We show how to use the input-output formalism to compute the propagator for a low-dimensional quantum system coupled to an optical field under the rotating wave and Markovian approximation. The propagator for this coupled system is expressed in terms of the Green's functions of the low-dimensional system, and it is shown that these Green's functions can be computed entirely from the evolution of the low-dimensional system under an effective non-Hermitian Hamiltonian. Our formalism generalizes the previous works that have focused on time-independent Hamiltonians to systems with time-dependent Hamiltonians (e.g., coherently driven systems), making it a suitable computational tool for the analysis of a number of experimentally interesting quantum systems. We illustrate our formalism by applying it to analyze photon emission and scattering from the driven and undriven two-level system and the three-level lambda system.

We study equilibration and ordering in the classical dipolar kagome Ising antiferromagnet, which we show behaves as a disorder-free fragile spin glass. By identifying an appropriate order parameter, we demonstrate a transition to the ordered state proposed by Chioar et al. [Phys. Rev. B 93, 214410 (2016)] with a 12-site unit cell that breaks time-reversal and sublattice symmetries, and further provide evidence that the nature of the transition is first order. Upon approaching the transition, the spin dynamics slow dramatically. The system readily falls out of equilibrium, overshooting the transition and entering a supercooled liquid regime. Using extensive Monte Carlo simulations, we show that the system exhibits super-Arrhenius behavior above the ordering transition. The best fit to the relaxation time is of the Vogel-Fulcher form with a divergence at a finite “glass transition” temperature in the supercooled regime. Such behavior, characteristic of fragile glasses, is particularly remarkable as the model is free of quenched disorder, does not straightforwardly conform to the avoided criticality paradigm, and is simple and eminently realizable in engineered nanomagnetic arrays.

Electron spin resonance (ESR) experiments in the quasi-one-dimensional (quasi-1D) $S=\frac{1}{2}$ antiferromagnet ${\mathrm{K}}_2{\mathrm{CuSO}}_4{\mathrm{Cl}}_2$ reveal the opening of a gap in the absence of magnetic ordering, as well as an anisotropic shift of the resonance magnetic field. These features of the magnetic excitation spectrum are explained by a crossover between a gapped spinon-type doublet ESR formed in a 1D antiferromagnet with uniform Dzyaloshinskii-Moriya interaction and a Larmor-type resonance of a quasi-1D Heisenberg system.

The angular dependence of the colossal magnetoresistance as the magnetic field is swept in different planes is investigated in a tensile strained La-Pr-Ca-Mn-O microbridge. For the in-plane sweep, the rotation of the magnetic field drives percolation/depercolation of electron conduction channels and in the spatially confined system produces abrupt resistance jumps. As the magnetic field is swept out of the plane of the film towards the direction normal to the film's plane, the relative volume fraction of the ferromagnetic phase is reduced. This leads to depercolation of the conduction channels. This process is reversible when the magnetic field is swept back into the plane of the film.

We study the coexistence of pair- (PDW) and charge-density-wave (CDW) states within the single-band $t\text{−}J\text{−}U$ and Hubbard models of $d$-wave superconductivity and discuss our results in the context of the experimental observations for the copper-based compounds. In order to take the correlation effects into account with proper precision, we use the approach based on the diagrammatic expansion of the Gutzwiller wave function (DE-GWF), which goes beyond the renormalized mean-field theory in a systematic manner. According to our analysis of the $t\text{−}J\text{−}U$ model, the transition between the pure $d$-wave superconducting phase and the coexistent CDW+PDW phase takes place at $\delta \approx 0.18$ (close to the optimal doping), with the modulated phase located in the underdoped regime. The situation is different for the case of the Hubbard model, where a narrow stability regime of a precursor nematic phase sets in preceding the formation of the modulated CDW+PDW state, with decreasing hole doping. The results conclude our comprehensive discussion of the standard phase diagram for high-$T_C$ superconducting compounds within the DE-GWF variational approach in the single narrow-band case [see J. Spałek et al., Phys. Rev. B 95, 024506 (2017); M. Zegrodnik and Spałek, Phys. Rev. B 95, 024507 (2017); Phys. Rev. B 96, 054511 (2017); New J. Phys. 20, 063015 (2018)].

