Applying the method of [Nucl. Phys. B 972, 115565 (2021)], which bosonizes massless relativistic free fermions, we derive the (non-Abelian) bosonized theory for free fermion topological insulators and superconductors that have, in addition to the U(1) charge, time reversal and charge conjugation symmetries and flavor symmetries. For the case we consider, the flavor symmetries render the topological classification $\mathbb{Z}$. The results are nonlinear $\sigma$ models with the topological $\theta$ term. In addition, we present the theory of a class of bosonic symmetry-protected topological states, whose boundaries are critical spin liquids.

Dirac semimetals show nontrivial physical properties and can host exotic quantum states like Weyl semimetals and topological insulators under suitable external conditions. Here, by combining angle-resolved photoemission spectroscopy measurements (ARPES) and first-principle calculations, we demonstrate that the Zintl-phase compound ${\mathrm{SmMg}}_2{\mathrm{Bi}}_2$ is in close proximity to a topological Dirac semimetallic state. ARPES results show a Dirac-like band crossing at the zone center near the Fermi level ($E_{\mathrm{F}}$), which is further confirmed by first-principle calculations. Theoretical studies also reveal that ${\mathrm{SmMg}}_2{\mathrm{Bi}}_2$ belongs to a $Z_2$ topological class and hosts spin-polarized states around the $E_{\mathrm{F}}$. Zintl's theory predicts that the valence state of Sm in this material should be ${\mathrm{Sm}}^{2+}$, however, we detect many Sm-$4f$ multiplet states (flat-bands) whose energy positions and relative intensities suggest the presence of both dominant ${\mathrm{Sm}}^{2+}$ and minor ${\mathrm{Sm}}^{3+}$. The small concentration (2.5%) of ${\mathrm{Sm}}^{3+}$ in the bulk of a crystal is inferred to arise from Sm vacancies in the crystal. It is also evident that these flat bands and other dispersive states are strongly hybridized when they cross each other. Due to the presence of ${\mathrm{Sm}}^{3+}$ ions, the temperature dependence of the magnetic susceptibility $\chi \left(T\right)$ shows a Curie-Weiss-like contribution in the low-temperature region, in addition to the Van Vleck-like behavior expected for the ${\mathrm{Sm}}^{2+}$ ions. The present study will help to better understand the electronic structure, magnetism, and transport properties of related materials.

Variational Monte Carlo is a many-body numerical method that scales well with system size. It has been extended to study the Green function only recently by Charlebois and Imada [Phys. Rev. X 10, 041023 (2020)]. Here we generalize the approach to systems with open boundary conditions in the absence of translational invariance. Removing these constraints permits the application of embedding techniques like cluster perturbation theory (CPT). Using this approach we provide robust evidence of the existence of Fermi arcs in the one-band Hubbard model, an enduring problem in the physics of the pseudogap in cuprate high-temperature superconductors. We study the behavior of the Fermi surface and of the density of states as a function of hole doping for clusters of up to 64 sites, well beyond the reach of modern exact diagonalization solvers. We observe that the technique reliably captures the transition from a Mott insulator at half filling to a pseudogap, evidenced by the formation of Fermi arcs, and finally to a metallic state at large doping. The ability to treat large clusters with quantum cluster methods helps to minimize potential finite-size effects and enables the study of systems with long-range orders, which will help extend the reach of these already powerful methods and provide important insights on the nature of various strongly correlated many-electron systems, including the high-${\mathrm{T}}_c$ cuprate superconductors.

We derive the universal real-time $\text{U}\left(1\right)$ topological gauge field action for mixed Dirac states of fermions, described by a density matrix weighted by a gapped Dirac operator, in all dimensions. The key prerequisites are charge quantization and charge conservation; in fact, charge quantization is the root of the action's topological properties. The gauge action encodes nonquantized linear responses as expected for mixed states, but also quantized nonlinear responses, which are accessible in experiment. Our construction furthermore demonstrates how the physical pictures of anomaly inflow and bulk-boundary correspondence extend to nonequilibrium systems. Finally, we demonstrate the independence of the gauge action of the underlying equilibrium or nonequilibrium nature of dynamics stabilizing the state.

We propose a method to enhance the spatial coupling between ballistic exciton-polariton condensates in a semiconductor microcavity based on available spatial light modulator technologies. Our method, verified by numerically solving a generalized Gross-Pitaevskii model, exploits the strong nonequilibrium nature of exciton-polariton condensation driven by localized nonresonant optical excitation. Tailoring the excitation beam profile from a Gaussian into a polygonal shape results in refracted and focused radial streams of outflowing polaritons from the excited condensate which can be directed towards nearest neighbors. Our method can be used to lower the threshold power needed to achieve polariton condensation and increase spatial coherence in extended systems, paving the way towards creating extremely large-scale quantum fluids of light.

