${\mathrm{NbSe}}_2$ is one of metallic two-dimensional (2D) transition-metal dichalcogenide (TMDC) materials. Because of broken crystal inversion symmetry, large spin splitting is induced by Ising-type spin-orbit coupling in odd-number-layered ${\mathrm{NbSe}}_2$, but absent for even-number-layered ${\mathrm{NbSe}}_2$ with the inversion symmetry. In this paper we numerically calculate nonlinear optical charge and spin Hall conductivities of few-layered ${\mathrm{NbSe}}_2$ based on an effective tight-binding model which includes $d_{z^2}$, $d_{x^2-y^2}$, and $d_{xy}$ orbitals of Nb atoms. We show that the nonlinear optical Hall conductivity for the second harmonic generation (SHG) process has a nonvanishing value in odd-number-layered ${\mathrm{NbSe}}_2$. Also, we provide a nonlinear optical selection rule in few-layered ${\mathrm{NbSe}}_2$ and their polarization dependencies. Furthermore, for the even-number-layered case, the nonlinear optical Hall currents can be generated by applying electric fields which break inversion symmetry. We also discuss that the nonlinear optical Hall effect is expected to occur in TMDC materials in general. Thus, our results will serve to design potential opt-spintronics devices based on 2D materials to generate the spin Hall current by SHG.

Quantum geometry is a key quantity that distinguishes electrons in a crystal from those in the vacuum. Its study continues to provide insights into quantum materials, uncovering new design principles for their discovery. However, unlike the Berry curvature, an intuitive understanding of the quantum metric is lacking. Here, we show that the quantum metric of Bloch electrons leads to a momentum-space gravity. In particular, by extending the semiclassical formulation of electron dynamics to second order, we find that the resulting velocity is modified by a geodesic term and becomes the momentum-space dual of the Lorentz force in curved space. We calculate this geodesic response for magic-angle twisted bilayer graphene and show that moiré systems with flat bands are ideal candidates to observe this effect. Extending this analogy with gravity further, we find that the momentum-space dual of the Einstein field equations remains sourceless for pure states, while for mixed states it acquires a source term that depends on the von Neumann entropy for small entropies. We compare this stress-energy equation with the weak-field limit of general relativity, and we conclude that the von Neumann entropy is the momentum-space dual of the gravitational potential. Consequently, the momentum-space geodesic equation for mixed states is modified by a term resembling an entropic force. Our results highlight connections between quantum geometry, momentum-space gravity, and quantum information, prompting further exploration of this dual gravity in quantum materials.

We study the DC current generation in a periodically driven Bloch system connected to a heat bath. Under a relaxation time approximation, the density matrix for such a system is obtained, which is related to two equilibria: a Floquet quasiequilibrium where the density matrix is diagonal under the Floquet-Bloch eigenbasis and an instantaneous Bloch thermal equilibrium. Then, the current responses and their power features, i.e., the power input behavior, are discussed in a unified manner, which reveals that there exist an intrinsic current and an extrinsic correction. Remarkably, the intrinsic part consumes no energy and corresponds to the Floquet quasiequilibrium, while the extrinsic part needs a sustained energy input and originates from a shift between two equilibrium ensembles. We further investigate the role of the external driving field strength finding that large DC currents can be generated under a relatively strong but not too strong driving field.

The bulk photovoltaic effect (BPVE) converts light into a coherent dc current at zero bias, through what is commonly known as the shift current. This current has previously been attributed to the displacement of the electronic wave function center in real space, when the sample is excited by light. We reveal that materials like twisted bilayer graphene (TBG) with a flatband dispersion are uniquely suited to maximize the BPVE because they lead to an enhanced shift in the momentum space, unlike any previously known shift current mechanism. We identify properties of quantum geometry, which go beyond the quantum geometric tensor, and are unrelated to Berry charges, as the physical origin of the large BPVE we observe in TBG. Our calculations show that TBG with a band gap of several meV exhibits a giant BPVE in a range of 0.2–1 THz, which represents the strongest BPVE reported so far at this frequency in a two-dimensional material and partially persists even a room temperature. Our paper provides a design principle for shift current generation, which applies to a broad range of twisted heterostructures with the potential to overcome the so-called “terahertz gap” in THz sensing.

