We study a model which can describe a superconducting single-electron transistor or a double quantum dot coupled to a transmission-line oscillator. In both cases the degree of freedom is given by a charged particle, which couples strongly to the electromagnetic environment or phonons. We consider the case where a lasing condition is established and study the dependence of the average photon number in the resonator on the spectral function of the electromagnetic environment. We focus on three important cases: a strongly coupled environment with a small cutoff frequency, a structured environment peaked at a specific frequency, and $1/f$ noise. We find that the electromagnetic environment can have a substantial impact on the photon creation. Resonance peaks are in general broadened and additional resonances can appear.

We show that charge fluctuation processes are crucial for the nonlinear heat conductance through an interacting nanostructure, even far from a resonance. We illustrate this for an Anderson quantum dot accounting for the first two leading orders of the tunneling in a master equation. The often made assumption that off-resonant transport proceeds entirely by virtual occupation of charge states, underlying exchange-scattering models, can fail dramatically for heat transport. The identified energy-transport resonances in the Coulomb blockade regime provide qualitative information about relaxation processes, for instance, by a strong negative differential heat conductance relative to the heat current. These can go unnoticed in the charge current, making nonlinear heat-transport spectroscopy with energy-level control a promising experimental tool.

When using Wannier functions to study the electronic structure of multiparameter Hamiltonians $H^{(\mathit{k},\mathbf{\lambda })}$ carrying a dependence on crystal momentum $\mathit{k}$ and an additional periodic parameter $\mathbf{\lambda }$, one usually constructs several sets of Wannier functions for a set of values of $\mathbf{\lambda }$. We present the concept of higher-dimensional Wannier functions (HDWFs), which provide a minimal and accurate description of the electronic structure of multiparameter Hamiltonians based on a single set of HDWFs. The obstacle of nonorthogonality of Bloch functions at different $\mathbf{\lambda }$ is overcome by introducing an auxiliary real space, which is reciprocal to the parameter $\mathbf{\lambda }$. We derive a generalized interpolation scheme and emphasize the essential conceptual and computational simplifications in using the formalism, for instance, in the evaluation of linear response coefficients. We further implement the necessary machinery to construct HDWFs from ab initio within the full potential linearized augmented plane-wave method (FLAPW). We apply our implementation to accurately interpolate the Hamiltonian of a one-dimensional magnetic chain of Mn atoms in two important cases of $\mathbf{\lambda }$: (i) the spin-spiral vector $\mathit{q}$ and (ii) the direction of the ferromagnetic magnetization $\widehat{\mathit{m}}$. Using the generalized interpolation of the energy, we extract the corresponding values of magnetocrystalline anisotropy energy, Heisenberg exchange constants, and spin stiffness, which compare very well with the values obtained from direct first principles calculations. For toy models we demonstrate that the method of HDWFs can also be used in applications such as the virtual crystal approximation, ferroelectric polarization, and spin torques.

Time-reversal-protected three-dimensional (3D) topological paramagnets are magnetic analogs of the celebrated 3D topological insulators. Such paramagnets have a bulk gap and no exotic bulk excitations, but have non-trivial surface states protected by symmetry. We propose that frustrated spin-1 quantum magnets are a natural setting for realizing such states in three dimensions. We describe a physical picture of the ground-state wave function for such a spin-1 topological paramagnet in terms of loops of fluctuating Haldane chains with nontrivial linking phases. We illustrate some aspects of such loop gases with simple exactly solvable models. We also show how 3D topological paramagnets can be very naturally accessed within a slave particle description of a spin-1 magnet. Specifically, we construct slave-particle mean-field states which are naturally driven into the topological paramagnet upon including fluctuations. We propose bulk projected wave functions for the topological paramagnet based on this slave-particle description. An alternate slave-particle construction leads to a stable $\mathrm{U}\left(1\right)$ quantum spin liquid from which a topological paramagnet may be accessed by condensing the emergent magnetic monopole excitation of the spin liquid.

We discuss the stability of zero-energy states appearing in a dirty normal metal attached to a superconducting thin film with Dresselhaus [110] spin-orbit coupling under an in-plane Zeeman field. The Dresselhaus superconductor preserves an additional chiral symmetry and traps more than one zero-energy state at its edges. All the zero-energy states at an edge belong to the same chirality in large Zeeman fields due to the effective $p$-wave pairing symmetry. The pure chiral nature of the wave function enables the zero-energy states to penetrate the dirty normal metal while retaining their high degree of degeneracy. We prove the perfect Andreev reflection into the dirty normal metal at zero energy.

