We propose a scheme based on the neural-network quantum states to simulate the stationary states of open quantum many-body systems. Using the high expressive power of the variational ansatz described by the restricted Boltzmann machines, which we dub as the neural stationary state ansatz, we compute the stationary states of quantum dynamics obeying the Lindblad master equations. The mapping of the stationary-state search problem into finding a zero-energy ground state of an appropriate Hermitian operator allows us to apply the conventional variational Monte Carlo method for the optimization. Our method is shown to simulate various spin systems efficiently, i.e., the transverse-field Ising models in both one and two dimensions and the XYZ model in one dimension.

${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ presents an ongoing conundrum in the study of rare-earth pyrochlores. Despite the expectation that it should be the prototypical unfrustrated noncollinear Ising antiferromagnet on the pyrochlore lattice, it presents a puzzling correlated state that persists to the lowest temperatures. Effects which can reintroduce frustration or fluctuations are therefore sought, and quadrupolar operators have been implicated. One consequence of strong quadrupolar effects is the possible coupling of magnetic and lattice degrees of freedom, and it has previously been shown that a hybrid magnetoelastic mode with both magnetic and phononic character is formed in ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ by the interaction of a crystal field excitation with a transverse-acoustic phonon. Here, using polarized and unpolarized inelastic neutron scattering, we present a detailed characterization of the magnetic and phononic branches of this magnetoelastic mode, particularly with respect to their composition, the anisotropy of any magnetic fluctuations, and also the temperature dependence of the different types of fluctuation that are involved. We also examine the dispersion relations of the exciton branches that develop from the crystal field excitation in the same temperature regime that the coupled mode appears, and find three quasidispersionless branches where four are expected, each with a distinctive structure factor indicating that they are nonetheless cooperative excitations. We interpret the overall structure of the spectrum as containing four branches, one hybridized with the phonons and gaining a strong dispersion, and three remaining dispersionless.

Quantum dots (QDs) can serve as near perfect energy filters and are therefore of significant interest for the study of thermoelectric energy conversion close to thermodynamic efficiency limits. Indeed, recent experiments in [Nat. Nano. 13, 920 (2018)] realized a QD heat engine with performance near these limits and in excellent agreement with theoretical predictions. However, these experiments also highlighted a need for more theory to help guide and understand the practical optimization of QD heat engines, in particular regarding the role of tunnel couplings on the performance at maximum power and efficiency for QDs that couple seemingly weakly to electronic reservoirs. Furthermore, these experiments also highlighted the critical role of the external load when optimizing the performance of a QD heat engine in practice. To provide further insight into the operation of these engines we use the Anderson impurity model together with a Master equation approach to perform power and efficiency calculations up to co-tunneling order. This is combined with additional thermoelectric experiments on a QD embedded in a nanowire where the power is measured using two methods. We use the measurements to present an experimental procedure for efficiently finding the external load $R_P$ which should be connected to the engine to optimize power output. Our theoretical estimates of $R_P$ show good agreement with the experimental results, and we show that second order tunneling processes and nonlinear effects have little impact close to maximum power, allowing us to derive a simple analytic expression for $R_P$. In contrast, we find that the electron contribution to the thermoelectric efficiency is significantly reduced by second order tunneling processes, even for rather weak tunnel couplings.

Competing magnetic anisotropies in chiral crystals with Dzyaloshinskii-Moriya exchange interactions can give rise to nontrivial chiral topological magnetization configurations with new and interesting properties. One such configuration is the magnetic soliton, where the moment continuously rotates about an axis. This magnetic system can be considered to be one dimensional and, because of this, it supports a macroscale coherent magnetization, giving rise to a tunable chiral soliton lattice (CSL) that is of potential use in a number of applications in nanomagnetism and spintronics. In this paper, we characterize the transitions between the forced-ferromagnetic (F-FM) phase and the CSL one in ${\mathrm{CrNb}}_3{\mathrm{S}}_6$ using differential phase contrast imaging in a scanning transmission electron microscope, conventional Fresnel imaging, ferromagnetic resonance spectroscopy, and mean-field modeling. We find that the formation and movement of dislocations mediate the formation of CSL and F-FM regions and that these strongly influence the highly hysteretic static and dynamic properties of the system. Sample size and morphology can be used to tailor the properties of the system and, with the application of magnetic field, to locate and stabilize normally unstable dislocations and modify their dimensions and magnetic configurations in ways beyond that predicted to occur in uniform films.

