We develop a simple method to study the zero-point and thermally renormalized electron energy ${\varepsilon }_{\mathbf{k}n}\left(T\right)$ for $\mathbf{k}n$ the conduction band minimum or valence maximum in polar semiconductors. We use the adiabatic approximation, including an imaginary broadening parameter $i\delta$ to suppress noise in the density-functional integrations. The finite $\delta$ also eliminates the polar divergence which is an artifact of the adiabatic approximation. Nonadiabatic Fröhlich polaron methods then provide analytic expressions for the missing part of the contribution of the problematic optical phonon mode. We use this to correct the renormalization obtained from the adiabatic approximation. Test calculations are done for zinc-blende GaN for an $18\times 18\times 18$ integration grid. The Fröhlich correction is of order $-0.02$ eV for the zero-point energy shift of the conduction band minimum, and $+0.03$ eV for the valence band maximum; the correction to renormalization of the 3.28 eV gap is $-0.05$ eV, a significant fraction of the total zero point renormalization of $-0.15$ eV.

Quantum-statistical effects occur during the propagation of electromagnetic (EM) waves inside the dielectric media or metamaterials, which include a large class of nanophotonic and plasmonic waveguides with dissipation and noise. Exploiting the formal analogy between the Schrödinger equation and the Maxwell equations for dielectric linear media, we rigorously derive the effective Hamiltonian operator which describes such propagation. This operator turns out to be essentially non-Hermitian in general, and pseudo-Hermitian in some special cases. Using the density operator approach for general non-Hermitian Hamiltonians, we derive a master equation that describes the statistical ensembles of EM wave modes. The method also describes the quantum dissipative and decoherence processes which happen during the wave's propagation, and, among other things, it reveals the conditions that are necessary to control the energy and information loss inside the above-mentioned materials.

We theoretically study the stability of three-dimensional Dirac semimetals against short-range electron-electron interaction and quenched time-reversal symmetric disorder (but excluding mass disorder). First, we focus on the clean interacting and the noninteracting dirty Dirac semimetal separately and show that they support two distinct quantum critical points. Using renormalization group techniques, we find that while interaction driven quantum critical points are Gaussian (mean-field) in nature, describing quantum phase transitions into various broken symmetry phases, the ones controlled by disorder are non-Gaussian, capturing the transition to a metallic phase. We classify such diffusive quantum critical points based on the transformation of disorder vertices under a continuous chiral rotation. Our weak coupling renormalization group analysis suggests that two distinct quantum critical points are stable in an interacting dirty Dirac semimetal (with chiral symmetric randomness), and a multicritical point (at finite interaction and disorder) results from their interplay. By contrast, the chiral symmetry breaking disorder driven critical point is unstable against weak interactions. Effects of weak disorder on the ordering tendencies in Dirac semimetal are analyzed. The clean interacting critical points, however, satisfy the Harris criterion, and are therefore expected to be unstable against bond disorder. Although the weak coupling analysis is inadequate to establish the ultimate stability of these fixed points in the strong coupling regime (when both interaction and disorder are strong), they can still govern crossover behaviors in Dirac semimetals over a large length scale, when either interaction or randomness is sufficiently weak. Scaling behavior of various physical quantities (e.g., spectral gap, specific heat, density of states, conductivity) and associated experimental signatures across various quantum phase transitions are discussed.

Combining the effect of layer mixing, mass mismatch, and intrinsic defects, we have investigated the origin of very low phonon conductivity $k_p$ in thermoelectric (TE) $\text{BiCuO}Q$ $(Q$: S, Se, Te) compounds. Based on the first-principles anharmonic, lattice dynamics calculations, we use the single-mode relaxation time approximation of the linearized phonon Boltzmann equation, which shows good agreement with experiments. Here, we found that the most important parameter for low $k_p$ is the interlayer interaction between the BiO and $\text{Cu}Q$ layers. By analyzing the phonon linewidth distribution, which indicates the phonon scattering rate, we propose that the interlayer interactions play a critical role on suppressing $k_p$, i.e., the heterolayered crystal controls these interlayer interactions, achieving low $k_p$ and optimal TE properties.