Recently, there has been a renewed interest in properties of the higher-spin Kitaev models, especially their low-dimensional analogs with additional interactions. These quasi-one-dimensional systems exhibit rich phase diagrams with symmetry-protected topological phases, Luttinger liquids, hidden order, and higher-rank magnetism. However, the nature of the pure spin-$S$ Kitaev chains is not yet fully understood. Earlier works found a unique ground state with short-ranged correlations for $S=1$ and an intriguing double-peak structure in the heat capacity associated with an entropy plateau. To understand the low-energy excitations and thermodynamics for general $S$, we study the anisotropic spin-$S$ Kitaev chain. Starting from the dimerized limit, we derive an effective low-energy Hamiltonian at finite anisotropy. For half-integer spins we find a trivial effective model, reflecting a nonlocal symmetry protecting the degeneracy, while for integer $S$ we find interactions among the flux degrees of freedom that select a unique ground state. The effective model for integer spins is used to predict the low-energy excitations and thermodynamics, and we make a comparison with the semiclassical limit through linear spin wave theory. Finally, we speculate on the nature of the isotropic limit.

In this work, we study the real-time evolution of periodically driven (Floquet) systems on a quantum computer using IBM quantum devices. We consider a driven Landau-Zener model and compute the transition probability between the Floquet steady states as a function of time. We find that for this simple one-qubit model, Floquet states can develop in real time, as indicated by the transition probability between Floquet states. Next, we model light-driven spin chains and compute the time-dependent antiferromagnetic order parameter. We consider models arising from light coupling to the underlying electrons as well as those arising from light coupling to phonons. For the two-spin chains, the quantum devices yield time evolutions that match the effective Floquet Hamiltonian evolution for both models once readout error mitigation is included. For three-spin chains, zero-noise extrapolation yields a time dependence that follows the effective Floquet time evolution. Therefore, the current IBM quantum devices can provide information on the dynamics of small Floquet systems arising from light drives once error mitigation procedures are implemented.

Low-temperature (down to $\sim 50$ mK) thermal conductivity measurements with the heat flow direction along the interplane tetragonal $c$ axis, ${\kappa }_c$, were used to study the superconducting state of heavy fermion ${\mathrm{CeIrIn}}_5$. Measurements were performed in the magnetic fields both parallel to the heat flow direction $H\parallel c$, and transverse to it $H\parallel a$. Interplane heat conductivity in $H\parallel c$ configuration shows negligible initial increase with magnetic field and a rapid rise on approaching $H_{c2}$ from below, similar to the expectations for the superconducting gap without line nodes. This observation is in stark contrast to monotonic increase found in the previous in-plane heat transport measurements. In the configuration with the magnetic field breaking the tetragonal symmetry of the lattice $H\parallel a$, ${\kappa }_c$ reveals nonmonotonic evolution with temperature and magnetic field suggesting subphase boundary in the superconducting state. The characteristic temperature $T_{\mathrm{kink}}\sim$ 0.07 K of the subboundary is well within the domain of bulk superconductivity $T_c\sim$ 0.4 K and $H_{c2}\sim$ 1.0 T. These results are consistent with a superconducting gap with an equatorial line node and polar point nodes, a gap symmetry of the ${\mathrm{D}}_{4h}$ point group, for which magnetic field along the tetragonal plane breaks the degeneracy of the multicomponent order parameter and induces a phase transition with nodal topology change.