A quantum anomalous Hall state with a high Chern number has so far been realized in multilayer structures consisting of alternating magnetic and undoped topological insulator (TI) layers. However, in previous proposals, the Chern number can only be tuned by varying the doping concentration or the width of the magnetic TI layers. This drawback largely restricts the applications of dissipationless chiral edge currents in electronics since the number of conducting channels remains fixed. In this paper, we propose a way of varying the Chern number at will in these multilayered structures by means of an external electric field applied along the stacking direction. In the presence of an electric field in the stacking direction, the inverted bands of the unbiased structure coalesce and hybridize, generating new inverted bands and collapsing the previously inverted ones. In this way, the number of Chern states can be tuned externally in the sample, without the need for modifying the number and width of the layers or the doping level. We showed that this effect can be uncovered by the variation of the transverse conductance as a function of the electric field at constant injection energy at the Fermi level.

The spin-1/2 kagome Heisenberg antiferromagnet is generally accepted as one of the most promising two-dimensional models to realize a quantum spin liquid state. Previous experimental efforts were almost exclusively on only one archetypal material, the herbertsmithite ${\mathrm{ZnCu}}_3{\left(\mathrm{OH}\right)}_6{\mathrm{Cl}}_2$, which unfortunately suffers from the notorious orphan spin problem caused by magnetic disorders. Here, we turn to ${\mathrm{YCu}}_3{\left(\mathrm{OH}\right)}_{6.5}{\mathrm{Br}}_{2.5}$, recently recognized as another host of a globally undistorted kagome ${\mathrm{Cu}}^{2+}$ lattice free from orphan spins, and thus a more feasible system for studying the intrinsic kagome quantum spin liquid physics. Our high-resolution low-temperature thermal conductivity measurements yield a vanishingly small residual linear term of $\kappa /T$ ($T\to 0$), and thus clearly rule out itinerant gapless fermionic excitations. An unusual scattering of phonons grows exponentially with temperature, suggesting thermally activated phonon-spin scattering and hence a gapped magnetic excitation, consistent with a ${\mathbb{Z}}_2$ quantum spin liquid ground state. Additionally, an analysis of the magnetic field impact on the thermal conductivity reveals a field closing of the spin gap, while the excitations remain localized.

We investigate a Josephson junction in an electron-hole superfluid in a double-layer transition metal dichalcogenide heterostructure. The observation of a critical tunneling current is a clear signature of superfluidity. In addition, we find the BCS-BEC crossover physics in the narrow barrier region controls the critical current across the entire system. The corresponding critical velocity, which is measurable in this system, has a maximum when the excitations pass from bosonic to fermionic. Remarkably, this occurs for the density at the boundary of the BEC to BCS-BEC crossover regime determined from the condensate fraction. This provides, in a semiconductor system, an experimental way to determine the position of this boundary.

Kagome metals possess peculiar optical spectra consisting of contributions from free charge carriers in a Drude-type response, localized carriers seen as a strongly temperature-dependent localization peak, and, in some cases, phonons displaying strong anomalies. The rare-earth kagome metal series, $R{\mathrm{Mn}}_6{\mathrm{Sn}}_6$, provides a marvelous playground to study the electronic properties of kagome metals in the presence of variable magnetic order. Here, we report temperature-dependent reflectivity studies on two members of the $R{\mathrm{Mn}}_6{\mathrm{Sn}}_6$ family, ${\mathrm{GdMn}}_6{\mathrm{Sn}}_6$ (in-plane ferrimagnet) and ${\mathrm{TbMn}}_6{\mathrm{Sn}}_6$ (out-of-plane ferrimagnet), in a broad energy range (50–18 000 ${\mathrm{cm}}^{-1}$, equivalent to 6.2 meV–2.23 eV) down to 10 K. At high temperatures, a phonon mode at approximately 160 ${\mathrm{cm}}^{-1}$ is observed, which becomes screened out in ${\mathrm{TbMn}}_6{\mathrm{Sn}}_6$ below $\sim$150 K as the localization peak linearly passes through the mode. In ${\mathrm{GdMn}}_6{\mathrm{Sn}}_6$, the disappearance of the phonon is accompanied by the onset of saturation of the peak position, suggesting an unusual interplay between the two features.