In the presence of crystalline symmetries, certain topological insulators present a filling anomaly: a mismatch between the number of electrons in an energy band and the number of electrons required for charge neutrality. In this paper, we show that a filling anomaly can arise when corners are introduced in $C_n$-symmetric crystalline insulators with vanishing polarization, having as a consequence the existence of corner-localized charges quantized in multiples of $\frac{e}{n}$. We characterize the existence of this charge systematically and build topological indices that relate the symmetry representations of the occupied energy bands of a crystal to the quanta of fractional charge robustly localized at its corners. When an additional chiral symmetry is present, $\frac{e}{2}$ corner charges are accompanied by zero-energy corner-localized states. We show the application of our indices in a number of atomic and fragile topological insulators and discuss the role of fractional charges bound to disclinations as bulk probes for these crystalline phases.

Despite the concerted effort of several research groups, a detailed experimental account of defect dynamics in high-quality single- and few-layer transition-metal dichalcogenides remains elusive. In this paper we report an experimental study of the temperature dependence of conductance and conductance fluctuations on few-layer ${\mathrm{MoS}}_2$ exfoliated on hexagonal boron nitride and covered by a capping layer of high-$\kappa$ dielectric ${\mathrm{HfO}}_2$. The presence of the high-$\kappa$ dielectric made the device extremely stable against environmental degradation as well as resistant to changes in device characteristics upon repeated thermal cycling, enabling us to obtain reproducible data on the same device over a timescale of more than 1 year. Our device architecture helped bring down the conductance fluctuations of the ${\mathrm{MoS}}_2$ channel by orders of magnitude compared to previous reports. The extremely low noise levels in our devices made it possible to detect the generation-recombination noise arising from charge fluctuation between the sulfur-vacancy levels in the band gap and energy levels at the conductance band edge. Our work establishes conduction fluctuation spectroscopy as a viable route to quantitatively probe in-gap defect levels in low-dimensional semiconductors.

In this work we study the evolution of intrinsic domain wall magnetoresistance (DWMR) with domain wall confinement. Notched half-ring nanocontacts are fabricated from Permalloy using a special ultrahigh vacuum electromigration procedure to tailor the size of the wire in situ and through the resulting domain wall confinement, we tailor the domain wall width from a few tens of nm down to a few nm. Through measurements of the dependence of the resistance with respect to the applied field direction, we extract the contribution of a single domain wall to the MR of the device, as a function of the width of the domain wall in the confining potential at the notch. In this size range, an intrinsic positive MR is found which dominates over anisotropic MR, as confirmed by comparison to micromagnetic simulations. Moreover, the MR is found to scale monotonically with the size of the domain wall, ${\delta }_{\text{DW}}$, as $1/{\delta }_{\text{DW}}^b$, with $b=2.31\pm 0.39$. The experimental result is supported by quantum-mechanical transport simulations based on ab initio density functional theory calculations.

Recent experiments have observed hints of hydrodynamic electron flow in a number of materials, not all of which have an isotropic Fermi surface. We revisit these experiments in ${\mathrm{PdCoO}}_2$, a quasi-two-dimensional material whose Fermi surface is a rounded hexagon, and observe that the data appears quantitatively consistent with a nonhydrodynamic interpretation. Nevertheless, motivated by such experiments, we develop a simple model for the low-temperature kinetics and hydrodynamics of a two-dimensional Fermi liquid with a polygonal Fermi surface. A geometric effect leads to a finite number of additional long-lived quasihydrodynamic “imbalance” modes and corresponding qualitative changes in transport at the ballistic-to-hydrodynamic crossover. In the hydrodynamic limit, we find incoherent diffusion and a new dissipative component of the viscosity tensor arising from the explicit breaking of rotational invariance by the Fermi surface. Finally, we compute the conductance of narrow channels across the ballistic-to-hydrodynamic crossover and demonstrate a modification of the Gurzhi effect that allows for nonmonotonic temperature and width dependence in the channel conductance.

