We develop a comprehensive theory for the effective dynamics of Bloch electrons based on symmetry. We begin with a scheme to systematically derive the irreducible representations (IRs) characterizing the Bloch eigenstates in a crystal. Starting from a tight-binding (TB) approach, we decompose the TB basis functions into localized symmetry-adapted atomic orbitals and crystal-periodic symmetry-adapted plane waves. Each of these two subproblems is independent of the details of a particular crystal structure and it is largely independent of the relevant aspects of the other subproblem, hence permitting for each subproblem an independent universal solution. Taking monolayer ${\mathrm{MoS}}_2$ and few-layer graphene as examples, we tabulate the symmetrized $p$ and $d$ orbitals as well as the symmetrized plane-wave spinors relevant for these crystal structures. The symmetry-adapted basis functions block-diagonalize the TB Hamiltonian such that each block yields eigenstates transforming according to one of the IRs of the group of the wave vector ${\mathcal{G}}_{\mathbf{k}}$. For many crystal structures, it is possible to define multiple distinct coordinate systems such that for wave vectors $\mathbf{k}$ at the border of the Brillouin zone the IRs characterizing the Bloch states depend on the coordinate system, i.e., these IRs of ${\mathcal{G}}_{\mathbf{k}}$ are not uniquely determined by the symmetry of a crystal structure. The different coordinate systems are related by a coordinate shift that results in a rearrangement of the IRs of ${\mathcal{G}}_{\mathbf{k}}$ characterizing the Bloch states. We illustrate this rearrangement with three coordinate systems for ${\mathrm{MoS}}_2$ and trilayer graphene. The freedom to choose different distinct coordinate systems can simplify the symmetry analysis of the Bloch states. Given the IRs of the Bloch states in one coordinate system, a rearrangement lemma yields immediately the IRs of the Bloch states in the other coordinate systems. The rearrangement of the IRs in different coordinate systems does not affect observable physics such as selection rules or the effective Hamiltonians for the dynamics of Bloch states in external fields. Using monolayer ${\mathrm{MoS}}_2$ as an example, we combine the symmetry analysis of its bulk Bloch states with the theory of invariants to construct a generic multiband Hamiltonian for electrons near the $\mathbf{K}$ point of the Brillouin zone. The Hamiltonian includes the effect of spin-orbit coupling, strain, and external electric and magnetic fields. Invariance of the Hamiltonian under time reversal yields additional constraints for the allowed terms in the Hamiltonian and it determines the phase (real or imaginary) of the prefactors.

We estimate the depairing current of superconducting nanowire single-photon detectors (SNSPDs) by studying the dependence of the nanowires' kinetic inductance on their bias current. The kinetic inductance is determined by measuring the resonance frequency of resonator-style nanowire coplanar waveguides both in transmission and reflection configurations. Bias current dependent shifts in the measured resonant frequency correspond to the change in the kinetic inductance, which can be compared with theoretical predictions. We demonstrate that the fast relaxation model described in the literature accurately matches our experimental data and provides a valuable tool for determination of the depairing current. Accurate measurement of the depairing current is critical for nanowire quality analysis, as well as modeling efforts aimed at understanding the detection mechanism in SNSPDs.

Scalar spin chirality is expected to induce a finite contribution to the Hall response at low temperatures. We study this spin-chirality-driven Hall effect, known as the topological Hall effect, at the manganite side of the interface between ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_x{\mathrm{MnO}}_3$ and ${\mathrm{SrIrO}}_3$. The ferromagnetic double-exchange hopping at the manganite layer, in conjunction with the Dzyaloshinskii-Moriya (DM) interaction which arises at the interface due to broken inversion symmetry and strong spin-orbit coupling from the iridate layer, could produce a skyrmion-crystal (SkX) phase in the presence of an external magnetic field. Using the Monte Carlo technique and a two-orbital spin-fermion model for manganites, supplemented by an in-plane DM interaction, we obtain phase diagrams which reveal at low temperatures a clear SkX phase and also a low-field spin-spiral phase. Increasing temperature, a skyrmion-gas phase, precursor of the SkX phase upon cooling, was identified. The topological Hall effect primarily appears in the SkX phase, as observed before in oxide heterostructures. We conclude that the manganite-iridate superlattices provide another useful platform to explore a plethora of unconventional magnetic and transport properties.

