A precise characterization of the recently discovered crossover to hydrodynamic transport in electron liquids, and in particular of a conjectured exotic odd-parity transport regime, requires a full solution of the Fermi-liquid collision integral at all temperatures beyond state-of-the-art analytic leading-logarithmic approximations. We develop a general basis expansion of the linearized collision integral applicable at all temperatures, and employ this to determine the decay rates of Fermi surface perturbations in two-dimensional electron liquids. In particular, we provide exhaustive data on the decay rates for a new odd-parity regime, in which parity-even Fermi surface deformations decay rapidly but odd-parity modes are anomalously longlived. We find that this transport regime exists at fairly large temperatures $T\lesssim 0.1T_F$, putting this regime within the reach of current experiments.

We investigate the possibility of a many-body mobility edge in the generalized Aubry-André (GAA) model with interactions using the Shift-Invert Matrix Product States (SIMPS) algorithm [Phys. Rev. Lett. 118, 017201 (2017)]. The noninteracting GAA model is a one-dimensional quasiperiodic model with a self-duality-induced mobility edge. To search for a many-body mobility edge in the interacting case, we exploit the advantages of SIMPS that it targets many-body states in an energy-resolved fashion and does not require all many-body states to be localized for some to converge. Our analysis indicates that the targeted states in the presence of the single-particle mobility edge match neither “MBL-like” (where MBL denotes many-body localization) fully converged localized states nor the fully delocalized case in which SIMPS fails to converge. We benchmark the algorithm's output both for parameters that give fully converged, “MBL-like” localized states and for delocalized parameters where SIMPS fails to converge. In the intermediate cases, where the parameters produce a single-particle mobility edge, we find many-body states that develop entropy oscillations as a function of cut position at larger bond dimensions. These oscillations at larger bond dimensions, which are also found in the fully localized benchmark but not the fully delocalized benchmark, occur both at the band edge and center and may indicate convergence to a nonthermal state (either localized or critical).

The disorder-free localization that occurred in the study of relaxation dynamics in far-from-equilibrium quantum systems has been widely explored. Here we investigate the interplay between the dipole-dipole interaction (DDI) and disorder in the hard-core polar bosons in a one-dimensional lattice. We find that the localized dynamics will eventually thermalize in the clean gas but can be stabilized with the existence of a small disorder proportional to the inverse of DDI strength. From the effective dimer Hamiltonian, we show that the effective second-order hopping of quasiparticles between nearest-neighbor sites is suppressed by the disorder with strength similar to the effective hopping amplitude. The significant gap between the largest two eigenvalues of the entanglement spectrum indicates the dynamical confinement. We also find that the disorder related sample-to-sample fluctuation is suppressed by the DDI. Finally, we extend our research from the uncorrelated random disorder to the correlated quasiperiodic disorder and from the two-dimer model to the half-filling system, obtaining similar results.

We consider the properties of the random regular graph with node degree $d$ perturbed by chemical potentials ${\mu }_k$ for a number of short $k$-cycles. We analyze both numerically and analytically the phase diagram of the model in the $({\mu }_k,d)$ plane. The critical curve separating the homogeneous and clusterized phases is found and it is demonstrated that the clusterized phase itself generically is separated as the function of $d$ into the phase with ideal clusters and phase with coupled ones when the continuous spectrum gets formed. The eigenstate spatial structure of the model is investigated and it is found that there are localized scarlike states in the delocalized part of the spectrum, that are related to the topologically equivalent nodes in the graph. We also reconsider the localization of the states in the nonperturbative band formed by eigenvalue instantons and find the semi-Poisson level spacing distribution. The Anderson transition for the case of combined ($k$-cycle) structural and diagonal (Anderson) disorders is investigated. It is found that the critical diagonal disorder gets reduced sharply at the clusterization phase transition but does it unevenly in nonperturbative and mid-spectrum bands, due to the scars, present in the latter. The applications of our findings to $2\mathrm{d}$ quantum gravity are discussed.

The spin-fermion model was previously successful to describe the complex phase diagrams of colossal magnetoresistive manganites and iron-based superconductors. In recent years, two-dimensional magnets have rapidly risen up as a new attractive branch of quantum materials, which are theoretically described based on classical spin models in most studies. Alternatively, here the two-orbital spin-fermion model is established as a uniform scenario to describe the ferromagnetism in a two-dimensional honeycomb lattice. This model connects the magnetic interactions with the electronic structures. Then the continuous tuning of magnetism in these honeycomb lattices can be predicted, based on a general phase diagram. The electron/hole doping, from the empty $e_{\mathrm{g}}$ to half-filled $e_{\mathrm{g}}$ limit, is studied as a benchmark. Our Monte Carlo result finds that the ferromagnetic $T_{\mathrm{C}}$ reaches the maximum at the quarter-filled case. In other regions, the linear relationship between $T_{\mathrm{C}}$ and doping concentration provides a theoretical guideline for the experimental modulations of two-dimensional ferromagnetism tuned by ionic liquid or electrical gating.