The plasmon is a ubiquitous collective mode in charged liquids. Due to the long-range Coulomb interaction, the massless zero sound mode of the neutral system acquires a finite plasmon frequency in the long-wavelength limit. In the zero-temperature state of conventional metals—the Fermi liquid—the plasmon lives infinitely long at long wavelength when the system is (effectively) translationally invariant. In contrast, we will show that in strongly entangled strange metals the protection of zero sound fails at finite frequency and plasmons are always short lived regardless of their wavelength. Computing the explicit plasmon response in holographic strange metals as an example, we show that decay into the quantum critical continuum replaces Landau damping and this happens for any wavelength.

We present core level nonresonant inelastic x-ray scattering (NIXS) data of the heavy-fermion compounds ${\mathrm{CeCoIn}}_5$ and ${\mathrm{CeRhIn}}_5$ measured at the Ce $N_{4,5}$ edges. The higher than dipole transitions in NIXS allow determining the orientation of the ${\mathrm{\Gamma }}_7$ crystal-field ground-state orbital within the unit cell. The crystal-field parameters of the $\mathrm{Ce}M{\mathrm{In}}_5$ compounds and related substitution phase diagrams have been investigated in great detail in the past; however, whether the ground-state wave function is the ${\mathrm{\Gamma }}_7^{+}\left(x^2-y^2\right)$ or ${\mathrm{\Gamma }}_7^{-}(xy$ orientation) remained undetermined. We show that the ${\mathrm{\Gamma }}_7^{-}$ doublet with lobes along the (110) direction forms the ground state in ${\mathrm{CeCoIn}}_5$ and ${\mathrm{CeRhIn}}_5$. For ${\mathrm{CeCoIn}}_5$, however, we find also some contribution of the first excited state crystal-field state in the ground state due to the stronger hybridization of $4f$ and conduction electrons, suggesting a smaller ${\alpha }^2$ value than originally anticipated from x-ray absorption. A comparison is made to the results of existing density functional theory plus dynamical mean-field theory calculations.

Critical behavior is very common in many fields of science and a wide variety of many-body systems exhibit emergent critical phenomena. The beauty of critical phase transitions lies in their scale-free properties, such that the temperature dependence of physical parameters of systems differing at the microscopic scale can be described by the same generic power laws. In this work we establish the critical properties of the antiferromagnetic phase transition in artificial square ice, showing that it belongs to the two-dimensional Ising universality class, which extends the applicability of such concepts from atomistic to mesoscopic magnets. Combining soft x-ray resonant magnetic scattering experiments and Monte Carlo simulations, we characterize the transition to the low-temperature long-range order expected for the artificial square-ice system. By measuring the critical scattering, we provide direct quantitative evidence of a continuous magnetic phase transition, obtaining critical exponents which are compatible with those of the two-dimensional Ising universality class. In addition, by varying the blocking temperature relative to the phase transition temperature, we demonstrate its influence on the out-of-equilibrium dynamics due to critical slowing down at the phase transition.

