We obtain a phase diagram of the spin-imbalanced Hubbard model on the Lieb lattice, which is known to feature a flat band in its single-particle spectrum. Using the BCS mean-field theory for multiband systems, we find a variety of superfluid phases with imbalance. In particular, we find four different types of FFLO phases, i.e., superfluid phases with periodic spatial modulation. They differ by the magnitude and direction of the center-of-mass momentum of Cooper pairs. We also see a large region of stable Sarma phase, where the density imbalance is associated with zero Cooper pair momentum. In the mechanism responsible for the formation of those phases, the crucial role is played by the flat band, wherein particles can readjust their density at zero energy cost. The multiorbital structure of the unit cell is found to stabilize the Sarma phase by allowing for a modulation of the order parameter within a unit cell. We also study the effect of finite temperature and a lattice with staggered hopping parameters on the behavior of these phases.

We employ a variational Monte Carlo approach to efficiently obtain the dynamical structure factor for the spin-$1/2J_1\text{−}{J}_2$ Heisenberg model on the square lattice. Upon increasing the frustrating ratio $J_2/J_1$, the ground state undergoes a continuous transition from a Néel antiferromagnet to a ${\mathbb{Z}}_2$ gapless spin liquid. We identify the characteristic spectral features in both phases and highlight the existence of a broad continuum of excitations in the proximity of the spin-liquid phase. The magnon branch, which dominates the spectrum of the unfrustrated Heisenberg model, gradually loses its spectral weight, thus releasing nearly deconfined spinons, whose signatures are visible even in the magnetically ordered state. Our results provide an important example on how magnons fractionalize into deconfined spinons across a quantum critical point.

We demonstrate how pump engineering drives the emergence of frustration-induced quasi-long-range order in a low-dimensional photonic cavity array. We consider a Lieb chain of nonlinear cavities as described by the Bose-Hubbard model and featuring a photonic flatband in the single-particle spectrum. Incoherent pumping of the Lieb lattice leads to a photonic density wave which manifests an algebraic decay of correlations with twice the period of the lattice unit cell. This work opens up other directions for the emergence of strongly correlated phases in quantum optical frustrated systems through pump design.

A phonon hydrodynamic equation has been recently derived from the kinetic theory of phonons for nanoscale heat transport at ordinary temperatures. The classical irreversible thermodynamics is no longer valid due to the failure of the local equilibrium hypothesis from temporal and spatial strong nonequilibrium effects. In the present paper, we investigate the thermodynamic consistency of the phonon hydrodynamic equation for heat transport based on the phonon kinetic theory. The macroscopic expressions of entropy density and entropy flux in the bulk region as well as interfacial entropy generation in the boundary region are derived from their mesoscopic definitions in terms of the nonequilibrium phonon distribution solution. The phonon hydrodynamic equation is demonstrated to be consistent with the second law in the frame of extended irreversible thermodynamics. This paper provides a solid mesoscopic theoretical foundation to the previous nonequilibrium thermodynamics of the phonon hydrodynamic model for heat transport in nanosystems on a macroscopic basis.

We report the role of exchange frustration on the magnetocaloric properties of ${\mathrm{GdCrTiO}}_5$. Due to the highly frustrated nature of magnetic interactions, in ${\mathrm{GdCrTiO}}_5$, the long-range antiferromagnetic ordering of ${\mathrm{Gd}}^{3+}$ moments occurs at a much lower temperature $T_N=0.9$ K and the magnetic cooling power enhances dramatically relative to that observed in several geometrically frustrated systems. Below 5 K, the isothermal magnetic entropy change ($-\mathrm{\Delta }{S}_{\mathrm{m}}$) is found to be 36 J ${\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ for a field change ($\mathrm{\Delta }H$) of 7 T. $-\mathrm{\Delta }{S}_{\mathrm{m}}$ shows saturationlike behavior with decreasing $T$ down to 2 K and is reversible in nature. The adiabatic temperature change $\mathrm{\Delta }{T}_{\mathrm{ad}}$ is 15.5 K for $\mathrm{\Delta }H=7$ T. These magnetocaloric parameters are significantly larger than that reported for several potential magnetic refrigerants, even for small and moderate field changes. The present result not only suggests that ${\mathrm{GdCrTiO}}_5$ could be considered as a potential magnetic refrigerant at cryogenic temperatures but also promotes further studies on the role of exchange frustration on the magnetocaloric effect. In contrast, only the role of geometrical frustration on the magnetocaloric effect has been previously reported theoretically and experimentally investigated on very few systems.

