We provide a natural generalization of a Riemannian structure, i.e., a metric, recently introduced by Sjöqvist for the space of nondegenerate density matrices, to the degenerate case, i.e., the case in which the eigenspaces have dimension greater than or equal to 1. We present a physical interpretation of the metric in terms of an interferometric measurement. We apply this metric, physically interpreted as an interferometric susceptibility, to the study of topological phase transitions at finite temperatures for band insulators. We compare the behaviors of this susceptibility and the one coming from the well-known Bures metric, showing them to be dramatically different. While both infer zero-temperature phase transitions, only the former predicts finite-temperature phase transitions as well. The difference in behaviors can be traced back to a symmetry-breaking mechanism, akin to Landau-Ginzburg theory, by which the Uhlmann gauge group is broken down to a subgroup determined by the type of the system's density matrix (i.e., the ranks of its spectral projectors).

We study a model of correlated electrons coupled by tunneling to a layer of itinerant metallic electrons, which allows us to interpolate from a frustrated limit favorable to spin liquid states to a Kondo-lattice limit favorable to interlayer coherent heavy metallic states. We study the competition of the spinon Fermi-surface state and the interlayer coherent heavy Kondo metal that appears with increasing tunneling. Employing a slave rotor mean-field approach, we obtain a phase diagram and describe two regimes where the spin liquid state is destroyed by weak interlayer tunneling: (i) the Kondo limit in which the correlated electrons can be viewed as localized spin moments and (ii) near the Mott metal-insulator transition where the spinon Fermi surface transitions continuously into a Fermi liquid. We study the shape of local density of states (LDOS) spectra of the putative spin liquid layer in the heavy Fermi-liquid phase and describe the temperature dependence of its width arising from quasiparticle interactions and disorder effects throughout this phase diagram, in an effort to understand recent scanning tunneling microscopy experiments of the candidate spin liquid $1\mathrm{T}\text{−}{\mathrm{TaSe}}_2$ residing on metallic $1\mathrm{H}\text{−}{\mathrm{TaSe}}_2$. Comparison of the shape and temperature dependence of the theoretical and experimental LDOS suggests that this system is either close to the localized Kondo limit or in an intermediate coupling regime where the Kondo coupling and the Heisenberg exchange interaction are comparable.

While the disorder-induced quantum Hall (QH) effect has been studied previously, the effect of disorder potential on microscopic features of the integer QH effect remains unclear, particularly for the incompressible (IC) strip. In this research, a scanning gate microscope incorporated with the nonequilibrium transport technique is used to image the region of QH IC strip that emerges near the sample edge. It was found that different mobility samples with varying disorder potentials showed the same spatial dependence of the IC strip on the filling factor ($\nu$). In the low-mobility sample alone, scattering centers such as bright, dark, and annular patterns, alternately appear within the IC strip. These observed patterns are ascribed to inter-Landau level scattering assisted by resonance tunneling through an impurity bound state. It is concluded that disorder-induced scattering can be effectively detected using the applied technique in a low-mobility sample.

We investigate the roles of non-Hermitian topology in spectral properties and entanglement structures of open systems. In terms of spectral theory, we give a unified understanding of two interpretations of non-Hermitian topology: quantum anomaly and non-Hermitian skin effects, in which the bulk spectra extremely depend on the boundary conditions. In this context, the fact that the intrinsic higher-dimensional skin effects under the full open boundary condition need the presence of the topological defects is understood in terms of the anomalous fermion production such as the Rubakov-Callan effect in the presence of the magnetic monopole. By using the unified interpretation, we classify the symmetry-protected and higher-dimensional skin effects. In terms of the entanglement structure, we investigate steady states of fermionic open systems whose Liouvillian (rapidity) spectra host non-Hermitian topology. We analyze dissipation-driven Majorana steady states in zero-dimensional open systems and relate them to the Majorana edge modes of topological superconductors by using the entanglement entropy. We also analyze a steady state of a one-dimensional open Fermi system with a non-Hermitian topological spectrum and relate it to the chiral edge states of the Chern insulator on the basis of the trace index defined from the entanglement spectrum. This correspondence indicates that the entanglement generates circular nonreciprocal currents under the periodic boundary condition and the skin-effect voltage with fermion accumulation under the open boundary condition. Finally, we discuss several related topics such as pseudospectral behaviors of Liouvillian dynamics and skin effects in interacting systems.