Nitride semiconductors are ubiquitous in optoelectronic devices such as LEDs and Blu-Ray optical disks. A major limitation for further adoption of GaN in power electronics is its low hole mobility. In order to address this challenge, here we investigate the phonon-limited mobility of wurtzite GaN using the ab initio Boltzmann transport formalism, including all electron-phonon scattering processes, spin-orbit coupling, and many-body quasiparticle band structures. We demonstrate that the mobility is dominated by acoustic deformation-potential scattering, and we predict that the hole mobility can significantly be increased by lifting the split-off hole states above the light and heavy holes. This can be achieved by reversing the sign of the crystal-field splitting via strain or via coherent excitation of the $A_1$ optical phonon through ultrafast infrared optical pulses.

We experimentally investigate spectral statistics in Anderson localization in two-dimensional amorphous disordered media. Intensity distributions captured over an ultrabroad wavelength range of $\sim 600$ nm and averaged over numerous configurations provided the Ioffe-Regel parameter to be $\sim 2.5$ over the investigated wavelength range. The spectra of the disordered structures provided access to several quasimodes, whose widths and separations allowed one to directly estimate the optical Thouless conductance $g_{Th}$, consistently observed to be below unity. The probability distribution of $g_{Th}$ was measured to be a log-normal. Despite being in the Anderson localization regime, the spacings of energy levels of the system were seen to follow a near Wigner-Dyson function. Theoretical calculations based on the tight-binding model, modified to include coupling to a bath, yielded results that were in excellent agreement with experiments. From the model, the level-spacing behavior was attributed to the degree of localization obtained in the optical disordered system.

Spatially inhomogeneous electronic states are expected to be key ingredients for the emergence of superconducting phases in quantum materials hosting charge-density waves (CDWs). Prototypical materials are transition-metal dichalcogenides (TMDCs) and among them, $1T\text{−}{\mathrm{TiSe}}_2$ exhibiting intertwined CDW and superconducting states under Cu intercalation, pressure, or electrical gating. Although it has been recently proposed that the emergence of superconductivity relates to CDW fluctuations and the development of spatial inhomogeneities in the CDW order, the fundamental mechanism underlying such a phase separation (PS) is still missing. Using angle-resolved photoemission spectroscopy and variable-temperature scanning tunneling microscopy, we report on the phase diagram of the CDW in $1T\text{−}{\mathrm{TiSe}}_2$ as a function of Ti self-doping, an overlooked degree of freedom inducing CDW texturing. We find an intrinsic tendency towards electronic PS in the vicinity of Fermi surface (FS) “hot spots,” i.e., locations with band crossings close to, but not at the Fermi level. We therefore demonstrate an intimate relationship between the FS topology and the emergence of spatially textured electronic phases which is expected to be generalizable to many doped CDW compounds.

We present the study of the structural changes of cobalt oxide ${\text{Co}}_3{\text{O}}_4$ under high pressure. At room temperature and atmospheric pressure, ${\text{Co}}_3{\text{O}}_4$ crystallizes in a cubic $Fd-3m$ structure. We found that within the pressure range 0–60 GPa the system undergoes three phase transitions, which take place at 23, 45, and 52 GPa. In the first one, the original cubic structure distorts to an $Fddd$ orthorhombic lattice. At 45 GPa, a first order phase transition induces a distortion to a monoclinic phase with $C2/m$ space group and a volume per formula unit reduction of 4%. This phase has not been reported in the literature previously. Finally, at 52 GPa the orthorhombic phase disappears and a phase transition towards the formation of $P{2}_1/c$ crystal structure is evidenced. This last phase coexists with the $C2/m$ phase up to 55 GPa. From the diffractograms measured at 57 GPa it was possible to solve the structure of the $P{2}_1/c$ phase. Results showed the layered character of the structure and a change in the ${\mathrm{Co}}^{+2}$ coordination number from 4 to 6.