The low-temperature magnetic properties of polycrystalline ${\mathrm{Na}}_2{\mathrm{IrO}}_3$, a candidate material for the realization of a quantum spin-liquid state, were investigated by means of muon-spin relaxation and nuclear magnetic resonance methods under chemical and hydrostatic pressure. The Li-for-Na chemical substitution promotes an inhomogeneous magnetic order, whereas hydrostatic pressure (up to 3.9 GPa) results in an enhancement of the ordering temperature $T_{\mathrm{N}}$. In the first case, the inhomogeneous magnetic order suggests either short- or long-range correlations of broadly distributed $j=$½ ${\mathrm{Ir}}^{4+}$ magnetic moments, reflecting local disorder. The increase of $T_{\mathrm{N}}$ under applied pressure points at an increased strength of three-dimensional interactions arising from interlayer compression.

As emerging topological nodal-line semimetals, the family of $\text{ZrSi}X(X=\mathrm{S},\text{Se},\text{Te})$ has attracted broad interest in condensed matter physics due to its future applications in spintronics. Here, we apply scanning tunneling microscopy to study the structural symmetry and electronic topology of ZrSiSe. Bias selective topographies are detected and applied to quantify the lattice structure of the ZrSe bilayer. A quasiparticle interference analysis is used to probe the band structure of ZrSiSe. We observe the mergence of two concentric squares $\sim 300$ meV above the Fermi level, which shows a nodal-line state consistent with a first principle calculation. An extra surface-state Dirac point is determined $\sim 400$ meV below the Fermi level.

The electronic structures, charge, and spin dynamics of the cobalt pnictide compounds $A\mathrm{C}{\mathrm{o}}_2\mathrm{A}{\mathrm{s}}_2\left(A=\mathrm{Ba},\mathrm{Sr},\mathrm{Ca}\right)$ in the paramagnetic state are investigated by using density functional theory combined with dynamical mean-field theory. In contrast to their iron counterparts, these cobalt pnictide compounds have three-dimensional electronic structures and strong ferromagnetic low-energy spin excitations. The $\mathrm{Co}3d{e}_g$ orbitals dominate the electronic states around the Fermi level and have stronger electronic correlation strength than the $\mathrm{Co}3d{t}_{2g}$ orbitals. The overall electronic correlation strength is much weaker than that in the iron arsenides; however, the most strongly correlated $\mathrm{Co}3d{x}^2-y^2$ orbital, especially in ${\mathrm{CaCo}}_2{\mathrm{As}}_2$, has electronic correlation strength comparable to $\mathrm{Fe}3d{t}_{2g}$ orbitals in iron arsenides. $A\mathrm{C}{\mathrm{o}}_2\mathrm{A}{\mathrm{s}}_2\left(A=\mathrm{Ba},\mathrm{Sr},\mathrm{Ca}\right)$ shows similar electronic structures where a conduction band of primarily $\mathrm{Co}3d{x}^2-y^2$ orbital character is close to a Van Hove singularity around the Brillouin-zone corner, which promotes ferromagnetic low-energy spin excitations. Originated from its increased nearest-neighbor Co-Co distance and significantly reduced As height from the Co plane, the strong electronic correlation strength and close proximity to the Van Hove singularity of the $\mathrm{Co}3d{x}^2-y^2$ orbital in ${\mathrm{CaCo}}_2{\mathrm{As}}_2$ is responsible for its unique A-type antiferromagnetic order observed in experiments. In comparison, despite substantial ferromagnetic low-energy spin excitations, ${\mathrm{BaCo}}_2{\mathrm{As}}_2$ and ${\mathrm{SrCo}}_2{\mathrm{As}}_2$ remain paramagnetic down to very low temperature because the $\mathrm{Co}3d{x}^2-y^2$ orbital has weaker electronic correlation strength and is further away from the Van Hove singularity.