The substitution of iron atoms by chromium in CoFeB films has been proposed to reduce the critical current density $J_c$ for current-driven magnetization switching in spin transfer torque devices by reducing its magnetization. Yet the effect of Cr on the magnetic damping has remained elusive. Ferromagnetic resonance (FMR) measurements up to 110 GHz and 5 T, as well as angle-dependent FMR measurements at 9.5 and 17 GHz, are used to discriminate between different mechanisms of FMR damping in ${\mathrm{Co}}_{40}{\mathrm{Fe}}_{40-x}{\mathrm{Cr}}_x{\mathrm{B}}_{20}$ thin films ($x=0$, 4, 8, and 18). A constant isotropic Gilbert parameter is used to phenomenologically describe the magnetization damping for each composition, increasing from 0.005 to 0.022 as the amount of Cr increases from 0% to 18%. Two thirds of this contribution appear to be accounted for by intrinsic spin-orbit damping, and the balance is mostly due to extrinsic two-magnon scattering. While the introduction of Cr increases the spin-orbit damping, it nevertheless reduces the corresponding magnetic relaxation rate. The amorphous films with a high scattering rate exhibit a so-called conductivitylike damping at room temperature, in agreement with the breathing Fermi surface model. The presence of Cr also seems to inhibit internal fluctuations of the magnetization, reducing the two-magnon damping. The reduction of $J_c$ due to lower magnetization is partly mitigated by the overall increase in magnetic damping.

A recent study has demonstrated that ${\mathrm{MoB}}_2$, transforming to the same structure as ${\mathrm{MgB}}_2$ ($P6/mmm$), superconducts at temperatures above 30 K near 100 GPa [C. Pei et al., Natl. Sci. Rev. 10, nwad034 (2023)], and Nb substitution in ${\mathrm{MoB}}_2$ stabilizes the $P6/mmm$ structure down to ambient pressure [A. C. Hire et al., Phys. Rev. B 106, 174515 (2022)]. The current work explores the high-pressure superconducting behavior of Nb-substituted ${\mathrm{MoB}}_2$ (${\mathrm{Nb}}_{0.25}{\mathrm{Mo}}_{0.75}{\mathrm{B}}_2$). High-pressure x-ray diffraction measurements show that the sample remains in the ambient pressure $P6/mmm$ structure to at least 160 GPa. Electrical resistivity measurements demonstrate that from an ambient pressure $T_{\mathrm{c}}$ of 8 K (confirmed by specific heat to be a bulk effect), the critical temperature is suppressed to 4 K at 50 GPa, before gradually rising to 5.5 K at 170 GPa. The critical temperature at high pressure is thus significantly lower than that found in ${\mathrm{MoB}}_2$ under pressure (30 K), revealing that Nb substitution results in a strong suppression of the superconducting critical temperature. Our calculations indeed find a reduced electron-phonon coupling in ${\mathrm{Nb}}_{0.25}{\mathrm{Mo}}_{0.75}{\mathrm{B}}_2$, but do not account fully for the observed suppression, which may also arise from inhomogeneity and enhanced spin fluctuations.

Two-dimensional (2D) model of a weak topological insulator with an $N$ stacked Su-Schrieffer-Heeger chain is studied. This study starts with a basic model with all the fundamental symmetries (chiral, time reversal, and particle hole) preserved. Different topological phases are introduced in this model by systematically breaking the system's symmetries. The symmetries are broken by introducing different bonds (hopping terms) in the system. First, the chiral symmetry is broken by introducing hopping within each sublattice or intrasublattice hopping, where the hopping strengths of the sublattices are equal in magnitudes but opposite in sign. Then, following Haldane, the time-reversal (TR) symmetry is broken by replacing the real intrasublattice hopping strengths with imaginary numbers without changing the magnitudes. We find that breaking chiral and TR symmetries are essential for the weak topological insulator to be a Chern insulator. These models exhibit nontrivial topology with the Chern number $C=\pm 1$. The preservation of the particle-hole (PH) symmetry in the system facilitates an analytical calculation of $C$, which agrees with the numerically observed topological phase transition in the system. An interesting class of topologically nontrivial systems with $C=0$ is also observed, where the nontriviality is identified by a quantized and fractional 2D Zak phase. Finally, the PH symmetry is broken in the system by introducing unequal amplitudes of intrasublattice hopping strengths, while the equal intrasublattice hopping strengths ensure the preservation of the inversion symmetry. We investigate the interplay of the PH and the inversion symmetries in the topological phase transition. A discussion on the possible experimental realizations of this model is also presented.

