantly, our first-principles analyses indicate that these nodal loops may be a crucial source of the mysterious giant AHC observed. Our results not only provide a clear picture to categorize the band structure topology of this family of materials, but also suggest the dominant role of topological nodal loops in shaping their transport behavior.

Spin transfer torque and spin pumping are central reciprocal phenomena in spintronics. These phenomena occur in hybrid systems of normal metals and magnets. Spin transfer is the conversion of spin currents in metals to a torque on the magnetization of magnets. Spin pumping is the emission of spin currents from precessing magnets. Here, we demonstrate a general way to understand these effects within a quantum out-of-equilibrium path-integral model. Our results agree with known expressions for spin transfer and spin pumping in terms of transverse (mixing) conductances when there are no fluctuations. However, at a finite temperature, frequency, or spin accumulation, the magnet also experiences fluctuating torques. In the classical regime, when the thermal energy is larger than the bias voltage and precession frequency, we reproduce the classical Brownian-Langevin forces associated with spin transfer and spin pumping. At low temperatures, in the quantum regime, we demonstrate that magnetization fluctuations differ in the elastic and inelastic electron transport regimes. Furthermore, we show how additional transport coefficients beyond the mixing conductance govern the fluctuations. Some of these coefficients are related to electron shot noise because of the discrete spin angular momentum of electrons. We estimate the fluctuation coefficients of clean, tunnel, and disordered junctions and in the case of an insulating magnet. Our results open a path for exploring low-temperature magnetization dynamics and spin caloritronics.

Robust edge transport can occur when charged particles in crystalline lattices interact with an applied external magnetic field. Such systems have a spectrum composed of bands of bulk states and in-gap edge states. For quasicrystalline systems, we still expect to observe the basic characteristics of bulk states and current-carrying edge states. We show that, for quasicrystals in magnetic fields, there is an additional third option—bulk localized transport (BLT) states. BLT states share the in-gap nature of the well-known edge states and can support transport, but they are fully contained within the bulk of the system, with no support along the edge. Thus, transport is possible along the edge and within distinct regions of the bulk. We consider both finite-size and infinite-size systems, using rigorous error controlled computational techniques that are not prone to finite-size effects. BLT states are preserved for infinite-size systems, in stark contrast to edge states. This allows us to observe transport in infinite-size systems, without any perturbations, defects, or boundaries being introduced. We confirm the in-gap topological nature of BLT states for finite- and infinite-size systems by computing the Bott index and local Chern marker (common topological measures). BLT states form due to magnetic aperiodicity, arising from the interplay of lengthscales between the magnetic field and the quasiperiodic lattice. BLT could have interesting applications similar to those of edge states, but now taking advantage of the larger bulk of the lattice. The infinite-size techniques introduced here, especially the calculation of topological measures, could also be widely applied to other crystalline, quasicrystalline, and disordered models.

We propose a realization of Kondo lattice physics in moiré superlattices at the interface between a $\mathrm{W}{X}_2$ homobilayer and $\mathrm{Mo}{X}_2$ monolayer $(X=\mathrm{S},\mathrm{Se})$. Under appropriate gating conditions, the interface $\mathrm{W}{X}_2$ layer forms a triangular lattice of local moments that couple to itinerant electrons in the other $\mathrm{W}{X}_2$ layer via a gate-tunable Kondo exchange interaction. Using a parton mean-field approach, we identify a range of twist angles which support a gate-tuned quantum phase transition between a heavy Fermi liquid with large anomalous Hall conductance and a chiral spin liquid coexisting with a light Fermi liquid and describe experimental signatures to distinguish among competing theoretical scenarios.

We theoretically propose a realization of nonlinear nonreciprocal transport in antiferromagnets without relying on the relativistic spin-orbit coupling. Through symmetry and microscopic model analyses, we show that a local spin scalar chirality inducing an asymmetric band modulation becomes a source of a Drude-type nonlinear transport, while an electric polarization induced by a collinear spin configuration in a triangle unit leads to a Berry-curvature-dipole-type nonlinear transport. We demonstrate ${120}^{\circ }$ antiferromagnetic ordering on a triangular lattice and a breathing kagome lattice in an external magnetic field as typical examples. Our results open another direction for the design and engineering of functional materials to show rich parity-violating transport phenomena induced by spontaneous magnetic phase transitions even without the spin-orbit coupling.

A central result in superconductivity is that flat bands, though dispersionless, can still host a nonzero superfluid weight due to quantum geometry. We show that the derivation of the mean field superfluid weight in previous literature is incomplete, which can lead to severe quantitative and even qualitative errors. We derive the complete equations and demonstrate that the minimal quantum metric, the metric with minimum trace, is related to the superfluid weight in isolated flat bands. We complement this result with an exact calculation of the Cooper pair mass in attractive Hubbard models with the uniform pairing condition. When the orbitals are located at high-symmetry positions, the Cooper pair mass is exactly given by the quantum metric, which is guaranteed to be minimal. Moreover, we study the effect of closing the band gap between the flat and dispersive bands, and develop a mean field theory of pairing for different band-touching points via the $S$-matrix construction. In mean field theory, we show that a nonisolated flat band can actually be beneficial for superconductivity. This is a promising result in the search for high-temperature superconductivity as the material does not need to have flat bands that are isolated from other bands by the thermal energy. Our work resolves a fundamental caveat in understanding the relation of multiband superconductivity to quantum geometry, and the results on band touchings widen the class of systems advantageous for the search of high-temperature flat band superconductivity.