We study a class of anomalies associated with time-reversal and spatial-reflection symmetry in (2+1)-dimensional bosonic topological phases of matter. In these systems, the topological quantum numbers of the quasiparticles, such as the fusion rules and braiding statistics, possess a ${\mathbb{Z}}_2$ symmetry which can be associated with either time reversal (denoted ${\mathbb{Z}}_2^{\mathbf{T}})$ or spatial reflections. Under this symmetry, correlation functions of all Wilson loop operators in the low-energy topological quantum field theory (TQFT) are invariant. However, the theories that we study possess a severe anomaly associated with the failure to consistently localize the symmetry action to the quasiparticles, precluding even defining a consistent notion of symmetry fractionalization in such systems. We present simple sufficient conditions which determine when ${\mathbb{Z}}_2^{\mathbf{T}}$ symmetry localization anomalies exist in general. We present an infinite series of TQFTs with such anomalies, some examples of which include $\mathrm{USp}{\left(4\right)}_2$ Chern-Simons (CS) theory and $\mathrm{SO}{\left(4\right)}_4$ CS theory. The theories that we find with these ${\mathbb{Z}}_2^{\mathbf{T}}$ anomalies can all be obtained by gauging the unitary ${\mathbb{Z}}_2$ subgroup of a different TQFT with a ${\mathbb{Z}}_4^{\mathbf{T}}$ symmetry. We further show that the anomaly can be resolved in several distinct ways: (1) the true symmetry of the theory is ${\mathbb{Z}}_4^{\mathbf{T}}$, or (2) the theory can be considered to be a theory of fermions, with ${\mathbf{T}}^2={(-1)}^{N_f}$ corresponding to fermion parity. Finally, we demonstrate that theories with the ${\mathbb{Z}}_2^{\mathbf{T}}$ localization anomaly can be compatible with ${\mathbb{Z}}_2^{\mathbf{T}}$ if they are “pseudorealized” at the surface of a (3+1)D symmetry-enriched topological phase. The “pseudorealization” refers to the fact that the bulk (3+1)D system is described by a dynamical ${\mathbb{Z}}_2$ gauge theory and thus only a subset of the quasiparticles are truly confined to the surface.

The electric field of high-intensity ultrashort laser pulses substantially perturbs an electron subsystem of a crystal and affects its band structure. Laser-driven oscillations of electrons and holes are frequently referred to as a major mechanism of the perturbation in dielectrics and semiconductors. New physical effects arise when the band structure is modified by an ultrashort pulse of the oscillations driven by a few-cycle laser pulse. Assuming the laser-pulse envelope varies slowly compared to the carrier frequency, we derive analytical relations for the laser-modified band structure by utilizing the Keldysh cycle-averaged nonperturbative approach under the approximation of constant effective mass. Formation of indirect-gap transient bands, suppression of the nonlinear absorption on the leading edge of a laser pulse, and cycle-averaged photocurrent generation driven by the pulse envelope are predicted. Analytical scaling with six laser and material parameters is obtained. The reported results establish the limits of validity of the Keldysh photoionization model and advance understanding of the fundamental effects involved in high-intensity ultrafast laser-solid interactions.

We show direct evidence for the impact of Heusler/semiconductor interfaces atomic structure on the spin transport signals in semiconductor-based lateral spin-valve (LSV) devices. Based on atomic scale Z-contrast scanning transmission electron microscopy and energy dispersive x-ray spectroscopy we show that atomic order/disorder of ${\mathrm{Co}}_2{\mathrm{FeAl}}_{0.5}{\mathrm{Si}}_{0.5}$ (CFAS)/$n$-Ge LSV devices is critical for the spin injection in Ge. By conducting a postannealing of the LSV devices, we find 90% decrease in the spin signal while there is no difference in the electrical properties of the $\mathrm{CFAS}\text{/}n$-Ge contacts and in the spin diffusion length of the $n$-Ge layer. We show that the reduction in the spin signals after annealing is attributed to the presence of intermixing phases at the Heusler/semiconductor interface. First-principles calculations show how that intermixed interface region has drastically reduced spin polarization at the Fermi level, which is the main cause for the significant decrease of the spin signal in the annealed devices above $300{}^{\circ }\mathrm{C}$.