Uncorrelated disorder in generalized three-dimensional Lieb models gives rise to the existence of bounded mobility edges, destroys the macroscopic degeneracy of the flat bands, and breaks their compactly localized states. We now introduce a mix of order and disorder such that this degeneracy remains and the compactly localized states are preserved. We obtain the energy-disorder phase diagrams and identify mobility edges. Intriguingly, for large disorder the survival of the compactly localized states induces the existence of delocalized eigenstates close to the original flat-band energies—yielding seemingly divergent mobility edges. For small disorder, however, a change from extended to localized behavior can be found upon decreasing disorder—leading to an unconventional “inverse Anderson” behavior. We show that transfer-matrix methods, computing the localization lengths, and sparse-matrix diagonalization, using spectral gap-ratio energy-level statistics, are in excellent quantitative agreement. The preservation of the compactly localized states even in the presence of this disorder might be useful for envisaged storage applications.

We report a generalized auxiliary coherent medium theory to settle the longstanding challenge of Anderson-type off-diagonal disorder (AODD) for simulating disordered alloys. The AODD is transformed into a diagonal-like disorder with a weighted discrete distribution in an auxiliary medium. This approach is demonstrated for simulating the phonon spectral in NiFe and NiPt alloys, and it is found that accounting for AODD substantially enhances the phonon linewidth to agree well with the supercell and experimental results, compared to results with averaged-value ODD. This paper provides an effective approach to treat the large fluctuation in ODD in disordered materials, presenting an important progress for mean-field simulations in the embedding framework.

We report a detailed study of the structural, magnetic, thermodynamic, and electronic properties of a coupled $J_{\mathrm{eff}}$ = $\frac{1}{2}$ alternating chain ${\mathrm{Sr}}_2\mathrm{Co}{\left({\mathrm{SeO}}_3\right)}_3$ compound using magnetic susceptibility $\chi \left(T\right)$, magnetic specific heat $C_{\mathrm{m}}\left(T\right)$, magnetization, and neutron diffraction measurements along with first-principles calculations. The first-principles calculations based on the density functional theory suggest that ${\mathrm{Sr}}_2\mathrm{Co}{\left({\mathrm{SeO}}_3\right)}_3$ forms a quasi-one-dimensional chain with bond alternation and interchain interactions. $\chi \left(T\right), C_{\mathrm{m}}\left(T\right),$ and neutron powder diffraction measurements confirm that no long-range magnetic ordering occurs down to 100 mK. Instead, a maximum in $\chi \left(T\right)$ and $C_{\mathrm{m}}\left(T\right)$ and an exponential drop of $\chi \left(T\right)$ and $C_p\left(T\right)$ as $T\to 0$ K point to a spin-singlet ground state. The analysis of $\chi \left(T\right)$ and $C_{\mathrm{m}}\left(T\right)$ based on a $J_1\text{−}{J}_2$ alternating Heisenberg model shows the bond alternation $\alpha =J_2/J_1\approx 0.7$ and a spin gap of $\mathrm{\Delta }\approx 3$ K. Our work demonstrates that ${\mathrm{Sr}}_2\mathrm{Co}{\left({\mathrm{SeO}}_3\right)}_3$ is a coupled alternating chain system based on spin-orbit entangled $J_{\mathrm{eff}}$ = $\frac{1}{2}$.

Although heavy metal materials, due to their large spin-orbit interaction, would be expected to act as an efficient converter of spin current to charge current, Bismuth does not obey this rule. Heterostructures of yttrium iron garnet (YIG)/Bi are investigated by means of the spin pumping technique and the results show that Bi exhibits negligible spin-charge conversion. In addition to not converting spin to charge, Bi exhibits an exotic spin relaxation mechanism, which is driven by its large diamagnetic response. By considering a nonlinear stochastic model of diffusing spin particles, the results show that the Bi layer acts as a binary classifier device that categorizes the pumped spins into relaxed spins and those that flow upwards and eventually reach the top layer of Pt. This shows that the investigation reported here opens different perspectives involving fundamental aspects in the fields of machine learning and condensed matter physics.