Motivated by recent nuclear magnetic resonance (NMR) experiments, we present a microscopic $s{p}^3$ tight-binding model calculation of the NMR shifts in bulk ${\mathrm{Bi}}_2{\mathrm{Se}}_3$  and ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. We compute the contact, dipolar, orbital and core polarization contributions to the carrier-density-dependent part of the NMR shifts in ${}^{209}\mathrm{Bi},{}^{125}\mathrm{Te}$, and ${}^{77}\mathrm{Se}$. The spin-orbit coupling and the layered crystal structure result in a contact Knight shift with strong uniaxial anisotropy. Likewise, because of spin-orbit coupling, dipolar interactions make a significant contribution to the isotropic part of the NMR shift. The contact interaction dominates the isotropic Knight shift in ${}^{209}\mathrm{Bi}$ NMR, even though the electronic states at the Fermi level have a rather weak $s$-orbital character. In contrast, the contribution from the contact hyperfine interaction to the NMR shift of ${}^{77}\mathrm{Se}$ and ${}^{125}\mathrm{Te}$ is weak compared to the dipolar and orbital shifts therein. In all cases, the orbital shift is at least comparable to the contact and dipolar shifts, while the shift due to core polarization is subdominant (except for Te nuclei located at the inversion centers). By artificially varying the strength of spin-orbit coupling, we evaluate the evolution of the NMR shift across a band inversion but find no clear signature of the topological transition.

The lattice thermal expansion and conductivity in bulk Mo and W-based transition metal dichalcogenides are investigated by means of density functional and Boltzmann transport theory calculations. To this end, a recent van der Waals density functional (vdW-DF-CX) is employed, which is shown to yield excellent agreement with reference data for the structural parameters. The calculated in-plane thermal conductivity compares well with experimental room-temperature values, when phonon-phonon and isotopic scattering are included. To explain the behavior over the entire available temperature range one must, however, include additional (temperature independent) scattering mechanisms that limit the mean free path. Generally, the primary heat carrying modes have mean free paths of $1\mu \text{m}$ or more, which makes these materials very susceptible to structural defects. The conductivity of Mo- and W-based transition metal dichalcogenides is primarily determined by the chalcogenide species and increases in the order Te-Se-S. While for the tellurides and selenides the transition metal element has a negligible effect, the conductivity of ${\mathrm{WS}}_2$ is notably higher than for ${\mathrm{MoS}}_2$, which may be traced to the much larger phonon band gap of the former. Overall, the present study provides a consistent set of thermal conductivities that reveal chemical trends and constitute the basis for future investigations of van der Waals solids.

The transition-metal dichalcogenide $1T\text{−}{\mathrm{TaS}}_2$ exhibits a rich set of charge-density-wave (CDW) orders. Recent investigations suggested that using light or an electric field can manipulate the commensurate CDW (CCDW) ground state. Such manipulations are considered to be determined by charge-carrier doping. Here we use first-principles calculations to simulate the carrier-doping effect on the CCDW in $1T\text{−}{\mathrm{TaS}}_2$. We investigate the charge-doping effects on the electronic structures and phonon instabilities of the $1T$ structure, and we analyze the doping-induced energy and distortion ratio variations in the CCDW structure. We found that both in bulk and monolayer $1T\text{−}{\mathrm{TaS}}_2$, the CCDW is stable upon electron doping, while hole doping can significantly suppress the CCDW, implying different mechanisms of such reported manipulations. Light or positive perpendicular electric-field-induced hole doping increases the energy of the CCDW, so that the system transforms to a nearly commensurate CDW or a similar metastable state. On the other hand, even though the CCDW distortion is more stable upon in-plane electric-field-induced electron injection, some accompanied effects can drive the system to cross over the energy barrier from the CCDW to a nearly commensurate CDW or a similar metastable state. We also estimate that hole doping can introduce potential superconductivity with a $T_c$ of 6–7 K. Controllable switching of different states such as a CCDW/Mott insulating state, a metallic state, and even a superconducting state can be realized in $1T\text{−}{\mathrm{TaS}}_2$. As a result, this material may have very promising applications in future electronic devices.