We study the time evolution of the reduced density matrix for the Ohmic spin boson model out of an uncorrelated but otherwise arbitrary initial state. We consider arbitrary bias $\epsilon$ and tunneling $\mathrm{\Delta }$ at zero temperature for a weak coupling $\alpha$ to the bosonic bath. Using the real-time renormalization group method, we present a consistent weak-coupling expansion one order beyond the Bloch-Redfield approximation within a renormalized perturbation theory with analytical results covering the whole crossover regime from small times $\mathrm{\Omega }t\ll 1$ to large times $\mathrm{\Omega }t\gg 1$, where $\mathrm{\Omega }=\sqrt{{\epsilon }^2+{\tilde{\mathrm{\Delta }}}^2}$ denotes the Rabi frequency in terms of the renormalized tunneling $\tilde{\mathrm{\Delta }}$. In addition, for exponentially small or large times, we perform a nonperturbative resummation of all logarithmic terms. We show that standard Born approximation schemes calculating the effective Liouvillian of the kinetic equation up to first order in $\alpha$ are not sufficient to account for various important corrections one order beyond the Bloch-Redfield solution. (1) The resummation of all secular terms $\sim {\left(\mathrm{\Gamma }t\right)}^n$ is necessary to obtain the correct exponential decay of all terms of the time evolution with decay rate $\mathrm{\Gamma }$ or $\mathrm{\Gamma }/2$, together with the correct pre-exponential functions. (2) The resummation of all logarithmic terms at high and low energies leads to a renormalized tunneling $\tilde{\mathrm{\Delta }}$ and to pre-exponential functions of logarithmic and power-law form. (3) The fact that two eigenvalues of $L\left(E\right)$ are close to each other by $O\left(\mathrm{\Gamma }\right)$ requires degenerate perturbation theory for times $\mathrm{\Gamma }t\sim O\left(1\right)$, where certain terms of the Liouvillian in $O\left({\alpha }^2\right)$ are needed to calculate the stationary state and the time evolution of the nonoscillating purely decaying modes up to $O\left(\alpha \right)$. In contrast to the zero-bias case, we find two further interesting results for the time dynamics of the oscillating modes. (4) The terms of the pre-exponential functions with a strong time dependence show a leading long-time tail $\sim \alpha /\left(\mathrm{\Omega }t\right)$, besides other subleading terms $\sim \alpha /{\left(\mathrm{\Omega }t\right)}^2$ well-known from the zero-bias case. (5) The terms of the pre-exponential functions with a weak (logarithmic) time dependence vary according to a power law ${\left(\frac{1}{\mathrm{\Omega }t}\right)}^{2\alpha \frac{{\epsilon }^2}{{\mathrm{\Omega }}^2}}$ for exponentially large times. The power-law exponent depends on the bias and has to be contrasted to the one at exponentially small times where it crosses over to the bias-independent result $2\alpha$. We discuss that the complexity to calculate one order beyond Bloch-Redfield approximation is rather generic and applies also to other models of dissipative quantum mechanics.

Monolayer transition metal dichalcogenides (TMDs) exhibit high nonlinear optical (NLO) susceptibilities. Experiments on ${\mathrm{MoS}}_2$ have indeed revealed very large second-order (${\chi }^{\left(2\right)}$) and third-order (${\chi }^{\left(3\right)}$) optical susceptibilities. However, third-harmonic generation results of other layered TMDs have not been reported. Furthermore, the reported ${\chi }^{\left(2\right)}$ and ${\chi }^{\left(3\right)}$ of ${\mathrm{MoS}}_2$ vary by several orders of magnitude, and a reliable quantitative comparison of optical nonlinearities across different TMDs has remained elusive. Here, we investigate second- and third-harmonic generation, and three-photon photoluminescence in TMDs. Specifically, we present an experimental study of ${\chi }^{\left(2\right)}$ and ${\chi }^{\left(3\right)}$ of four common TMD materials (${\mathrm{MoS}}_2$, ${\mathrm{MoSe}}_2$, ${\mathrm{WS}}_2$, and ${\mathrm{WSe}}_2$) by placing different TMD flakes in close proximity to each other on a common substrate, allowing their NLO properties to be accurately obtained from a single measurement. ${\chi }^{\left(2\right)}$ and ${\chi }^{\left(3\right)}$ of the four monolayer TMDs have been compared, indicating that they exhibit distinct NLO responses. We further present theoretical simulations of these susceptibilities in qualitative agreement with the measurements. Our comparative studies of the NLO responses of different two-dimensional layered materials allow us to select the best candidates for atomic-scale nonlinear photonic applications, such as frequency conversion and all-optical signal processing.