We introduce a model to study magnon scattering in skyrmion crystals, sandwiched between ferromagnets, which act as the source of magnons. Thanks to recent experimental advances, such a set-up can be realised in quantum Hall heterojunctions, and it is interesting as skyrmions are topological objects while the skyrmion crystals break internal and translational symmetries, thus allowing to study the interplay of topological and symmetry breaking physics. Starting from a basis of holomorphic theta functions, we construct an appropriate analytical ansatz for such a junction with finite spatially modulating topological charge density in the central region and vanishing in the leads. We then construct a suitably defined energy functional for the junction in terms of these spinors and derive the resulting equations of motion, which take the form of a Bogoliubov-de Gennes-like equation. Using a combination of analytical techniques, field theory, heuristic models, and fully microscopic recursive transfer-matrix numerics, we calculate the spectra and magnon transmission properties of the skyrmion crystal. We find that magnon transmission can be understood via a combination of low-energy Goldstone modes and effective emergent Landau levels at higher energies. The presence of the former manifests in discrete low-energy peaks in the transmission spectrum and we show how the these features reflect the nature of the Goldstone modes arising from symmetry breaking. In turn, the effective Landau levels, which reflect the topology of the skyrmion crystal, lead to band-like transmission features, from the structure of which further details of the excitation spectrum of the skyrmion crystal can be inferred. Such characteristic transmission features are not present in competing phases of either the quantum Hall phase diagram or in metallic magnets, and hence provide direct and unique signatures of skyrmion crystal phases and their properties. We discuss experimental considerations regarding the realisation of our model, which most directly apply to heterojunctions in monolayer graphene with the central region doped slightly away from unit filling and the two ends exactly at unit filling, a $\nu =1:1\pm \delta \nu :1$ junction. Such physics is also relevant to junctions formed by metallic magnets, which host skyrmion crystal phases, or partly in junctions with artificially realized and periodically modulated gauge fields.

Field-induced evolution of magnetic textures in a spatially confined geometry is investigated by transport and imaging techniques for a microfabricated thin plate of antiskyrmion-hosting ferromagnet ${\left(\mathrm{Fe},\mathrm{Ni},\mathrm{Pd}\right)}_3\mathrm{P}$. Magnetic textures and accompanying transport characteristics show history-dependent evolution under the magnetic fields. In the up-sweep of magnetic field for a metastable antiskyrmion state, the longitudinal and Hall resistivity monotonously develop without conspicuous anomalies, due to the gradual shrinkage of the topologically-protected antiskyrmions in size. On the other hand, a row of magnetic bubbles and/or a stripe domain sequentially emerges one by one in a discretized manner upon decreasing magnetic field from the field-polarized single domain state. This gives rise to contrasting behavior with the field-increasing process, namely anomalous jumps in Hall resistivity at the several field values that are dictated by the sample and magnetic texture sizes, over a broad temperature range. Micromagnetic simulations reproduce qualitative features of the down-sweep process well, and also indicate the importance of the inherent small uniaxial magnetic anisotropy. Our work demonstrates that such a microfabricated magnetic device with a comparable size of magnetic texture may enable an electrical readout of magnetic states.

We consider the design of metamaterials whose behavior embodies the equations of axion electrodynamics. We derive an effective medium description of an assembly of magneto-optical layers with out-of-plane magnetization analytically and show how to achieve effective axion response with tunable parameters. We display some key predictions and validate them numerically.

The recent discovery of unconventional surface-state pairs, which give rise to Fermi arcs and spin textures, in antiferromagnetically ordered NdBi raised the interest in rare-earth monopnictides. Several scenarios of antiferromagnetic (AFM) order have been suggested to explain the origin of these states with some of them being consistent with the presence of nontrivial topologies. In this paper, we use angle-resolved photoemission spectroscopy (ARPES) and density-functional-theory (DFT) calculations to investigate the electronic structure of NdSb. We found the presence of distinct domains that have different electronic structures at the surface. These domains correspond to different orientations of magnetic moments in the AFM state with respect to the surface. We demonstrated remarkable agreement between DFT calculations and ARPES that capture all essential changes in the band structure caused by the transition to a magnetically ordered state.