In this work, we revisit the issue of the nature of electronic transport in nickel oxide (NiO) and show that the widely used model of free small polaron hopping, initially raised to characterize transport in high-purity samples, is not appropriate for modeling intrinsically doped NiO. Instead, we present extensive evidence, collected by means of temperature- and frequency-dependent measurements of the electrical conductivity $\sigma$, that the model of polaronic interacceptor hopping can be used to consistently explain the electronic conduction process. In this framework, holes are localized to acceptors (Ni vacancies), forming a strongly bound, polaron-like state. They can only move through the film by hopping to a neighboring, at least partially unoccupied, acceptor. This renders the spatial overlap between neighboring polaronic wave functions a highly critical parameter. The signature of this process is the occurrence of two temperature regions of the dc conductivity, separated by about half the Debye temperature $\frac{{\theta }_{\mathrm{D}}}{2}\approx 200\mathrm{K}$. For $T>\frac{{\theta }_{\mathrm{D}}}{2}$, holes are transferred by phonon-assisted hopping over the potential barrier between two sites, whereas phonon-assisted tunneling through the barrier dominates below that temperature. We also show that the degree of structural and electronic disorder plays a vital role in determining the characteristics of the transport process: high disorder leads to strong energetic broadening of the acceptor states such that hopping to more distant sites may be favored over transfer to nearest neighbors (variable range hopping). The assumption of high binding energies of the charge carriers at ${\mathrm{V}}_{\mathrm{Ni}}$ is in accordance with the recent paradigm shift regarding the understanding of the electronic structure of NiO: holes doped into NiO couple to Ni $3d$ spins, thereby occupying deep polaron-like states within the band gap (Zhang-Rice bound doublets). This work explicitly takes this perception into account to explain carrier transport in NiO.

Recently, there has been a lot of activity in the research field of topological non-Hermitian physics, partly driven by fundamental interests and partly driven by applications in photonics. However, despite these activities, a general classification and characterization of non-Hermitian Dirac models that describe the experimental systems is missing. Here, we present a systematic investigation of massive Dirac models on periodic lattices, perturbed by general non-Hermitian terms. We find that there are three different types of non-Hermitian terms. For each case we determine the bulk exceptional points, the boundary modes, and the band topology. Our findings serve as guiding principles for the design of applications, for example, in photonic lattices. For instance, periodic Dirac systems with non-Hermitian mass terms can be used as topological lasers. Periodic Dirac systems with non-Hermitian anticommuting terms, on the other hand, exhibit exceptional points at the surface, whose nontrivial topology could be utilized for optical devices.

We develop a theoretical and computational framework to study polarons in semiconductors and insulators from first principles. Our approach provides the formation energy, excitation energy, and wave function of both electron and hole polarons, and takes into account the coupling of the electron or hole to all phonons. An important feature of the present method is that it does not require supercell calculations, and relies exclusively on electron band structures, phonon dispersions, and electron-phonon matrix elements obtained from calculations in the crystal unit cell. Starting from the Kohn-Sham (KS) equations of density-functional theory, we formulate the polaron problem as a variational minimization, and we obtain a nonlinear eigenvalue problem in the basis of KS states and phonon eigenmodes. In our formalism, the electronic component of the polaron is expressed as a coherent superposition of KS states, in close analogy with the solution of the Bethe-Salpeter equation for the calculation of excitons. We demonstrate the power of the methodology by studying polarons in LiF and ${\mathrm{Li}}_2{\mathrm{O}}_2$. We show that our method describes both small and large polarons, and seamlessly captures Fröhlich-type polar electron-phonon coupling and non-Fröhlich coupling to acoustic and optical phonons. To analyze in quantitative terms, the electron-phonon coupling mechanisms leading to the formation of polarons, we introduce spectral decompositions similar to the Eliashberg spectral function. We validate our theory using both analytical results and direct calculations on large supercells. This study constitutes a first step toward complete ab initio many-body calculations of polarons in real materials.

We reveal that due to the presence of disorder oscillations of the order parameter amplitude called the Higgs mode can be effectively excited by the external electromagnetic radiation in usual BCS superconductors. This mechanism works for superconductors with both isotropic s-wave and anisotropic, such as d-wave, pairings. The nonlinear response in the presence of impurities is captured by the quasiclassical formalism. We demonstrate that analytical solutions of the Eilenberger equation with impurity collision integral and external field drive coincide with the exact summation of ladder impurity diagrams. Using the developed formalism we show that resonant third-harmonic signal observed in recent experiments is naturally explained by the excitation of Higgs mode mediated by impurity scattering.