Recently, there has been a great deal of interest in the possibility to exploit quantum-mechanical effects to increase the performance of energy storage systems. Here, we introduce and solve a model of a quantum supercapacitor. This consists of two chains, one containing electrons and the other one holes, hosted by arrays of double quantum dots, the latter being a building block of experimental architectures for realizing charge and spin qubits. The two chains are in close proximity and embedded in the same photonic cavity, which is responsible for long-range coupling between all the qubits, in the spirit of the Dicke model. By employing a variational approach, we find the phase diagram of the model, which displays ferromagnetic and antiferromagnetic phases for suitable pseudospin degrees of freedom, together with phases characterized by collective superradiant behavior. Importantly, we show that when transitioning from the ferromagnetic/antiferromagnetic to the superradiant phase, the quantum capacitance of the model is enhanced. Our work offers opportunities for the experimental realization of a novel class of quantum supercapacitors with an enhanced capacitance stemming from quantum-mechanical effects.

We show that the large orbital degeneracy inherent in moiré heterostructures naturally gives rise to a “high-$T_c$” like phase diagram with a chiral twist—wherein an exotic quantum anomalous Hall insulator phase is flanked by chiral $d+id$ superconducting domes. Specifically, we analyze repulsively interacting fermions on hexagonal (triangular or honeycomb) lattices near Van Hove filling, with an $\text{SU}\left(N_f\right)$ flavor degeneracy. This model is inspired by recent experiments on graphene moiré heterostructures. At this point, a nested Fermi surface and divergent density of states give rise to strong (${ln}^2$) instabilities to correlated phases, the competition between which can be controllably addressed through a combination of weak coupling parquet renormalization group and Landau-Ginzburg analysis. For $N_f=2$ (i.e., spin degeneracy only), it is known that chiral $d+id$ superconductivity is the unambiguously leading weak coupling instability. Here we show that $N_f\ge 4$ leads to a richer (but still unambiguous and fully controllable) behavior, wherein at weak coupling the leading instability is to a fully gapped and chiral Chern insulator, characterized by a spontaneous breaking of time-reversal symmetry and a quantized Hall response. Upon doping this phase gives way to a chiral $d+id$ superconductor. We further consider deforming this minimal model by introducing an orbital splitting of the Van Hove singularities, and discuss the resulting RG flow and phase diagram. Our analysis thus bridges the minimal model and the practical moiré band structures, thereby providing a transparent picture of how the correlated phases arise under various circumstances. Meanwhile, a similar analysis on the square lattice predicts a phase diagram where (for $N_f>2$) a nodal staggered flux phase with “loop current” order gives way upon doping to a nodal $d$-wave superconductor.

We report the theoretical discovery and characterization of higher-order Floquet topological phases dynamically generated in a periodically driven system with mirror symmetries. We demonstrate numerically and analytically that these phases support lower-dimensional Floquet bound states, such as corner Floquet bound states at the intersection of edges of a two-dimensional system, protected by the nonequilibrium higher-order topology induced by the periodic drive. We characterize higher-order Floquet topologies of the bulk Floquet Hamiltonian using mirror-graded Floquet topological invariants. This allows for the characterization of a new class of higher-order “anomalous” Floquet topological phase, where the corners of the open system host Floquet bound states with the same as well as with double the period of the drive. Moreover, we show that bulk vortex structures can be dynamically generated by a drive that is spatially inhomogeneous. We show these bulk vortices can host multiple Floquet bound states. This “stirring drive protocol” leverages a connection between higher-order topologies and previously studied fractionally charged, bulk topological defects. Our work establishes Floquet engineering of higher-order topological phases and bulk defects beyond equilibrium classification, and it offers a versatile tool for dynamical generation and control of topologically protected Floquet corner and bulk bound states.

We show that thermal radiation from a topological insulator carries a nonzero average spin angular momentum. This effect can offer an approach to the generation of elliptically polarized thermal emission without the need of complicated surface structuring of the source.