We show that, in mesoscopic four-terminal thermoelectric devices with two electrodes (the source and the drain) and two heat baths, inelastic-scattering processes can lead to unconventional thermoelectric transport. The source (or the drain) can be cooled by passing a thermal current between the two heat baths, with no net heat exchange between the heat baths and the electrodes. This effect, termed “cooling by transverse heat current,” is a mesoscopic heat drag effect. In addition, there is a transverse thermoelectric effect where electrical current and power can be generated by a transverse temperature bias (i.e., the temperature bias between the two heat baths). This transverse thermoelectric effect originates from inelastic-scattering processes and may have advantages for improved figures of merit and power factor due to spatial separation of charge and heat transport. We study the Onsager current-affinity relations, the linear-response transport properties, and the transverse thermoelectric figure of merit of the four-terminal thermoelectric devices for various system parameters. We find that the figures of merit are optimized in different parameter regions for the transverse and the (conventional) longitudinal thermoelectric effects, respectively. Meanwhile, the maximum figure of merit for the transverse thermoelectric effect is higher than the figure of merit for the conventional longitudinal thermoelectric effect. In addition, we investigate the efficiency and power of the cooling by the transverse heat current effect in both linear and nonlinear transport regimes. Finally, we demonstrate that, by exploiting the inelastic transport in the quantum-dot four-terminal systems, a type of Maxwell demon can be realized using nonequilibrium heat baths.

We theoretically investigate the transmission of exchange-dominated spin waves in a one-dimensional magnonic crystal (MC) with a periodic exchange bias field. By recasting the Landau-Lifshitz-Gilbert equation into an effective Schrödinger equation and establishing spin-wave functions, it is found that MCs with upward (up) and downward (down) magnetization, respectively, correspond to the rectangular $N$-fold barriers and wells for magnons. The broadband transmission spectra in up and down states are systematically investigated. We show the phenomena of the magnon resonant transmission in both states and calculate the resonant transmission wave functions, which are related to the magnon density. Our results also show a transmission spectra shift effect (TSSE) between up and down states, which is found to be general in this system. Furthermore, the TSSE is useful to design a type of magnon valve, the magnonic-crystal-based magnon valve (MCMV), which has a large on/off ratio and bandwidth. By high-throughput screening, 125 000 groups of parameters of the MC are calculated, and 1948 parameter groups of high-performance MCMVs are screened out. Our work clarifies the physical details of the exchange-dominated spin-wave transmission in rectangular $N$-fold barriers and wells and also provides a promising route for designing novel magnonic devices.

We perform atomistic simulations of spin transfer torque switching dynamics in CoFeB/MgO/CoFeB magnetic tunnel junctions. We base our study on Slonczewski's model parametrized following the approach of Zhang, Levy, and Fert. We utilize excitation modes and the contour integral of the magnetization to perform a deeper analysis of the switching mechanism driven by spin transfer torque. Our results show a magnetization reversal driven by the combination of coherent and nonuniform excitation modes. These can be nonuniform and initiated by a coherent mode of the magnetization, or domain wall nucleated depending on the lateral size, temperature, and current density injected into the system. Larger current densities result in stronger excitation of nonuniform modes making the switching more easily subjected to thermal excitations and structural imperfections such as edge damage. Our findings agree with experimental works on spin transfer torque switching in similar CoFeB/MgO-based systems, and they suggest the presence of complex features in the magnetization dynamics. The analysis and the results presented here can help to gain a deeper understanding of spin transfer torque dynamics in nanoscale devices.