In a multiterminal setup, when time-reversal symmetry is broken by a magnetic field, the heat flows can be managed by designing a device with programmable Boolean behavior. We show that such a device can be used to implement operations, such as on/off switching, reversal, selected splitting, and swap of the heat currents. For each feature, the switching from one working condition to the other is obtained by inverting the magnetic field. This offers interesting opportunities for conceiving a programmable setup, whose operation is controlled by an external parameter (the magnetic field) without need to alter voltage and thermal biases applied to the system. Our results, generic within the framework of linear response, are illustrated by means of a three-terminal electronic interferometer model.

Understanding the interaction between cavity photons and electronic nanocircuits is crucial for the development of mesoscopic quantum electrodynamics (QED). One has to combine ingredients from atomic cavity QED, such as orbital degrees of freedom, with tunneling physics and strong cavity field inhomogeneities, specific to superconducting circuit QED. It is therefore necessary to introduce a formalism which bridges between these two domains. We develop a general method based on a photonic pseudopotential to describe the electric coupling between electrons in a nanocircuit and cavity photons. In this picture, photons can induce simultaneously orbital energy shifts, tunneling, and local orbital transitions. We study in detail the elementary example of a single quantum dot with a single normal metal reservoir, coupled to a cavity. Photon-induced tunneling terms lead to a nonuniversal relation between the cavity frequency pull and the damping pull. Our formalism can also be applied to multiple quantum dot circuits, molecular circuits, quantum point contacts, metallic tunnel junctions, and superconducting nanostructures enclosing Andreev bound states or Majorana bound states, for instance.

Topological phases of matter are distinct from conventional ones by their lack of a local order parameter. Still in the quantum Hall effect, hidden order parameters exist and constitute the basis for the celebrated composite-particle approach. Whether similar hidden orders exist in 2D and 3D symmetry protected topological phases (SPTs) is a largely open question. Here, we introduce a new approach for generating SPT ground states, based on a generalization of the Laughlin wave function. This approach gives a simple and unifying picture of some classes of SPTs in 1D and 2D, and reveals their hidden order and flux attachment structures. For the 1D case, we derive exact relations between the wave functions obtained in this manner and group cohomology wave functions, as well as matrix product state classification. For the 2D Ising SPT, strong analytical and numerical evidence is given to show that the wave function obtained indeed describes the desired SPT. The Ising SPT then appears as a state with quasi-long-range order in composite degrees of freedom consisting of Ising-symmetry charges attached to Ising-symmetry fluxes.

We report a comprehensive micro-Raman scattering study of electrochemically gated graphene field-effect transistors. The geometrical capacitance of the electrochemical top-gates is accurately determined from dual-gated Raman measurements, allowing a quantitative analysis of the frequency, linewidth, and integrated intensity of the main Raman features of graphene. The anomalous behavior observed for the G-mode phonon is in very good agreement with theoretical predictions and provides a measurement of the electron-phonon coupling constant for zone-center ($\mathit{}\mathbf{\Gamma }$ point) optical phonons. In addition, the decrease of the integrated intensity of the 2D-mode feature with increasing doping, makes it possible to determine the electron-phonon coupling constant for near zone-edge ($\mathbf{K}$ and ${\mathbf{K}}^{\prime }$ points) optical phonons. We find that the electron-phonon coupling strength at $\mathit{}\mathbf{\Gamma }$ is five times weaker than at $\mathbf{K}\left({\mathbf{K}}^{\prime }\right)$, in very good agreement with a direct measurement of the ratio of the integrated intensities of the resonant intra- (2D′ mode) and intervalley (2D mode) Raman features. We also show that electrochemical reactions, occurring at large gate biases, can be harnessed to efficiently create defects in graphene, with concentrations up to approximately $1.4\times {10}^{12}{\mathrm{cm}}^{-2}$. At such defect concentrations, we estimate that the electron-defect scattering rate remains much smaller than the electron-phonon scattering rate. The evolution of the G- and 2D-mode features upon doping remain unaffected by the presence of defects and the doping dependence of the D mode closely follows that of its two-phonon (2D mode) overtone. Finally, the linewidth and frequency of the G-mode phonon as well as the frequencies of the G- and 2D-mode phonons in doped graphene follow sample-independent correlations that can be utilized for accurate estimations of the charge carrier density.

