The nature of states in the quantum Hall regime of graphene in higher Landau levels remains poorly understood partly because of the lack of a model that captures its valley-dependent symmetry breaking interactions. In this paper we develop systematically such a model, which interestingly, and in contrast to the $N=0$ Landau level, features not only pure $\delta$ function interactions, but also some of its derivatives. We show that this model can lead to qualitatively new ground states relative to the $N=0$ Landau level, such as ground states with entangled spin and valley degrees of freedom that compete with simpler broken symmetry states. Moreover, at half-filling we have found a new phase that is absent in the $N=0$ Landau level which combines characteristics of a valence-bond solid and an antiferromagnet. We discuss the estimation of parameters of this model based on recent compressibility experiments.

The organic system $\kappa \text{−}{\left[{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_{1-x}{\left(\mathrm{BEDT}\text{−}\mathrm{STF}\right)}_x\right]}_2{\mathrm{Cu}}_2{\left(\mathrm{CN}\right)}_3$, showing a Mott transition between a nonmagnetic Mott insulating (NMI) state and a Fermi liquid (FL), is systematically studied using calorimetric measurements. An increase in the electronic heat capacity at the transition from the NMI state to the FL state which keeps the triangular dimer lattice demonstrates that the charge sector lost in the Mott insulating state is recovered in the FL state. We observed that the remaining low-energy spin excitations in the Mott insulating state show a unique temperature dependence and that the NMI state has a larger lattice entropy originating from the frustrated lattice, which leads to a Pomeranchuk-like effect on the electron localization. Near the Mott boundary, an unexpected enhancement and magnetic field dependence of the heat capacity are observed. This anomalous heat capacity is different from the behavior in a typical first-order Mott transition and shows similarities with quantum critical behavior. To reconcile our results with previously reported scenarios about a spin gap and the first-order Mott transition, further studies are desired.

Motivated by recent experiments, we theoretically analyze the flow past an obstacle of a one-dimensional “quantum fluid of light,” which is resonantly driven, and exhibits bistability. The flow is found to abruptly change several times when the fluid velocity or the obstacle potential strength is increased. These transitions display unusual features. In contrast to the cases of usual fluids and superfluids, the transitions take place between stationary states. They involve the fluid bistability in an essential way. Remarkably, at the transitions points, the fluid in the obstacle wake lies in the unstable intermediate density state.

The Kitaev model, characterized by bond-dependent Ising spin interactions among spin-orbit entangled dipole moments in Mott insulators, offered a new approach to quantum spin liquids. Motivated by another type of bond-dependent interaction among quadrupole moments in $5d^2$ Mott insulators, we provide a microscopic route to uncover the Kitaev multipolar liquid, featuring fractionalized excitations out of non-Kramers doublets carrying multipole moments. The key ingredient is the magnetic field that allows for bond-anisotropic quadrupole-octupole interactions via mixing with the excited triplet states. The conditions to realize signatures of this phase in real materials are also discussed.

A previous multitemperature model (MTM) resolving phonon temperatures at the polarization level and measurements have uncovered remarkable nonequilibrium among different phonon polarizations in laser-irradiated graphene and metals. Here, we develop a semiconductor-specific MTM (SC-MTM) by including electron-hole pair generation, diffusion, and recombination, and show that a phonon polarization-level model does not yield observable polarization-based nonequilibrium in laser-irradiated molybdenum disulfide (${\mathrm{MoS}}_2$). In contrast, appreciable nonequilibrium is predicted between zone-center optical phonons and the other modes. The momentum-based nonequilibrium ratio is found to increase with decreasing laser spot size and interaction with a substrate. This finding is relevant to the understanding of the energy relaxation process in two-dimensional optoelectronic devices and Raman measurements of thermal transport.

Periodicity is usually assumed to be the necessary and sufficient condition for the formation of band gaps, i.e., energy bands with a suppressed density of states. Here, we check this premise by analyzing the band gap properties of three structures that differ in the degree of periodicity and ordering. We consider a photonic crystal, disordered lattice, and ordered but nonperiodic quasicrystalline structure. A real-space metric allows us to compare the degree of periodicity of these different structures. Using this metric, we reveal that the disordered lattice and the ordered quasicrystal can be attributed to the same group of material structures. We examine the density of their photonic states both theoretically and experimentally. The analysis reveals that despite their dramatically different degrees of periodicity, the photonic crystal and the quasicrystalline structure demonstrate an almost similar suppression of the density of states. Our results give new insight into the physical mechanisms resulting in the formation of band gaps.