For an assembly of particles interacting with a two-dimensional periodic substrate, a series of commensuration effects can arise when the number of particles is an integer multiple of the number of substrate minima. Such commensuration effects can appear for vortices in type-II superconductors with periodic pinning or for colloidal particles on optical landscapes. Under bulk external driving, the pinning or drag on the particles is strongly enhanced at commensuration. Here we consider the active rheology of a single particle driven through an assembly of particles coupled to a periodic substrate at different commensurate conditions. For increasing density at fixed driving force, we observe nonmonotonic drag along with what we call an anticommensuration effect where the drag or pinning effectiveness is reduced in commensurate states, opposite from the behavior typically observed under bulk driving. The velocity enhancement or drag reduction appears when the background particles form a crystalline state that is coupled more strongly to the substrate than to the driven particle, while under incommensurate conditions, the background particles are disordered and produce enhanced drag on the probe particle. The velocity noise of the driven particle has a narrow band signature at commensuration and a broad band signature away from commensuration. We map out the regions in which viscous flow, periodic flow, and a pinned phase appear. We show that the effects we observe are robust on both square and triangular substrate arrays and for both vortices in type-II superconductors and colloidal particles on optical landscapes.

Orbital-selective superconductivity is crucial for understanding the pairing mechanism for multiband superconductors. Atomic $d$ orbitals with anisotropic spatial extension can directly determine the energy dispersion of subbands with two-dimensional (2D) or three-dimensional (3D) nature in band structure. Theoretically, owing to the coexistence of these 2D and 3D subbands, the orbital-selective superconductivity can exhibit band-dependent dimensionality in multiband superconductors. However, to experimentally confirm this orbital-selective 2D superconductivity remains challenging and elusive. Herein, based on angle-dependent upper critical magnetic field on $2\mathrm{H}\text{−}{\mathrm{NbS}}_2$ flakes, we observe a cusp peak associated with a 2D superconducting subband from the $d_{xy}$ and $d_{x^2-y^2}$ orbitals of Nb atoms, and a round peak related to a 3D subband, directly confirming the existence of intrinsic 2D superconductivity in $2\mathrm{H}\text{−}{\mathrm{NbS}}_2$ thick flake and its orbital-selective superconducting nature. The 2D superconductivity remains robust under large electric current or high pressure. Such observations shed light on the orbital-selective pairing mechanism and resulting band-dependent dimensionality for multiband superconductors.

In this paper, we study the spin Nernst effect of magnons in the nonlinear response regime. We derive the formula for the nonlinear magnon spin Nernst current by solving the Boltzmann equation and find out that it is described by an extended Berry curvature dipole of magnons. The nonlinear magnon spin Nernst effect is expected to occur in various Néel antiferromagnetic materials even without the Dzyaloshinskii-Moriya interaction. In particular, the nonlinear spin Nernst current in the honeycomb and diamond lattice antiferromagnets can be controlled by strain/pressure.

We reveal unconventional edge states in a one-dimensional Stub lattice of coupled waveguides with staggered hoppings. The edge states appear for the same values of hoppings as topological edge states in the Su-Schrieffer-Heeger model. They have different energies depending on the lattice termination and present a remarkable robustness against certain types of disorder. We evidence experimentally the phase transition at which these edge states appear, opening the door to the engineering of one-dimensional lattices with localized edge modes whose energy and location can be controlled at will.

Band bending at semiconductor surfaces and interfaces is the key to applications ranging from classical transistors to topological quantum computing. A semiconductor particularly important for optical as well as microwave devices is GaN. What makes the material useful is not only its large bandgap but also that it can be heavily doped to become metallic. Here, we apply soft-x-ray angle-resolved photoelectron spectroscopy (ARPES) to metallic Si-doped GaN to explore the electron density and momentum-resolved band dispersions of the valence and conduction electrons varying through the surface band-bending region. We find an upward band bending, where the measured band occupation reduces toward the surface, as probed with low photon energies $<0.5\mathrm{keV}$. The band occupation approaches the bulk value, matching Hall effect measurements, as the photon energy increases to $>1.4\mathrm{keV}$, where the photoelectron mean free path exceeds the spatial extent of the band-bending region. Our quantitative analysis of the experimental data describes the potential variation in the band-bending region via self-consistent Poisson-Schrödinger equations. We put forward an insightful model to simulate the ARPES spectra from this region through summing up the contribution from all atomic layers, weighted by the photoelectron mean free path, under in-phase conditions achieved at particular values of the photoelectron out-of-plane momentum. The model adequately describes the peculiarities of the ARPES spectra caused by the surface band bending, including the photon-energy dependence of the apparent band occupation and Fermi-surface area, and allows accurate determination of the band-bending profile and values of the photoelectron mean free path. Finally, comparison of our data with supercell density functional theory calculations reveals the preferential location of Si atoms as substitutional for Ga, with the doped electrons entering the GaN conduction bands without formation of separate impurity states as would occur for Si interstitials. Our theoretical and experimental results resolve fundamental questions underpinning device performance of the GaN-based and other semiconductor materials in general and demonstrate a general methodology for quantitative studies of electron states in the band-bending region.