Multifold fermions are generalizations of twofold degenerate Weyl fermions with three-, four-, six-, or eightfold degeneracies protected by crystal symmetries, of which only the last type is necessarily nonchiral. Their low-energy degrees of freedom can be described as emergent relativistic particles not present in the standard model of particle physics. We propose a range of experimental probes for multifold fermions in chiral symmetry groups based on the gyrotropic magnetic effect (GME) and the circular photogalvanic effect (CPGE). We find that, in contrast to Weyl fermions, multifold fermions can have zero Berry curvature yet a finite GME, leading to an enhanced response. The CPGE is quantized and independent of frequency provided that the frequency region at which it is probed defines closed optically activated momentum surfaces. We confirm the above properties by calculations in symmetry-restricted tight-binding models with realistic density functional theory parameters. We identify a range of previously unidentified ternary compounds able to exhibit chiral multifold fermions of all types (including a range of materials in the families AsBaPt and ${\mathrm{Gd}}_3{\mathrm{Cl}}_3\mathrm{C}$), and provide specific predictions for the known multifold material RhSi.

Novel controlled nonperturbative techniques are a must in the study of strongly correlated systems, especially near quantum criticality. One of these techniques, bosonization, has been extensively used to understand one-dimensional, as well as higher-dimensional electronic systems at finite density. In this paper, we generalize the theory of two-dimensional bosonization of Fermi liquids, in the presence of a homogeneous weak magnetic field perpendicular to the plane. Here, we extend the formalism of bosonization to treat free spinless fermions at finite density in a uniform magnetic field. We show that particle-hole fluctuations of a Fermi surface satisfy a covariant Schwinger algebra, allowing to express a fermionic theory with forward scattering interactions as a quadratic bosonic theory representing the quantum fluctuations of the Fermi surface. By means of a coherent-state path integral formalism, we compute the fermion propagator as well as particle-hole bosonic correlations functions. We analyze the presence of de Haas-van Alphen oscillations and show how the quantum oscillations of the orbital magnetization, the Lifshitz-Kosevich theory, are obtained by means of the bosonized theory. We also study the effects of forward scattering interactions. In particular, we obtain oscillatory corrections to the Landau zero sound collective mode.

The Ce atoms in CeIrSn form a quasikagome lattice in the hexagonal $c$ plane. Our single-crystal x-ray diffraction analysis has confirmed the absence of superstructure in the ZrNiAl-type structure. Motivated by the recent observation of quantum critical behaviors in the isostructural and isoelectronic compound CeRhSn, we have studied low-temperature properties of single-crystalline samples of CeIrSn by measuring the electrical resistivity, magnetic susceptibility $\chi$, magnetization $M$, and specific heat $C$ down to 0.05 K. Our study does not show evidence of a long-range magnetic ordering down to the lowest temperature. The $\chi \left(T\right)$ data show an Ising character, ${\chi }_c\gg {\chi }_a$, and power-law behaviors at low temperatures: ${\chi }_c\propto T^{-0.8}$ and ${\chi }_a\propto T^{-0.6}$. When external field $B$ is applied along the $a$ axis, both $M\left(B\right)$ and $C\left(B\right)/T$ exhibit metamagnetic anomalies at 5.5 T, which resemble those observed in CeRhSn at 3.5 T. We attribute the metamagnetic crossover under in-plane magnetic fields to the alleviation of magnetic frustration inherent in the quasikagome Ising Kondo lattice.

We report on the magnetic and electronic properties of single-crystalline ${\mathrm{Ga}}_{0.91}{\mathrm{Mn}}_{0.09}\mathrm{S}$, which is a quasi-two-dimensional diluted magnetic semiconductor (DMS). Through an analysis of magnetization data, we show the existence of an anomalously high spin-glass transition temperature at 11.2 K. Using density functional theory (DFT), we characterize the properties contributing to the spin-glass transition through an examination of the electronic and magnetic properties for ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{S}$ with $x$ varying from 0.00 to 0.18 by randomly substituting Mn atoms into the gallium (Ga) lattice sites. We show that the presence of magnetic atoms produces impurity bands in the electronic structure, where an analysis of the density of states shows an increase in magnetic impurity bands at the Fermi level that lowers the semiconducting gap and is consistent with diluted magnetic semiconductors. Furthermore, this indicates that the spin-glass transition in ${\mathrm{Ga}}_{0.91}{\mathrm{Mn}}_{0.09}\mathrm{S}$ is similar to other DMS materials, where the primary mechanism is likely through magnetic exchange. However, the increased electron density in the system with Mn doping could explain the anomalously higher spin-glass transition temperature in ${\mathrm{Ga}}_{0.91}{\mathrm{Mn}}_{0.09}\mathrm{S}$. In comparison with the substantially lower transition temperatures in related II-VI based systems (i.e., ${\mathrm{Zn}}_{1-x}\mathrm{Mn}{}_x\mathrm{Te}$), the high transition temperature is associated with more metallic spin-glass systems that interact through RKKY exchange, which leads to the conclusion that there may be a combination of interactions occurring in these systems. Further measurements on the other substitution percentages will hopefully clarify these interactions.