We have developed a comprehensive theoretical model for predicting the magnetic field response of a parallel superconducting quantum interference device (SQUID) array in the voltage state. The model predictions are compared with our experimental data from a parallel SQUID array made of a yttrium barium copper oxide thin film patterned into wide tracks, busbars, and leads, with 11 step-edge Josephson junctions. Our theoretical model uses the Josephson equations for resistively shunted junctions as well as the second Ginzburg-Landau equation to derive a system of coupled first-order nonlinear differential equations to describe the time evolution of the Josephson junction phase differences which includes Johnson noise. Employing the second London equation and Biot-Savart's law, the supercurrent density distribution is calculated, using the stream function approach, which leads to a two-dimensional second-order linear Fredholm integro-differential equation for the stream function with time-dependent boundary conditions. The model calculates the stream function everywhere in the thin-film structure to determine during the time evolution the fluxoids for each SQUID array hole. Our numerical model calculations are compared with our experimental data and predict the bias-current-versus-voltage and the voltage-versus-magnetic-field response with accuracy. The model elucidates the importance of fully taking Meissner shielding and current crowding into account in order to properly describe fluxoid focusing and bias-current injection. Furthermore, our model illustrates the failure of the simple lumped-element approach to describe a parallel SQUID array with a wide thin-film structure.

We report here a structural study of $R\mathrm{Ba}{\mathrm{Mn}}_2{\mathrm{O}}_6$ ($R=\mathrm{La}$, Pr, and Nd) compounds by means of synchrotron radiation x-ray powder diffraction and Raman spectroscopy. The three compounds are $A$-site ordered perovskites adopting the prototypical tetragonal structure at high temperature. A ferromagnetic transition is observed in the $\mathrm{LaBa}{\mathrm{Mn}}_2{\mathrm{O}}_6$ sample and the lattice parameters undergo anisotropic changes at $T_C$ related to the orientation of the magnetic moments. Both $\mathrm{PrBa}{\mathrm{Mn}}_2{\mathrm{O}}_6$ and $\mathrm{NdBa}{\mathrm{Mn}}_2{\mathrm{O}}_6$ have a structural transition coupled to an electronic localization and an antiferromagnetic transition. In both cases, the x-ray diffraction patterns reveal that the low-temperature phase is orthorhombic with lattice parameters $a+b,b-a$, and $c$ with respect to the tetragonal phase. Two possible solutions belonging to the space groups Pmam and $P{2}_{1}am$ can yield accurate refinements of the x-ray patterns. However, the active modes in the low-temperature phase disclosed by the Raman spectroscopy clearly point to the noncentrosymmetric space group, $P{2}_{1}am$. The symmetry analysis of this transition unveils that the primary modes belong to the irreducible representations M5− and GM5− and the main distortions correspond to rotations of the $\mathrm{Mn}{\mathrm{O}}_6$ octahedra and an asymmetric combination of stretching and scissoring modes of the basal oxygens in these octahedra. We conclude that the low-temperature phase is polar and the main contribution comes from the displacement of oxygen atoms from their centrosymmetric positions. However, negligible contribution from the asymmetric stretching associated with a Jahn-Teller distortion is found in this structural transition, suggesting the lack of ferroic orbital ordering of $e_g$ ($3d_{x^2-y^2}$) orbitals in the orthorhombic $ab$ plane. There is only one inequivalent site for the Mn atom in the low-temperature polar phase so charge ordering cannot account for the electronic localization having a structural origin.