We propose a versatile setup that allows performing spin-resolved spectroscopy of helical Andreev bound states, proving their existence and therefore the topological nature of the Josephson junction that hosts them. The latter is realized on the helical edge of a 2D topological insulator, proximitized with two superconducting electrodes. The spectroscopic analysis is enabled by a quantum point contact, which couples the junction with another helical edge acting as a spin-sensitive probe. By means of straightforward transport measurements, it is possible to detect the particular spin structure of the helical Andreev bound state and to shine light on the mechanism responsible for their existence, i.e., the presence of protected Andreev reflection within the Josephson junction. We discuss the robustness of this helical Andreev spectrometer with respect to processes that weaken spin to charge conversion.

We demonstrate that parametric driving of suitable collective modes in cuprate superconductors results in a reflectivity $R>1$ for frequencies in the low terahertz regime. We propose to exploit this effect for the amplification of coherent terahertz radiation in a laserlike fashion. As an example, we consider the optical driving of Josephson plasma oscillations in a monolayer cuprate at a frequency that is blue-detuned from the Higgs frequency. Analogously, terahertz radiation can be amplified in a bilayer cuprate by driving a phonon resonance at a frequency slightly higher than the upper Josephson plasma frequency. We show this by simulating a driven-dissipative $U\left(1\right)$ lattice gauge theory on a three-dimensional lattice, encoding a bilayer structure in the model parameters. We find a parametric amplification of terahertz radiation at zero and nonzero temperature.

Topological interface states (TISs) in multivalley systems are studied to unravel their valley sensitivity. For this purpose, multivalley IV–VI topological crystalline insulator (TCI) heterostructures are explored using magnetooptical Landau level spectroscopy up to 34 teslas. We characterize the TISs emerging from the distinct $L$ valleys in ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Se}$ multiquantum wells grown along the [111] direction. It is shown that the shape of the two-dimensional (2D) Fermi surfaces of TISs residing at the TCI-trivial insulator interfaces are strongly affected by the valley anisotropy of topologically trivial ${\mathrm{Pb}}_{1-y}{\mathrm{Eu}}_y\mathrm{Se}$ barriers. This phenomenon is shown to be due to the deep penetration of the TISs into the barriers. For the valleys tilted with respect to the confinement direction, a significant interaction between topological states and the conventional massive quantum well states is observed, evidenced by the resulting large anticrossings between Landau levels. These are theoretically well described by a $\mathbf{k}·\mathbf{p}$ model that considers tilt and anisotropy of the valleys in 2D. Therefore, in this paper, we provide a precise characterization of the TIS valley splitting as well as an accurate determination of the anisotropy of their Dirac cone dispersion.

Junctions composed of excitonic condensate (EC) bilayers exhibit intriguing physics due to the presence of interlayer tunneling. Together with the excitonic superflow, this tunneling induces a special kind of topological object which is analogous to the Josephson vortices in extended superconducting Josephson junction. We name such objects the “tunneling vortices.” In this work we propose to characterize the topological properties of these vortices in the current-injecting scheme under which multiple vortices can easily be introduced through current injection from one end of the EC junctions. We find theoretically that current responses demonstrate the quantized nature of vortices: the ejected currents show periodicity as a function of injected currents(or vortex numbers). Moreover, the injected-ejected current difference shows plateaus corresponding to different vortex numbers when varying tunneling strength ${\mathrm{\Delta }}_t$ or superfluid density ${\rho }_S$. Since all parameters are experimentally accessible, we expect real-world demonstrations of these enthralling quantization behaviors to come in the near future.