First-generation magnetic random access memories based on anisotropic magnetoresistance required magnetic fields for both writing and reading. Modern all-electrical read/write memories use instead nonrelativistic spin transport connecting the storing magnetic layer with a reference ferromagnet. Recent studies have focused on electrical manipulation of magnetic moments by relativistic spin torques requiring no reference ferromagnet. Here we report the observation of a counterpart magnetoresistance effect in such a relativistic system which allows us to electrically detect the sign of the magnetization without an auxiliary magnetic field or ferromagnet. We observe the effect in a geometry in which the magnetization of a uniaxial (Ga,Mn)As epilayer is set either parallel or antiparallel to a current-induced nonequilibrium spin polarization of carriers. In our structure, this linear-in-current magnetoresistance reaches 0.2% at current density of ${10}^6{\mathrm{A}\mathrm{cm}}^{-2}$.

Here we theoretically predict and experimentally verify that permeability µ-near-zero (MNZ) materials give the opportunity to supercouple waveguides with highly mismatched cross sections. Rather distinct from the supercoupling provided by permittivity-near-zero materials we discovered several years ago, the MNZ supercoupling can take place when the transition channel cross section is much wider than that of the input and output waveguides. We develop a simple analytical model that captures the physical mechanisms that enable this remarkable effect. The MNZ supercoupling effect is experimentally verified with rectangular waveguide technology by mimicking the µ-near-zero response with the help of cylindrical split ring resonators.

Braiding of Majorana zero modes provides a promising platform for quantum information processing, which is topologically protected against errors. Strictly speaking, however, the scheme relies on infinite braiding times as it utilizes the adiabatic limit. Here we show how to minimize nonadiabatic errors for finite braiding times by finding an optimal protocol for the Majorana movement. Interestingly, these protocols are characterized by sharp transitions between Majorana motion at maximal and minimal velocities. We find that these so-called bang-bang protocols can minimize the nonadiabatic transitions of the system by orders of magnitude in comparison with naive protocols.

We analyze the pump wavelength dependence for the photoinduced enhancement of interlayer coupling in $\mathrm{L}{\mathrm{a}}_{1.885}\mathrm{B}{\mathrm{a}}_{0.115}\mathrm{Cu}{\mathrm{O}}_4$, which is promoted by optical melting of the stripe order. In the equilibrium superconducting state $(T<T_C=13\mathrm{K})$ in which stripes and superconductivity coexist, time-domain terahertz spectroscopy reveals a photoinduced blueshift of the Josephson plasma resonance after excitation with optical pulses polarized perpendicular to the $\mathrm{Cu}{\mathrm{O}}_2$ planes. In the striped nonsuperconducting state $\left(T_C<T<T_{\mathrm{SO}}\simeq 40\mathrm{K}\right)$ a transient plasma resonance similar to that seen below $T_C$ appears from a featureless equilibrium reflectivity. Most strikingly, both these effects become stronger upon tuning of the pump wavelength from the midinfrared to the visible, underscoring an unconventional competition between stripe order and superconductivity, which occurs on energy scales far above the ordering temperature.

We investigate how field-effect doping affects the structural properties, the electronic structure, and the Hall coefficient of few-layers transition-metal dichalcogenides by using density-functional theory. We consider monolayers, bilayers, and trilayers of the H polytype of ${\mathrm{MoS}}_2$, ${\mathrm{MoSe}}_2$, ${\mathrm{MoTe}}_2$, ${\mathrm{WS}}_2$, and ${\mathrm{WSe}}_2$ and provide a full database of electronic structures and Hall coefficients for hole and electron doping. We find that, for both electron and hole doping, the electronic structure depends on the number of layers and cannot be described by a rigid band shift. Furthermore, it is important to relax the structure under the asymmetric electric field. Interestingly, while the width of the conducting channel depends on the doping, the number of occupied bands at each given $\mathbf{k}$ point is almost uncorrelated with the thickness of the doping-charge distribution. Finally, we calculate within the constant-relaxation-time approximation the electrical conductivity and the inverse Hall coefficient. We demonstrate that in some cases the charge determined by Hall-effect measurements can deviate from the real charge by up to 50%. For hole-doped ${\mathrm{MoTe}}_2$ the Hall charge has even the wrong polarity at low temperature. We provide the mapping between the doping charge and the Hall coefficient. We present more than 250 band structures for all doping levels of the transition-metal dichalcogenides considered within this work.