We propose a height-conserving quantum dimer model (hQDM) such that the lattice sum of its associated height field is conserved, and that it admits a Rokhsar-Kivelson (RK) point. The hQDM with a minimal interaction range on the square lattice exhibits Hilbert space fragmentation and maps exactly to the XXZ spin model on the square lattice in certain Krylov subspaces. We obtain the ground-state phase diagram of hQDM via quantum Monte Carlo simulations, and demonstrate that a large portion of it is within the Krylov subspaces which admit the exact mapping to the XXZ model, with dimer ordered phases corresponding to easy-axis and easy-plane spin orders. At the RK point, the apparent dynamical exponents obtained from the single mode approximation and the height correlation function show drastically different behavior across the Krylov subspaces, exemplifying Hilbert space fragmentation and emergent glassy phenomena.

It was recently suggested that the topology of magic-angle twisted bilayer graphene's (MATBG) flat bands could provide a novel mechanism for superconductivity distinct from both weakly coupled BCS theory and the $d$-wave phenomenology of the high-$T_c$ cuprates. In this work, we examine this possibility using a density matrix renormalization group (DMRG) study of a model which captures the essential features of MATBG's symmetry and topology. Using large-scale cylinder-DMRG calculations to obtain the ground state and its excitations as a function of the electron doping, we find clear evidence for superconductivity driven by the binding of electrons into charge-$2e$ skyrmions. Remarkably, this binding is observed even in the regime where the unscreened Coulomb repulsion is by far the largest energy scale, demonstrating the robustness of this topological, all-electronic pairing mechanism.

The electric and chiral current response to the time- and coordinate-dependent pseudoelectric field ${\mathbf{E}}_5$ in Weyl semimetals is studied. It is found that ${\mathbf{E}}_5$ leads to an electric current in the direction perpendicular to the field and the wave vector of the field-inducing perturbation. We dubbed this phenomenon the anomalous pseudo-Hall effect. The response of the chiral or valley current to the pseudoelectric field is also found to be nontrivial. Since the wave vector for ${\mathbf{E}}_5$ cannot be neglected, the frequency profile of the chiral conductivity is drastically different from its electric counterpart showing a steplike feature instead of a smooth Drude peak. The proposed effects can be investigated by driving sound waves in Weyl semimetals with broken time-reversal symmetry.

We show that triangle-based antiferromagnets with “antichiral” order display a nontrivial dependence of the spin orientation with an in-plane field. The spins evolve from rotating in the opposite sense to the field at very low fields to rotating in the same sense as the field above some critical field scale. In the latter regime the system displays first-order transitions at which the spin angles jump, and these first-order lines terminate in critical points in the Ising universality class. Application to ${\mathrm{Mn}}_3\mathrm{Sn}$ is discussed.

We provide a quantitative analysis of the splittings in low-lying numerical entanglement spectra (ES), at given momentum, of a number of quantum states that can be identified, based on “Li-Haldane state-counting”, as ground states of (2 $+$ 1)-dimensional chiral topological phases with global SU(2) symmetry. The ability to account for numerical ES splittings solely within the context of conformal field theory (CFT) is an additional diagnostic of the underlying topological theory, of finer sensitivity than “state-counting”. We use the conformal boundary state description of the ES, which can be viewed as a quantum quench. In this language, the ES splittings arise from local conservation laws in the chiral CFT besides the energy, which we view as a generalized Gibbs ensemble (GGE). Global SU(2) symmetry imposes strong constraints on the number of such conservation laws, so that only a small number of parameters can be responsible for the splittings. We work out these conservation laws for chiral SU(2) Wess-Zumino-Witten CFTs at levels one and two, and for the latter we notably find that some of the conservation laws take the form of local integrals of operators of fractional dimension, as proposed by Cardy for quantum quenches. We analyze numerical ES from systems with SU(2) symmetry including chiral spin-liquid ground states of local 2D Hamiltonians and two chiral projected entangled pair states (PEPS) tensor networks, which exhibit the “state-counting” of the SU(2)-level-one and SU(2)-level-two theories. We find that the low-lying ES splittings can be well understood by the lowest of our conservation laws, and we demonstrate the importance of accounting for the fractional conservation laws at level two. Thus the states we consider, including the PEPS, appear chiral also under our more sensitive diagnostic.

The spectral functions of the one-band half-filled one-dimensional Hubbard chain are calculated using the exchange-correlation potential formalism developed recently. The exchange-correlation potential is adopted from the exact potential derived from the Hubbard dimer. Within an approximation in which the full Green's function is replaced by a noninteracting one, the spectral functions can be calculated analytically. Despite the simplicity of the approximation, the resulting spectra are in favorable agreement with the more accurate results obtained from the dynamic density-matrix renormalization group method. In particular, the analytically calculated band gap as a function of $U$ is in close agreement with the exact gap obtained from the Bethe ansatz. In addition, the formal general solution to the equation of motion of the Green's function is presented, and the difference between the traditional self-energy approach and the exchange-correlation potential formalism is also discussed and elaborated. A simplified Holstein Hamiltonian is considered to further illustrate the general form of the exchange-correlation potential.

We investigate quantum-inspired algorithms to compute physical observables of quantum many-body systems at finite energies. They are based on the quantum algorithms proposed by S. Lu, M. C. Bañuls, and J. I. Cirac [PRX Quantum 2, 020321 (2021)], who use the quantum simulation of the dynamics of such systems, as well as classical filtering and sampling techniques. Here, we replace the quantum simulation by standard classical methods based on matrix product states and operators. As a result, we can address significantly larger systems than those reachable by exact diagonalization or by other algorithms. We demonstrate the performance with spin chains up to 80 sites.