Two-dimensional topologically ordered states such as fractional quantum Hall fluids host anyonic excitations, which are relevant for realizing fault-tolerant topological quantum computers. Classification and characterization of topological orders have been intensely pursued in both the condensed matter and mathematics literature. These topological orders can be bosonic or fermionic depending on whether the system hosts fundamental fermionic excitations or not. In particular, emergent topological orders in usual solid state systems are fermionic topological orders because the electron is a fermion. Recently, bosonic topological orders have been extensively completely classified up to rank 6 using representation theory. Inspired by their method, we provide in this paper a systematic method to classify the fermionic topological orders by explicitly building their modular data, which encodes the self and mutual statistics between anyons. Our construction of the modular data relies on the fact that the modular data of a fermionic topological order forms a projective representation of the ${\mathrm{\Gamma }}_{\theta }$ subgroup of the modular group ${\mathrm{SL}}_2\left(\mathbb{Z}\right)$. We carry out the classification up to rank 10 and obtain both unitary and nonunitary modular data. This includes all previously known unitary modular data, and also two new classes of modular data of rank 10. We also determine the chiral central charges (mod $\frac{1}{2}$) via a novel method, which does not require the explicit computation of modular extensions.

The distinction between chiral, trivial helical, and topological helical edge modes can be effectively made using quantum noise measurements at finite temperatures. Quantum noise measurements consist of mainly two components: The first is thermal noise, whose provenance is thermal fluctuations, and the second is shot noise, whose origin is the quantum nature of charge particles. Studying these edge modes at finite temperatures is important as it more accurately reflects the conditions in real-world experiments. Additionally, we have verified that our results for finite-temperature quantum noise correlations are valid at finite frequencies too.

After projection to the lowest Landau level translational invariance and particle conservation combine into dipole symmetry. We show that the new symmetry forbids spontaneous U(1) symmetry breaking at zero temperature. In the case of the spatially inhomogeneous magnetic field, where the translational invariance is absent, we show that the dipole symmetry disappears and the constraint on the symmetry breaking is lifted. We pay special attention to the fate of the Girvin-Macdonald-Platzman algebra in the inhomogeneous magnetic field and show that a natural generalization of it is still present even though the dipole symmetry is not.

In the ferrimagnetic nodal-line semiconductor ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$, colossal magnetoresistance (CMR) arises below $T_{\mathrm{c}}=78$ K due to the interplay of magnetism and topological nodal-line electronic structures. Here, we present electrical and thermoelectric transport properties of ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$. Below $T_{\mathrm{c}}$, the Nernst signal is dominated by anomalous Nernst effect (ANE) in the high-field region above 3 T. The scaling ratio between the ANE and magnetization is comparable to that in conventional magnetic materials, suggesting minor contributions from the nodal-line structure. In the low-field region (0 $\sim 3$ T) where the CMR is most apparent, possible signatures of topological Nernst effect (TNE) are found, which are likely associated with the noncollinear magnetic structure.

Motivated by topological equivalence between an extended Haldane model and a chiral-$\pi$-flux model on a square lattice, we apply $\pi$-flux models to two-dimensional bipartite quasicrystals with rhombus tiles in order to investigate topological properties in aperiodic systems. Topologically trivial $\pi$-flux models in the Ammann-Beenker tiling lead to massively degenerate confined states whose energies and fractions differ from the zero-flux model. This is different from the $\pi$-flux models in the Penrose tiling, where confined states only appear at the center of the bands as is the case of a zero-flux model. Additionally, Dirac cones appear in a certain $\pi$-flux model of the Ammann-Beenker approximant, which remains even if the size of the approximant increases. Nontrivial topological states with nonzero Bott index are found when staggered tile-dependent hoppings are introduced in the $\pi$-flux models. This finding suggests a direction in realizing nontrivial topological states without a uniform magnetic field in aperiodic systems.

Twisting bilayer sheets of graphene have been proven to be an efficient way to manipulate the electronic Dirac-like properties, resulting in flat bands at magic angles. Inspired by the electronic model, we develop a continuum model for the lattice dynamics of twisted bilayer graphene and we show that a remarkable band flattening applies to almost all the high-frequency in-plane lattice vibration modes, including the valley Dirac phonon, valley optical phonon, and zone-center optical phonon bands. Utilizing an approximate approach, we estimate small but finite magic angles at which a vanishing phonon bandwidth is expected. In contrast to the electronic case, the existence of a restoring potential prohibits the emergence of a magic angle in a more accurate modeling. The predicted phonon band flattening is highly tunable by the twist angle and this strong dependence is directly accessible by spectroscopic tools.