We investigate the topological properties of density matrices, motivated by the question to what extent phenomena such as topological insulators and superconductors can be generalized to mixed states in the framework of open quantum systems. The notion of geometric phases has been extended from pure to mixed states by Uhlmann [Rep. Math. Phys. 24, 229 (1986)], who discovered an emergent gauge theory over the density matrices based on their pure state representation in a larger Hilbert space. However, since the uniquely defined square root $\sqrt{\rho }$ of a density matrix $\rho$ provides a global gauge, this construction is always topologically trivial. Here, we study a more restrictive gauge structure which can be topologically nontrivial and is capable of resolving homotopically distinct mappings of density matrices subject to various spectral constraints. Remarkably, in this framework, topological invariants can be directly defined and calculated for mixed states. In the limit of pure states, the well-known system of topological invariants for gapped band structures at zero temperature is reproduced. We compare our construction with recent approaches to Chern insulators at finite temperature.

The capacitance of a parallel-plate capacitor can depend on the applied magnetic field. Previous studies have identified capacitance changes induced via classical Lorentz force or spin-dependent Zeeman effects. Here we measure a magnetization direction-dependent capacitance in parallel-plate capacitors where one plate is a ferromagnetic semiconductor, gallium manganese arsenide. This anisotropic magnetocapacitance is due to the anisotropy in the density of states dependent on the magnetization through the strong spin-orbit interaction.

Understanding the interplay between many-body phenomena and nonequilibrium in systems with entangled spin and orbital degrees of freedom is a central objective in nanoelectronics. We demonstrate that the combination of Coulomb interaction, spin-orbit coupling, and valley mixing results in a particular selection of the inelastic virtual processes contributing to the Kondo resonance in carbon nanotubes at low temperatures. This effect is dictated by conjugation properties of the underlying carbon nanotube spectrum at zero and finite magnetic field. Our measurements on a clean carbon nanotube are complemented by calculations based on a field-theoretical Keldysh approach to the nonequilibrium Kondo problem which well reproduces the rich experimental observations in Kondo transport.

We show that the magnetization of a single “qubit” spin weakly coupled to an otherwise isolated disordered spin chain exhibits periodic revivals in the localized regime, and retains an imprint of its initial magnetization at infinite time. We demonstrate that the revival rate is strongly suppressed upon adding interactions after a time scale corresponding to the onset of the dephasing that distinguishes many-body localized phases from Anderson insulators. In contrast, the ergodic phase acts as a bath for the qubit, with no revivals visible on the time scales studied. The suppression of quantum revivals of local observables provides a quantitative, experimentally observable alternative to entanglement growth as a measure of the “nonergodic but dephasing” nature of many-body localized systems.

Recent developments have improved the attainable energy resolution in electron energy-loss spectroscopy in aberration-corrected scanning transmission electron microscopy to the order of 10 meV. In principle, this allows spectroscopy and imaging of crystals using the phonon sector of the energy-loss spectrum at atomic resolution, a supposition supported by recent simulations for molecules. Here we show that the “quantum excitation of phonons” model encapsulates the physics necessary to simulate the atomic resolution imaging of crystals based on phonon excitation and we explore the predictions of such simulations.

Topological superconductivity, implying gapless protected surface states, has recently been proposed to exist in the compound ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$. Unfortunately, low diamagnetic shielding fractions and considerable inhomogeneity have been reported in this compound. In an attempt to understand and improve on the finite superconducting volume fractions, we have investigated the effects of various growth and postannealing conditions. With a melt-growth (MG) method, diamagnetic shielding fractions of up to 56% in ${\mathrm{Cu}}_{0.3}{\mathrm{Bi}}_2{\mathrm{Se}}_3$ have been obtained, the highest value reported for this method. We investigate the efficacy of various quenching and annealing conditions, finding that quenching from temperatures above ${560}^{\circ }\mathrm{C}$ is essential for superconductivity, whereas quenching from lower temperatures or not quenching at all is detrimental. A modified floating zone (FZ) method yielded large single crystals but little superconductivity. Even after annealing and quenching, FZ-grown samples had much less chance of being superconducting than MG-grown samples. From the low shielding fractions in FZ-grown samples and the quenching dependence, we suggest that a metastable secondary phase having a small volume fraction in most of the samples may be responsible for the superconductivity.