A large polaron is a quasiparticle that consists of a nearly free electron interacting with the phonons of a material, whose lattice parameters are much smaller than the polaron scale. The electron-phonon interaction also leads to an attractive interaction between electrons, which can allow two polarons to pair up and form a bipolaron. It has been shown that large bipolarons can form in theory due to strong one-electron–one-phonon coupling, but they have not been seen in real materials because the critical value of the required electron-phonon interaction is too large. Here, we investigate the effect of one-electron–two-phonon coupling on the large bipolaron problem. Starting from a generalization of the Fröhlich Hamiltonian that includes both the standard one-electron–one-phonon interaction as well as an anharmonic one-electron–two-phonon interaction, we use the path-integral method to find a semianalytical upper bound for the bipolaron energy that is valid at all values of the Fröhlich coupling strength $\alpha$. We find the bipolaron phase diagram and conditions for the bipolaron stability by comparing the bipolaron energy to the energy of two free polarons. The critical value of the Fröhlich coupling strength ${\alpha }_{\text{crit}}$ is calculated as a function of the strength of the one-electron–two-phonon interaction. The results suggest that large bipolaron formation is more likely in materials with significant one-electron–two-phonon interaction as well as strong one-electron–one-phonon interaction, such as strontium titanate.

Mechanical response of metals is strongly dependent on the strain rate and exhibits drastic change as the strain rate varies across >10 orders of magnitude from quasistatic to shock loading. In this paper, we developed a unified crystal plasticity model for face-centered cubic (fcc) metals to describe the mechanical response in a wide range of strain rate from ${10}^{-5}$ to ${10}^7/\mathrm{s}$. The plasticity framework adopts the dislocation-based Orowan equation. Specifically, the mobility law for dislocation velocity incorporates both the thermal activation mechanism dominating at low strain rates and drag mechanism dominating at high strain rates, through a repeating waiting-running model. The rate dependence of total dislocation density (${\rho }_t$) evolution in the Orowan equation (implicitly) is captured by coupling the rate-dependent annihilation and the stress-dependent nucleation. More importantly, to capture the huge variation in mobile/total dislocation ratio ($f={\rho }_m/{\rho }_t$) at different strain rates, we propose a physics-based law for mobile dislocation fraction $f$ based on the exponential distribution of dislocation link lengths through a critical link length determined by the local stress. In addition, a thermohyperelastic model is supplemented to account for the nonlinear elastic behavior and thermoelastic coupling at shock loading. This unified model is validated against the mechanical response of single-crystal aluminum from quasistatic $\left(10{}^{-}5/\mathrm{s}\right)$ to shock loading (${10}^7/\mathrm{s}$), where the features of thermal softening in static loading, thermal hardening in shock loading, and the strain-rate hardening in the medium strain-rate range are all quantitatively evaluated by a single set of parameters with a high average $R^2$ value of 0.93.

We investigate the pressure-temperature phase diagram of elemental potassium (K) up to multiterapascal (TPa) pressures using ab initio random structure searching (AIRSS), discovering eight structural phase transitions beyond the already known double hexagonal close-packed (dhcp) structure. Starting at 1.15 TPa, K transitions from the dhcp structure and passes through a variety of close-packed hexagonal and trigonal phases (dhcp $\to P{6}_3/mmc\to P3m1\to P\overline{6}m2)$, which differ only in their stacking sequence along the $c$ axis. At 2.55 TPa, K adopts the hexagonal close-packed (hcp) structure, and at 7.21 TPa transitions into a complex orthorhombic phase of $Fddd$ symmetry with 64 atoms in its (conventional) unit cell, before assuming an $Ibam$ structure at 8.60 TPa, and, eventually, the face centered cubic (fcc) structure at 23.6 TPa, which persists well into the petapascal (PPa) regime. Further, we calculate the full pressure-temperature dependence of the melting line of K through extensive molecular dynamics simulations. We study the evolution of the bonding topology of K with pressure, finding that K passes through two quasi-molecular phases featuring diatomic pairs (the $Fddd$ and $Ibam$ structures), before ultimately becoming a high pressure electride (HPE) in the fcc phase. The electron-phonon and superconducting properties of K at these extreme pressures are also investigated, where we find the critical temperature $T_c$ rises to a maximum of between 7.65 K and 15.70 K in the hcp phase, before eventually decreasing to essentially zero in the fcc phase. Our results fully elucidate the structural and electronic behavior of K under the most extreme conditions, and provide new case studies for multi-TPa dynamic compression experiments.