We present Hartree-Fock calculations on a simple model to obtain the conditions of formation of local magnetic moments due to loop currents $L_o$ and spin-loop currents $L_s$ and compare them to the conditions of formation of local spin moments $M$ which were given long ago in a similar approximation by Anderson. A model with three degenerate orbitals sitting on an equilateral triangle, with on-site and nearest-neighbor repulsions $U$ and $V$, respectively, and intersite kinetic energy, hybridizing with conduction electrons with a parameter $\mathrm{\Delta }$ is investigated. $L_o$ and $L_s$ are promoted by large $V/\mathrm{\Delta }$ and their magnitude is relatively unaffected by $U/\mathrm{\Delta }$. Spin-magnetic moments $M$ promoted by large $U/\mathrm{\Delta }$ on the other hand are adversely affected by $V/\mathrm{\Delta }$. In this model, $L_o$ for $V$ multiplied by the number of neighbors is approximately the same as the $M$ promoted by $U$ in Anderson's local model for $M$. $L_o$ and $L_s$ are degenerate if exchange interactions and Hund's rule are neglected but $L_o$ is favored when they are included. Many of the qualitative results are visible in an expression for the Hartree-Fock ground state energy derived as a function of small $L_o, L_s$, and $M$. Numerical minimization of the Hartree-Fock energy is presented for larger values. We also briefly discuss the connection and differences of the interaction-generated orbital currents and spin currents discussed here and generalized to a lattice with the topological states in metals and semiconductors.

The energy levels of a quasicontinuous spectrum in mesoscopic systems fluctuate in positions and the distribution of the fluctuations reveals information about the microscopic nature of the structure under consideration. Here, we investigate mesoscopic fluctuations of a secondary gap that appears in the quasiclassical spectrum of a chaotic cavity coupled to one or more superconductors. Utilizing a random matrix model, we compute numerically the energies of Andreev levels and access the distribution of the gap widths. We mostly concentrate on the universal regime $E_{\mathrm{Th}}\gg \mathrm{\Delta }$, with $E_{\mathrm{Th}}$ being the Thouless energy of the cavity and $\mathrm{\Delta }$ being the superconducting gap. We find that the distribution is determined by an intermediate energy scale ${\mathrm{\Delta }}_g$ with the value between the level spacing in the cavity ${\delta }_s$ and the quasiclassical value of the gap $E_g$. From our numerics we extrapolate the first two cumulants of the gap distribution in the limit of large level and channel number. We find that the scaled distribution in this regime is the Tracy-Widom distribution: the same as found by Vavilov et al. [Phys. Rev. Lett. 86, 874 (2001)] for the distribution of the minigap edge in the opposite limit $E_{\mathrm{Th}}\ll \mathrm{\Delta }$. This leads us to the conclusion that the distribution found is a universal property of chaotic proximity systems at the edge of a continuous spectrum in agreement with the known random matrix models featuring a square root singularity in the density of states.

We report on high-order harmonic generation in the two-band superconductor ${\mathrm{MgB}}_2$ driven by intense terahertz electromagnetic pulses. Third- and fifth-order harmonics are resolved in time domain and investigated as a function of temperature and in applied magnetic fields crossing the superconducting phase boundary. The high-order harmonics in the superconducting phase reflects nonequilibrium dynamics of the superconducting order parameter in ${\mathrm{MgB}}_2$, which is probed via nonlinear coupling to the terahertz field. The observed temperature and field dependence of the nonlinear response allows to establish the superconducting phase diagram.

One of the universal features of unconventional superconductors is that the superconducting (SC) state is developed in the proximity of an antiferromagnetic (AFM) state. Unified understanding the interplay between these two states in different superconducting systems is one of the key issues to uncover the underlying physics of unconventional SC mechanism. Here, we report a pressure-induced superconductivity in the quasi-one-dimensional $\mathrm{Cs}{\mathrm{Mn}}_6{\mathrm{Bi}}_5$ compound that bears an AFM state at ambient pressure. The SC state appears at the critical pressure $\left(P_c\right)$ of $\sim 12$ GPa and stabilizes up to $\sim 27$ GPa. The high-pressure x-ray-diffraction measurements on $\mathrm{Cs}{\mathrm{Mn}}_6{\mathrm{Bi}}_5$ indicate that no structural phase transition occurs at the $P_c$, indicating that the AFM-SC transition is electronic in origin. By comparing the previous results of $A{\mathrm{Mn}}_6{\mathrm{Bi}}_5$ ($A=\mathrm{K}$, Rb), we identify that all members of the family possess the genetic flipping behavior of AFM-SC states at almost the same $P_c$, though their ambient-pressure unit-cell volumes vary quite differently. Our theoretical calculations suggest that the pressure-induced changes of partial density of state contributed by the $d_{yz}$ and $d_{xz}/d_{z^2}$ orbital electrons near Fermi energy may be associated with the origin of the flipping. These results provide a diverse picture of the connection between the AFM and SC states in the $3d–$ transition-metal compounds.