Phonons are a promising simulation platform for single particles trapped in quantum wells, interatomic molecular dynamics, and, in general, potentials. Earlier implementations to simulate coherent wave propagation in one-dimensional potentials using acoustic phonons with gigahertz-terahertz frequencies were based on coupled nanoacoustic resonators. Here we generalize the concept of adiabatic tuning of periodic superlattices for the implementation of effective one-dimensional potentials giving access to cases that cannot be realized by previously reported phonon engineering approaches, in particular the acoustic simulation of electrons and holes in a quantum well or a double-well potential. In addition, the resulting structures are much more compact and hence experimentally feasible. We demonstrate that potential landscapes can be tailored with great versatility in these multilayered devices, apply this general method to the cases of parabolic, Morse, and double-well potentials, and study the resulting stationary phonon modes. The phonon cavities and potentials presented in this work could be probed by all-optical techniques like pump-probe coherent phonon generation and Brillouin scattering.

Phonon heat conduction over length scales comparable to their mean free paths is a topic of considerable interest for basic science and thermal management technologies. However, debate exists over the appropriate constitutive law that defines thermal conductivity in the nondiffusive regime. Here, we derive a generalized Fourier's law that links the heat flux and temperature fields, valid from ballistic to diffusive regimes and for general geometries, using the Peierls-Boltzmann transport equation within the relaxation time approximation. This generalized Fourier's law predicts that thermal conductivity not only becomes nonlocal at length scales smaller than phonon mean free paths but also requires the inclusion of an inhomogeneous nonlocal source term that has been previously neglected. We provide evidence for the validity of this generalized Fourier's law through direct comparison with time-domain thermoreflectance measurements in the nondiffusive regime without adjustable parameters. Furthermore, we show that interpreting experimental data without the generalized Fourier's law can lead to inaccurate measurement of thermal transport properties.

Topological states of matter and two-dimensional (2D) magnetism are two fascinating topics attracting tremendous interest in current research. In this work, we explore their interplay in a single 2D material system by proposing a different topological quantum state of matter—the 2D Weyl half-semimetal (WHS), which features 2D Weyl points at the Fermi level belonging to a single spin channel, such that the low-energy electrons are described by fully spin polarized 2D Weyl fermions. We provide the condition to realize this state, which requires an in-plane magnetization and a preserved vertical mirror symmetry. Remarkably, we prove that the WHS state is a critical state sitting at the topological phase transition between two quantum anomalous Hall (QAH) insulator phases with opposite Chern numbers, such that a switching of the QAH states as well as the direction of chiral edge channels can be readily achieved by rotating the magnetization direction. Furthermore, we predict a concrete 2D material, monolayer ${\mathrm{PtCl}}_3$, as a candidate for realizing the 2D WHS state and the above intriguing effects. Our findings open up a new direction of research at the confluent point of topology and magnetism in two dimensions, and the revealed route towards switchable QAH phases will enable new designs of topological nanoelectronic devices.

In the vast majority of cases, superconducting transition takes place at exponentially low temperature $T_c$ out of the Fermi liquid regime. We discuss the problem of determining $T_c$ from known system properties at temperatures $T\gg T_c$, and stress that this cannot be done reliably by following the standard protocol of solving for the largest eigenvalue of the original gap-function equation. However, within the implicit renormalization approach, the gap-function equation can be used to formulate an alternative eigenvalue problem, where solving leads to an accurate prediction for both $T_c$ and the gap function immediately below $T_c$. With diagrammatic Monte Carlo techniques, this eigenvalue problem can be solved without invoking the matrix inversion or even explicitly calculating the four-point vertex function.