The Ni self-diffusion, density, and viscosity of the densely packed liquid ${\mathrm{Ni}}_{66.7}{\mathrm{B}}_{33.3}$ and the more loosely packed liquid ${\mathrm{Ge}}_{66.7}{\mathrm{Ni}}_{33.3}$ were measured with high accuracy using different experimental methods. The viscosity $\eta$ was obtained using the oscillating-drop method combined with electrostatic levitation and the oscillating-cup technique in a rheometer. The Ni self-diffusion coefficient $D_{Ni}$ was obtained from quasielastic neutron scattering experiments. For ${\mathrm{Ni}}_{66.7}{\mathrm{B}}_{33.3}$, it was found that the activation energies for self-diffusion and viscous flow, $E_D$ and $E_{\eta }$, respectively, are almost equal. Hence, the product of the viscosity $\eta$ and self-diffusion coefficient $D$ is fairly constant over the entire temperature range measured, spanning almost 800 K. In contrast, for ${\mathrm{Ge}}_{66.7}{\mathrm{Ni}}_{33.3}, D\eta$ increases with increasing temperature, indicating that the dynamics in liquid ${\mathrm{Ge}}_{66.7}{\mathrm{Ni}}_{33.3}$ shows better agreement with an activated process. This temperature dependence is in line with the Stokes-Einstein relation.

The recent successful experimental observation of quantum anomalous Hall effect in graphene under laser irradiation demonstrates the feasibility of controlling single-particle band structure by lasers. Here we study superconductivity in a Hubbard honeycomb model in the presence of an electromagnetic drive. We start with Hubbard honeycomb model in the presence of an electromagnetic field drive, both circularly and linearly polarized light and map it onto a Floquet $t-J$ model. We explore conditions on the drive under which one can induce superconductivity (SC) in the system. We study the Floquet $t-J$ model within the mean-field theory in the singlet pairing channel and explore superconductivity for small doping in the system using the Bogoliubov–de Gennes approach. We uncover several superconducting phases, which break lattice or time-reversal symmetries in addition to the standard U(1) symmetry. We show that the unconventional chiral SC order parameter ($d\pm id$) can be driven to a nematic SC order parameter ($s+d$) in the presence of a circularly polarized light. The $d+id$ SC order parameter breaks time-reversal symmetry and is topologically nontrivial and supports chiral edge modes. We further show that the threefold nematic degeneracy can be lifted using linearly polarized light. Our work, therefore, provides a generic framework for inducing and controlling SC in the Hubbard honeycomb model, with possible application to graphene and other two-dimensional materials.

Determining the statistics of elementary excitations supported by fractional quantum Hall states is crucial to understanding their properties and potential applications. In this paper, we use the topological entanglement entropy as an indicator of Abelian statistics to investigate the single-component $\nu =2/5$ and $3/7$ states for the Hofstadter model in the band mixing regime. We perform many-body simulations using the infinite cylinder density matrix renormalization group and present an efficient algorithm to construct the area law of entanglement, which accounts for both numerical and statistical errors. Using this algorithm, we show that the $\nu =2/5$ and $3/7$ states exhibit Abelian topological order in the case of two-body nearest-neighbor interactions. Moreover, we discuss the sensitivity of the proposed method and fractional quantum Hall states with respect to interaction range and strength.

We study the influence of anisotropy, treated as a dimensional crossover between 1D and 3D systems, on the topological instability induced by a (self-consistent) uniaxial periodic potential. The mechanism on which the instability is based involves the topological reconstruction of the Fermi surface, from initially closed pockets to the surface with open Fermi sheets, creating two peculiar points in the band dispersion—the saddle point and elliptical point, between which the pseudogap in electron density of states develops. The self-consistent periodic potential appears as a result of interactions, either electron-phonon or electron-electron, which, linked with the topological instability of the system, results in formation of a new ground state of the system—the density wave provided that the relevant coupling constant is larger than critical. Our analysis shows that the phase transition takes place along the whole continuous interval of a dimensional crossover between 1D and 3D, but that the critical coupling strength significantly increases with the dimensionality of the system. It is our intention to give an initial framework for understanding the nature of charge density waves experimentally observed in a number of materials, like $\mathrm{high}\text{−}{T}_c$ cuprates or graphite intercalates, both being materials with a closed, rather isotropic Fermi surface far from the nesting regime.