We study the interface exciton at lateral type II heterojunctions of monolayer transition metal dichalcogenides (TMDs), where the electron and hole prefer to stay at complementary sides of the junction. We find that the 1D interface exciton has giant binding energy in the same order as 2D excitons in pristine monolayer TMDs although the effective radius (electron-hole separation) of interface exciton is much larger than that of 2D excitons. The binding energy, exciton radius, and optical dipole strongly depends on the band offset at the junction. The intervalley coupling induced by the electron-hole Coulomb exchange interaction and the quantum confinement effect at interfaces of a closed triangular shape are also investigated. Small triangles realize 0D quantum dot confinement of excitons, and we find a transition from nondegenerate ground state to degenerate ones when the size of the triangle varies. Our findings may facilitate the implementation of the optoelectronic devices based on the lateral heterojunction structures in monolayer semiconductors.

We investigate the effects of randomly distributed atomic defects on the magnetic properties of graphene nanoribbons with zigzag edges using an extended mean-field Hubbard model. For a balanced defect distribution among the sublattices of the honeycomb lattice in the bulk region of the ribbon, the ground-state antiferromagnetism of the edge states remains unaffected. By analyzing the excitation spectrum, we show that while the antiferromagnetic ground state is susceptible to single spin-flip excitations from edge states to magnetic defect states at low defect concentrations, its overall stability is enhanced with respect to the ferromagnetic phase.

We examine the Hall conductivity of a macroscopic two-dimensional quantum system and show that the observed quantities can sometimes violate the fluctuation dissipation theorem (FDT), even in the linear response (LR) regime infinitesimally close to equilibrium. At low temperature and in strong magnetic field, which are experimentally accessible, the violation can be by an order of magnitude larger than the Hall conductivity itself. We further generalize the results and obtain a necessary condition for such large-scale violation to happen. This violation is a genuine quantum phenomenon that appears on a macroscopic scale when the time-reversal symmetry is broken (by, e.g., a magnetic field). Our results are not only bound to the development of the fundamental issues of nonequilibrium physics, but the idea is also meaningful for practical applications, since the FDT is widely used for the estimation of noises from the LRs. We give an alternative formula evaluating precisely the fluctuations from the LRs even in the quantum systems with large FDT violation.

Topological insulators have been predicted to exhibit a variety of interesting phenomena including a quantized magnetoelectric response and novel spintronics effects due to spin textures on their surfaces. However, experimental observation of these phenomena has proved difficult due to the finite bulk carrier density which may overwhelm the intrinsic topological responses that are expressed at the surface. Here, we demonstrate an ionic gel gating technique to tune the chemical potential of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ thin films while simultaneously performing THz spectroscopy. We can tune the carrier concentration by an order of magnitude and shift the Fermi energy $E_F$ to as low as $\simeq 10$ meV above the Dirac point. At high-bias voltages and magnetic fields, we observe a quantized Faraday angle consistent with the topological magnetoelectric effect that can be tuned by ionic gel gating through a number of plateau states.

We report on microwave-induced resistance oscillations (MIROs) in a tunable-density 30-nm-wide GaAs/AlGaAs quantum well. We find that the MIRO amplitude increases dramatically with carrier density. Our analysis shows that the anticipated increase in the effective microwave power and quantum lifetime with density is not sufficient to explain the observed growth of the amplitude. We further observe that the fundamental oscillation extrema move towards cyclotron resonance with increasing density, which also contradicts theoretical predictions. These findings reveal that the density dependence is not properly captured by existing theories, calling for further studies.

The topological phase transitions in static and periodically driven Kitaev chains are investigated by means of a renormalization group (RG) approach. These transitions, across which the numbers of static or Floquet Majorana edge modes change, are accompanied by divergences of the relevant Berry connections. These divergences at certain high-symmetry points in momentum space form the basis of the RG approach, through which topological phase boundaries are identified as a function of system parameters. We also introduce several aspects to characterize the quantum criticality of the topological phase transitions in both static and Floquet systems: a correlation function that measures the overlap of Majorana-Wannier functions, the decay length of the Majorana edge mode, and a scaling law relating the critical exponents. These indicate a common universal critical behavior for topological phase transitions, in both static and periodically driven chains. For the latter, the RG flows additionally display intriguing features related to gap closures at non-high-symmetry points due to momentarily frozen dynamics.