Proximity effects in two-dimensional (2D) van der Waals heterostructures offer controllable ways to tailor the electronic band structure of adjacent materials. Proximity exchange in particular is important for making materials magnetic without hosting magnetic ions. Such synthetic magnets could be used for studying magnetotransport in high-mobility 2D materials, or magneto-optics in highly absorptive nominally nonmagnetic semiconductors. Using first-principles calculations, we show that the proximity exchange in monolayer ${\mathrm{MoSe}}_2$ and ${\mathrm{WSe}}_2$ due to ferromagnetic monolayer ${\mathrm{CrI}}_3$ can be tuned (even qualitatively) by twisting and gating. Remarkably, the proximity exchange remains the same when using antiferromagnetic ${\mathrm{CrI}}_3$ bilayer, paving the way for optical and electrical detection of layered antiferromagnets. Interestingly, the proximity exchange is opposite to the exchange of the adjacent antiferromagnetic layer. Finally, we show that the proximity exchange is confined to the layer adjacent to ${\mathrm{CrI}}_3$, and that adding a separating hBN barrier drastically reduces the proximity effect. We complement our ab initio results with tight-binding modeling and solve the Bethe-Salpeter equation to provide experimentally verifiable optical signatures (in the exciton spectra) of the proximity exchange effects.

We report spin-polarized inelastic neutron scattering of the dynamical structure factor of the conical magnetic helix in the cubic chiral magnet MnSi. We find that the spectral weight of spin-flip scattering processes is concentrated on single branches for wave-vector transfer parallel to the helix axis as inferred from well-defined peaks in the neutron spectra. In contrast, for wave-vector transfers perpendicular to the helix the spectral weight is distributed among different branches of the magnon band structure as reflected in broader features of the spectra. Taking into account the effects of instrumental resolution, our experimental results are in excellent quantitative agreement with parameter-free theoretical predictions. Whereas the dispersion of the spin waves in MnSi appears to be approximately reciprocal at low energies and small applied fields, the associated spin-resolved spectral weight displays a pronounced nonreciprocity that implies a distinct nonreciprocal response in the limit of vanishing uniform magnetization at zero magnetic field.

We found that thermodynamic quantum time crystals in Fermi systems, defined as quantum orders oscillating periodically in the imaginary Matsubara time with zero mean, are metastable for two general classes of solutions. Mean-field time independent solutions proved to have lower free energy manifesting true thermodynamic equilibrium with either single or multiple (competing) charge, spin, and superconducting symmetry breaking orders. The “no-go” theorem is proven analytically for a case of long-range interactions between fermions in momentum space in electron-hole and Cooper channels.

Topology now plays a central role in physics, yet its applications have so far been restricted to closed, lossless systems in thermodynamic equilibrium. Given that many physical systems are open and may include gain and loss mechanisms, there is an eminent need to reexamine topology within the context of non-Hermitian theories that describe open, lossy systems. The generalization of the Chern number to non-Hermitian Hamiltonians initiated this reexamination; however, there is no established connection between a non-Hermitian topological invariant and the quantization of an observable. Using field-theoretical techniques, we show that no such relationship exists between the non-Hermitian Chern number and the Hall conductivity, a consequence of the discontinuous nature of Green's functions of non-Hermitian Hamiltonians. Furthermore, we derive an exact formula for the Chern-Simons Hall response of a generic two-level non-Hermitian Hamiltonian and present an illustrative calculation for a non-Hermitian massive Dirac Hamiltonian in $\left(2+1\right)$ dimensions. We conclude by clarifying how these results extend to higher-dimensional systems and detailing their implications for recent experiments.

The discovery of topological insulators has reformed modern materials science, promising to be a platform for tabletop relativistic physics, electronic transport without scattering, and stable quantum computation. Topological invariants are used to label distinct types of topological insulators. But, it is not generally known how many or which invariants can exist in any given crystalline material. Using a new and efficient counting algorithm, we study the topological invariants that arise in time-reversal symmetric crystals. This results in a unified picture that explains the relations between all known topological invariants in these systems. It also predicts new topological phases and one entirely new topological invariant. We present explicitly the classification of all two-dimensional crystalline fermionic materials, and give a straightforward procedure for finding the analogous result in any three-dimensional structure. Our study represents a single, intuitive physical picture applicable to all topological invariants in real materials, with crystal symmetries.