The critical exponents of continuous phase transitions of a Hermitian system depend on and only on its dimensionality and symmetries. This is the celebrated notion of the universality of continuous phase transitions. Here we numerically study the Anderson localization transitions in non-Hermitian two-dimensional (2D) systems with exceptional points by using the finite-size scaling analysis of the participation ratios. At the exceptional points of either second order or fourth order, two non-Hermitian systems with different symmetries have the same critical exponent $\nu \simeq 2$ of correlation lengths, which differs from all known 2D disordered Hermitian and non-Hermitian systems. These feature is reminiscent of the superuniversality notion of Anderson localization transitions. In the symmetry-preserved and symmetry-broken phases, the non-Hermitian models with time-reversal symmetry and without spin-rotational symmetry, and without both time-reversal and spin-rotational symmetries, are in the same universality class of 2D Hermitian electron systems of Gaussian symplectic and unitary ensembles, where $\nu \simeq 2.7$ and $\nu \simeq 2.3$, respectively. The universality of the transition is further confirmed by showing that the critical exponent $\nu$ does not depend on the form of disorders and boundary conditions.

Layered BiSe in the trigonal $P\overline{3}m1$ phase is a weak topological insulator and a candidate topological crystalline insulator. Here using structural, spectroscopic, resistance measurements at high pressure and density functional theory calculations, we report that BiSe exhibits a rich phase diagram with the emergence of superconductivity above 7 GPa. Structural transitions into SnSe-type energetically tangled orthorhombic structures and, subsequently, into a CsCl-type cubic structure having distinct superconducting properties are identified at 8 and 13 GPa, respectively. Superconductivity is preserved as the system transforms back to the trigonal phase upon release of pressure. Spin-orbit coupling plays a significant role in enhancement of $T_c$ in the trigonal and cubic phases. In the orthorhombic $Cmcm$ phase, $T_c$ decreases monotonically with increasing pressure, whereas unusual pressure-independent $T_c$ is observed in the cubic $Pm\overline{3}m$ phase. Theoretical analysis reveals topological surface states in the cubic phase. The emergence of superconductivity within the topological phases makes BiSe a candidate topological superconductor.

Topological photonics has recently emerged as a very general framework for the design of unidirectional edge waveguides immune to backscattering and deformations, as well as other platforms that feature extreme nonreciprocal wave phenomena. While the topological classification of time-invariant crystals has been widely discussed in the literature, the study of spacetime crystals formed by time-variant materials remains largely unexplored. Here, we extend the methods of topological band theory to photonic crystals formed by “inclusions” that are subject to a spacetime rotating-wave modulation that imitates a physical rotating motion. By resorting to an approximate nonhomogeneous effective description of the electromagnetic response of the inclusions, it is shown that they possess a bianisotropic response that breaks the time-reversal symmetry and may give rise to nontrivial topologies. In particular, we propose an implementation of the Haldane model in a spacetime modulated photonic crystal.

Over the past few decades, magnetic frustration has been under intense debate due to its unusual properties. For instance, frustration in the kagome lattice suppresses long-range spin correlations, and it is expected to be a candidate for a spin liquid system. Therefore, with the advent of experiments with ultracold atoms, the interest in frustrated geometries has increased. Given this, in the present work we investigate the repulsive Hubbard model on the kagome lattice using unbiased quantum Monte Carlo simulations. We examine its thermodynamic properties, as well as the magnetic and transport response of the system at finite temperatures and different values of the repulsive interaction. From these results, we discuss the possible occurrence of adiabatic cooling, a quite important feature in ultracold systems, and the presence of a metal-to-insulator transition at a finite interaction strength. Our findings may guide future experiments in ultracold fermionic atoms on the kagome lattice.

The Chamon model is an exactly solvable spin Hamiltonian exhibiting nontrivial fracton order. In this paper, we dissect two distinct aspects of the model. First, we show that it exhibits an emergent fractonic gauge theory coupled to a fermionic subsystem symmetry-protected topological state under four stacks of ${\mathbb{Z}}_2$ planar symmetries. Second, we show that the Chamon model hosts 4-foliated fracton order by describing an entanglement renormalization group transformation that exfoliates four separate stacks of 2D toric codes from the bulk system.

We study the topological properties of a Haldane model on a band deformed dice lattice, which has three atoms per unit cell (call them A, B, and C) and the spectrum comprises of three bands, including a flat band. The bands are systematically deformed with the aim to study the evolution of topology and transport properties. The deformations are induced through hopping anisotropies and are achieved in two distinct ways. In one of them, the hopping amplitudes between the sites of B and C sublattices and those between A and B sublattices are varied along a particular direction, and in the other, the hopping between the sites of A and B sublattices are varied (keeping B-C hopping unaltered) along the same direction. The first case retains some of the spectral features of the familiar dice lattice and yields Chern insulating lobes in the phase diagram with $C=\pm 2$ till a certain critical deformation. The topological features are supported by the presence of a pair of chiral edge modes at each edge of a ribbon and the plateaus observed in the anomalous Hall conductivity support the above scenario. Whereas, a selective tuning of only the A-B hopping amplitudes distorts the flat band and has important ramifications on the topological properties of the system. The insulating lobes in the phase diagram have distinct features compared to the case above, and there are dips observed in the Hall conductivity near the zero bias. The dip widens as the hopping anisotropy is made larger, and thus the scenario registers significant deviation from the familiar plateau structure observed in the anomalous Hall conductivity. However, a phase transition from a topological to a trivial insulating region demonstrated by the Chern number changing discontinuously from $\pm 2$ to zero beyond a certain critical hopping anisotropy remains a common feature in the two cases.