We experimentally and numerically investigate the exchange interaction of the yellow excitons in cuprous oxide. By varying the material parameters in the numerical calculations, we can interpret experimental findings and understand their origin in the complex band structure and central-cell corrections. In particular, we experimentally observe the reversal of the ortho- and paraexciton for the $2S$ yellow exciton and explain this phenomenon by an avoided crossing with the green $1S$ orthoexciton in a detailed numerical analysis. Furthermore, we discuss the exchange splitting as a function of the principal quantum number $n$ and its deviation from the $n^{-3}$ behavior expected from a hydrogenlike model. We also explain why the observed exchange splitting of the green $1S$ exciton is more than twice the splitting of the yellow $1S$ state.

We thoroughly investigate two methods for estimating electric field strength across semiconductor heterostructure quantum wells from electron holograms. Due to the small width of quantum wells these holograms must often be taken under dynamical diffraction conditions, since projection effects forbid the investigation under larger tilt angles. We especially investigated the robustness of the evaluation methods against dynamical diffraction artifacts due to excitation conditions and strain, artifacts due to the material contrast, as well as limited resolution effects. For this we developed ways to incorporate polarization effects into combined strain and multislice simulations. It turns out that errors estimated from detection noise of single measurements alone mostly underestimate the true error, since variation due to hardly controlled diffraction effects and measurement details often prevails.

In metallic noncentrosymmetric crystals and at surfaces the response of spin currents and charge currents to applied electric fields contains contributions that are second order in the electric field, which are forbidden by symmetry in centrosymmetric systems. Thereby, photocurrents and spin photocurrents can be generated in inversion asymmetric metals by the application of femtosecond laser pulses. We study the laser-induced charge current in the ferromagnetic Rashba model with in-plane magnetization and find that this magnetic photogalvanic effect can be tuned to be comparable in size to the laser-induced photocurrents measured experimentally in magnetic bilayer systems such as Co/Pt. Additionally, we show that femtosecond laser pulses excite strong spin currents in the nonmagnetic Rashba model when the Rashba parameter is large.

We studied the electronic structure of ${\mathrm{PtPb}}_4$ using laser angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) calculations. This material is closely related to ${\mathrm{PtSn}}_4$, which exhibits exotic topological properties such as Dirac node arcs. The Fermi surface (FS) of ${\mathrm{PtPb}}_4$ consists of two electron pockets at the center of the Brillouin zone (BZ) and several hole pockets around the zone boundaries. Our ARPES data reveal significant Rashba splitting at the $\mathrm{\Gamma }$ point, in agreement with DFT calculations. The presence of Rashba splitting may render this material of potential interest for spintronic applications.

${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ has attracted tremendous interest as the first discovered intrinsic magnetic topological insulator. Due to its heavily $n$-doped nature, hole doping is required to isolate the effects of the topological states from the bulk, which is necessary for further electronic applications. Here, we systematically measure the resistivity, Seebeck coefficient, and thermal conductivity of $\mathrm{Mn}{\left({\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x\right)}_2{\mathrm{Te}}_4(0\le x\le 0.51)$ single crystals. We find that the carrier concentrations at room temperature can be continuously tuned from $-9.47\times {10}^{19}$ to $5.21\times {10}^{19}{\mathrm{cm}}^{-3}$ while varying $x$ from 0 to 0.51. In the crystals with the Fermi level located close to the charge neutral point in the bulk band gap, drastic changes in the resistivity, Seebeck coefficient, and thermal conductivity are observed around a certain temperature $T^{*}$. Our results suggest that the bipolar effect possibly plays an important role in determining the transport properties in narrow bulk band topological insulators when the Fermi level is located near the charge neutral point inside the bulk gap.