We propose a realistic scheme to construct anomalous Floquet Chern topological insulators using spin-$\frac{1}{2}$ particles carrying out a discrete-time quantum walk in a two-dimensional lattice. By Floquet engineering the quantum-walk protocol, an Aharonov-Bohm geometric phase is imprinted onto closed-loop paths in the lattice, thus realizing an Abelian gauge field, the analog of a magnetic flux threading a two-dimensional electron gas. We show that in the strong-field regime, when the flux per plaquette is a sizable fraction of the flux quantum, magnetic quantum walks give rise to nearly flat energy bands featuring nonvanishing Chern numbers. Furthermore, we find that because of the nonperturbative nature of the periodic driving, a second topological number, the so-called RLBL invariant, is necessary to fully characterize the anomalous Floquet topological phases of magnetic quantum walks and to compute the number of topologically protected edge modes expected at the boundaries between different phases. In the second part of this paper, we discuss an implementation of this scheme using neutral atoms in two-dimensional spin-dependent optical lattices, which enables the generation of arbitrary magnetic-field landscapes, including those with sharp boundaries. The robust atom transport, which is observed along boundaries separating regions of different field strength, reveals the topological character of the Floquet Chern bands.

The isostructural series of $S=1$ quantum magnets ${\mathrm{Cs}}_{1-x}{\mathrm{Rb}}_x{\mathrm{FeCl}}_3$ is investigated, using both thermodynamic measurements and inelastic neutron scattering experiments. It is found that with increasing Rb content the system evolves from the gapped state at $x=0$, through a quantum phase transition at $x\sim 0.35$, and to the magnetically ordered state at larger $x$. Inelastic neutron experiments for $x=0, x=0.3$, and $x=1$ demonstrate that the magnetic anisotropy and spin interactions are continuously tuned by the chemical composition. For the intermediate concentration all magnetic excitations are substantially broadened suggesting that disorder plays a key role in this species. For the two end compounds, excitations remain sharp.

We study numerically the critical behavior at the localization transition in the Anderson model on infinite Bethe lattice and on random regular graphs. The focus is on the case of coordination number $m+1=3$, with a box distribution of disorder and in the middle of the band (energy $E=0$), which is the model most frequently considered in the literature. As a first step, we carry out an accurate determination of the critical disorder, with the result $W_c=18.17\pm 0.01$. After this, we determine the dependence of the correlation volume $N_{\xi }=m^{\xi }$ (where $\xi$ is the associated correlation length) on disorder $W$ on the delocalized side of the transition $W<W_c$, by means of population dynamics. The asymptotic critical behavior is found to be $\xi \propto {(W_c-W)}^{-1/2}$, in agreement with analytical prediction. We find very pronounced corrections to scaling, in similarity with models in high spatial dimensionality and with many-body localization transitions.

Between space crystals and amorphous materials there exists a third class of aperiodic structures which lack translational symmetry but reveal long-range order. They are dubbed quasicrystals and their formation, similar to the formation of space crystals, is related to spontaneous breaking of translational symmetry of underlying Hamiltonians. Here, we investigate spontaneous emergence of quasicrystals in periodically driven systems. We consider a quantum many-body system which is driven by a harmonically oscillating force and show that interactions between particles result in spontaneous self-reorganization of the motion of a quantum many-body system and in the formation of a quasicrystal structure in time.

Polar metals exist as a rather unique class of materials as they combine two seemingly mutually exclusive properties (polar order and metallicity) in one system. So far only a few polar metals have been unambiguously identified; the magnetic ones are exceptionally rare. Here we investigate a 5% Fe-doped polar metal $\mathrm{C}{\mathrm{a}}_3\mathrm{R}{\mathrm{u}}_2{\mathrm{O}}_7$, via electrical transport, magnetization, microstrain, and optical second-harmonic generation measurements. We report the full magnetic phase diagrams (in the field-temperature space) for magnetic field $H\parallel a$ and $H\parallel b$, which exhibit distinct field-dependent magnetizations behavior. In particular, for $H\parallel a$ we found a ferromagnetic incommensurate spin structure, which is absent in the pure $\mathrm{C}{\mathrm{a}}_3\mathrm{R}{\mathrm{u}}_2{\mathrm{O}}_7$. We propose a microscopic spin model to understand this behavior, highlighting the role of Fe doping in tipping the delicate balance of the underlying exchange-interaction energy in this system.