Our understanding of bias-dependent scanning-tunneling-microscopy (STM) images is complicated not only by the multiplicity of the surface electronic structure, but also the manifold tunneling effects in probing semiconductor surfaces having directional dangling- and covalent-bond orbitals. Here we present a refined interpretation of empty-state STM images from the model semiconductor surface, Ge(100), on the basis of measurements at low temperature (12 K) combined with density-functional-theory calculations. In the lower-bias regime ($\le 1.6\mathrm{V}$), the electron tunneling is found to occur predominantly in antibonding dangling-bond or/and dimer-bond states (${\pi }_1^{*},{\pi }_2^{*}$, and ${\sigma }^{*}$) of Ge(100) at the surface-parallel wave vector $k_{\parallel }=0$, leading to the tunneling current maxima located directly on the dimer rows. At higher biases (e.g., at 2 V), the current maxima are shifted to the position in the troughs between the dimer rows, because the tunneling occurs efficiently in the ${\pi }_2^{*}$ states at $k_{\parallel }\ne 0$ associated with the dimer-up atoms of two adjacent dimer rows, i.e., because of increased sideways tunneling. Thus, the empty-state STM images of Ge(100), albeit strongly bias-dependent, reflect the dimer arrangement rather than the backbonds and surface resonances at all experimental conditions used. The results are also discussed in comparison with the counterpart system of Si(100).

Proximity phenomena between superconductors and topological semimetals are at the heart of the search for novel quantum states of matter. Here we show that the epitaxial interface between one- to three-atomic-layer Pb and the Sb(111) substrate has extremely high electronic transparency. As a result, Pb loses its superconducting and even its metallic properties; its electronic spectrum mimics the semimetallic density of states of Sb. Additional states arise from a threefold symmetric potential which develops at the Pb/Sb interface. Our experimental results are supported by DFT simulations which demonstrate that this potential arises from the corrugated structure of the Pb/Sb interface.

At low temperatures, elementary excitations of a one-dimensional quantum liquid form a gas that can move as a whole with respect to the center of mass of the system. This internal motion attenuates at exponentially long time scales. As a result, in a broad range of frequencies, the liquid is described by two-fluid hydrodynamics, and the system supports two sound modes. The physical nature of the two sounds depends on whether the particles forming the quantum liquid have a spin degree of freedom. For particles with spin, the modes are analogous to the first and second sound modes in superfluid ${}^4\mathrm{He}$, which are the waves of density and entropy, respectively. When dissipative processes are taken into account, we find that at low frequencies, the second sound is transformed into heat diffusion, while the first sound mode remains weakly damped and becomes the ordinary sound. In a spinless liquid, the entropy and density oscillations are strongly coupled and the resulting sound modes are hybrids of the first and second sound. As the frequency is lowered and dissipation processes become important, the crossover to a single-fluid regime occurs in two steps. First the hybrid modes transform into predominantly density and entropy waves, similar to the first and second sound, and then the density wave transforms to the ordinary sound and the entropy wave becomes a heat-diffusion mode. Finally, we account for the dissipation due to viscosity and intrinsic thermal conductivity of the gas of excitations, which controls attenuation of the sound modes at high frequencies.

We study the particle-hole asymmetry of the scattering rate in strongly correlated electron systems by examining the cubic ${\omega }^3$ and $\omega T^2$ terms in the imaginary part of the self-energy of the Anderson impurity model. We show that the sign is opposite in the weak-coupling and strong-coupling limits, explaining the differences found in theoretical approaches taking the respective limits as the starting points. The sign change in fact precisely delineates the crossover between the weak- and strong-correlation regimes of the model. For weak interaction $U$ the sign reversal occurs for small values of the doping $\delta =1-n$, while for interaction of order $U\approx 2\mathrm{\Gamma }$, $\mathrm{\Gamma }$ being the hybridization strength, the crossover curve rapidly shifts to the large-doping range. This curve, based on the impurity dynamics, is genuinely different from other crossover curves defined through impurity thermodynamic and static properties.