A phase of solid state matter which exists in time dimension is investigated theoretically for a linear chain of quantum dots or atomic sites using the evolution operator technique and the Laplace transform technique.. The studies focus on the spectral density of states (DOS) function and its modifications after a sudden quench in the system. It is shown that this function reveals a very regular structure which oscillates in time and which corresponds to the stationary DOS of one-dimensional crystals. Thus, such a system stands for a transient crystal material which exists in time dimension but appears only for a short period and suddenly vanishes. Moreover, we observe different impulse propagation velocities due to the local DOS inertia, i.e., it is more difficult to rebuild a many-peaked structure of DOS related to longer chains. We also show that the transient crystal pattern in a linear chain can be observed for real electrodes characterized by the van Hove singularities or by a flat spectral density.

Topology is a central notion in the classification of band insulators and the characterization of entangled many-body quantum states. In some cases, it manifests as quantized observables such as quantum Hall conductance. However, being inherently a global property depending on the entirety of the system, its direct measurement has remained elusive to local experimental probes in many cases. Here, we demonstrate that various topological band indices can be directly probed by resonant inelastic x-ray scattering. Specifically, we show that the crystalline symmetry eigenvalues at the high-symmetry momentum points, which determine the band topology, lead to distinct scattering intensity for particular momentum and energy. Our approach can be explicitly demonstrated in several examples such as 1D Su-Schrieffer-Heeger chain, 2D quadrupole insulator, 3D topological band insulator, and chiral hinge insulator. Our result establishes an incisive bulk probe for the measurement of band topology.

It is known that a two-dimensional spin system can acquire a topological Hopf term by coupling to massless Dirac fermions whose energy spectrum has a single cone. But it is challenging to realize the Hopf term in condensed matter physics due to the fermion-doubling in the low-energy spectrum. In this work we propose a scenario to realize the Hopf term in lattice models. The central aim is tuning the coupling between the spins and the Dirac fermions such that the topological terms contributed by the two cones do not cancel each other. To this end, we consider $p_x$ and $p_y$ orbitals for the Dirac fermions on the honeycomb lattice such that there are totally four bands. By utilizing the orbital degrees of freedom, a $\theta =2\pi$ Hopf term is successfully generated for the spin system after integrating out the Dirac fermions. If the fermions have a small gap $m_0$ or if the spin-orbit coupling is considered, then $\theta$ is no longer quantized, but it may flow to multiple of $2\pi$ under renormalization. The ground state and the physical response of a spin system having the Hopf term are discussed.

Properties of bulk and boundaries of materials can, in general, be quite different, both for topological and nontopological reasons. One of the simplest boundary problems to pose is the tight-binding problem of noninteracting electrons on a finite honeycomb lattice. Despite its simplicity, the problem is quite rich and directly related to the physics of graphene. We revisit this long-studied problem and present an analytical derivation of the electron spectrum and wave functions for graphene rectangular derivatives. We provide an exact analytical description of extended and localized states, the transition between them, and a special case of a localized state when the wave function is nonzero only at the edge sites. The latter state has zero energy, and we discuss its existence in zigzag nanoribbons, zigzag nanotubes with a number of sites along a zigzag edge divisible by 4, and rectangular graphene nanoflakes with an odd number of sites along both zigzag and armchair edges.

We investigate the diffusion process of negatively charged excitons (trions) in a $\mathrm{W}{\mathrm{Se}}_2$ transition-metal dichalcogenide monolayer. We measure the time-resolved photoluminescence spatial profiles of these excitonic complexes. They exhibit nonlinear diffusion corresponding to an effective negative diffusion behavior. Specifically, we examine the dynamics of the two negatively charged bright excitons (intervalley and intravalley trions) and of the dark trion. The time evolution allows us to identify the interplay of the different excitonic species: the trionic species appear after the neutral excitonic one. This is consistent with a bimolecular formation mechanism. Based on our experimental observations, we propose a phenomenological model suggesting the coexistence of two populations: a first one exhibiting a fast and efficient diffusion mechanism and a second one with a slower dynamics and a less efficient diffusion process. These two contributions could be, respectively, attributed to hot and cold trion populations.