We analyze a disordered central spin model, where a central spin interacts equally with each spin in a periodic one-dimensional (1D) random-field Heisenberg chain. If the Heisenberg chain is initially in the many-body localized (MBL) phase, we find that the coupling to the central spin suffices to delocalize the chain for a substantial range of coupling strengths. We calculate the phase diagram of the model and identify the phase boundary between the MBL and ergodic phase. Within the localized phase, the central spin significantly enhances the rate of the logarithmic entanglement growth and its saturation value. We attribute the increase in entanglement entropy to a nonextensive enhancement of magnetization fluctuations induced by the central spin. Finally, we demonstrate that correlation functions of the central spin can be utilized to distinguish between MBL and ergodic phases of the 1D chain. Hence, we propose the use of a central spin as a possible experimental probe to identify the MBL phase.

We examine the effect of acoustic phonon scattering on the conductivity of two-dimensional Dirac electrons. The temperature ($T$) dependence of the conductivity ($\sigma$) is calculated using the electron Green's function with damping by both the impurity (${\mathrm{\Gamma }}_0$) and phonon (${\mathrm{\Gamma }}_{\mathrm{ph}}$). For zero or small doping, on which the present Rapid Communication focuses, $\sigma \left(T\right)$ increases and becomes almost constant due to the competition between the Dirac electrons and the phonon scattering. Such strange behavior of $\sigma \left(T\right)$ is ascribed to an exotic mechanism of phonon scattering, whose momentum space is strongly reduced in the presence of a Dirac cone. For large doping, $\sigma$ decreases due to the interplay of the Fermi surface and the phonon. The unconventional $T$ dependence of the resistivity $\rho$ ($=1/\sigma$) for small doping is compared with that of the experiment of Dirac electrons in an organic conductor.

To elucidate the pairing states in Fe-based superconductors, we perform a careful calculation of the dynamical spin susceptibility ${\chi }^S(\mathit{q},\omega )$ at very low temperatures ($T\gtrsim 1\mathrm{meV}$). The feedback effect on both the self-energy and ${\chi }^S(\mathit{q},\omega )$ from the superconducting gap is self-consistently analyzed based on the fluctuation-exchange (FLEX) approximation. In the $s_{\pm }$-wave state, which has sign reversal in the gap function, ${\chi }^S(\mathit{q},\omega )$ at the nesting momentum $\mathit{q}=\mathit{Q}$ shows a resonance peak even when the system is away from the magnetic quantum critical point (QCP). In the $s_{++}$-wave state that has no sign reversal, ${\chi }^S(\mathit{q},\omega )$ shows a large hump structure when the system is close to the magnetic QCP. This result confirms the validity of a self-energy driven resonancelike peak in the $s_{++}$-wave state proposed in our previous semimicroscopic study: The enhancement in ${\chi }^S(\mathit{q},\omega )$ due to the self-energy effect exceeds the suppression due to the coherence factor effect near the magnetic QCP. We stress that the hump structure in the $s_{++}$-wave state given by the FLEX method smoothly changes to a resonancelike sharp peak structure as the system approaches the magnetic QCP, which was not reported in our previous studies. The obtained $\omega$ and $T$ dependence of ${\chi }^S(\mathit{q},\omega )$ in the $s_{++}$-wave states resembles the resonancelike feature in inelastic neutron scattering spectra recently observed in Na(Fe,Co)As and FeSe.

Conventional topological superconductors are fully gapped in the bulk but host gapless Majorana modes on their boundaries. We instead focus on a new class of superconductors, second-order topological superconductors, that have gapped, topological surfaces and gapless Majorana modes instead on lower-dimensional boundaries, i.e., corners of a two-dimensional system or hinges for a three-dimensional system. Here, we propose two general scenarios in which second-order topological superconductivity can be realized spontaneously with weak-pairing instabilities. First, we show that $\left(p_x+i{p}_y\right)$-wave pairing in a (doped) Dirac semimetal in two dimensions with four mirror-symmetric Dirac nodes realizes second-order topological superconductivity. Second, we show that $p+id$ pairing on an ordinary spin-degenerate Fermi surface realizes second-order topological superconductivity as well. In the latter case, we find that the topological invariants describing the system can be written using simple formulas involving only the low-energy properties of the Fermi surfaces and superconducting pairing. In both cases, we show that these exotic superconducting states can be intrinsically realized in a metallic system with electronic interactions. For the latter case, we also show it can be induced by proximity effect in a heterostructure of cuprate and topological superconductors.