We study the charge and spin density distributions of excitonic insulator (EI) states in the tight-binding approximation. We first discuss the charge and spin densities of the EI states when the valence and conduction bands are composed of orthogonal orbitals in a single atom. We show that the anisotropic charge or spin density distribution occurs in a unit cell (or atom) and a higher rank electric or magnetic multipole moment becomes finite, indicating that the EI state corresponds to the multipole order. A full description of the multipole moments for the $s$, $p$, and $d$ orbitals is then given in general. We find that, in contrast to the conventional density-wave states, the modulation of the total charge or net magnetization does not appear in this case. However, when the conduction and valence bands include the component of the same orbital, the modulation of the total charge or net magnetization appears, as in the conventional density-wave state. We also discuss the electron density distribution in the EI state when the valence and conduction bands are composed of orbitals located in different atoms. We show that the excitonic ordering in this case corresponds to the bond order formation. Based on the results thus obtained we discuss the EI states of real materials recently reported.

A theoretical frame for two-photon photoemission is derived from the general theory of pump-probe photoemission, assuming that not only the probe but also the pump pulse is sufficiently weak. This allows us to use a perturbative approach to compute the lesser Green function within the Keldysh formalism. Two-photon photoemission spectroscopy is a widely used analytical tool to study nonequilibrium phenomena in solid materials. Our theoretical approach aims at a material-specific, realistic, and quantitative description of the time-dependent spectrum based on a picture of effectively independent electrons as described by the local-density approximation in band-structure theory. To this end we follow Pendry's one-step theory of the photoemission process as close as possible and heavily make use of concepts of relativistic multiple-scattering theory, such as the representation of the final state by a time-reversed low-energy electron diffraction state. The formalism allows for a quantitative calculation of the time-dependent photocurrent for moderately correlated systems like simple metals or more complex compounds like topological insulators. An application to the Ag(100) surface is discussed in detail.

When composite particles—such as small molecules, nuclei, or photogenerated excitons in semiconductors—are scattered by an external potential, energy may be transferred between the c.m. and the internal degrees of freedom. An accurate dynamical modeling of this effect is pivotal in predicting diverse scattering quantities and reaction cross sections, and allows us to rationalize time-resolved energy and localization spectra. Here, we show that time-dependent scattering of a quantum composite particle with an arbitrary, nonperturbative external potential can be obtained by propagating the c.m. degrees of freedom with a properly designed local self-energy potential. The latter embeds the effect of internal virtual transitions and can be obtained by the knowledge of the stationary internal states. The case is made by simulating Wannier-Mott excitons in one- and two-dimensional semiconductor heterostructures. The self-energy approach shows very good agreement with numerically exact Schrödinger propagation for scattering potentials where a mean-field model cannot be applied, at a dramatically reduced computational cost.

We propose a simple yet efficient mechanism for passive error correction in topological quantum memories. Our scheme relies on driven-dissipative ancilla systems which couple to local excitations (anyons) and make them “sink” in energy, with no required interaction among ancillae or anyons. Through this process, anyons created by some thermal environment end up trapped in potential “trenches” that they themselves generate, which can be interpreted as a “memory foam” for anyons. This self-trapping mechanism provides an energy barrier for anyon propagation and removes entropy from the memory by favoring anyon recombination over anyon separation (responsible for memory errors). We demonstrate that our scheme leads to an exponential increase of the memory-coherence time with system size $L$, up to an upper bound $L_{\max }$, which can increase exponentially with $\mathrm{\Delta }/T$, where $T$ is the temperature and $\mathrm{\Delta }$ is some energy scale defined by potential trenches. This results in a double exponential increase of the memory time with $\mathrm{\Delta }/T$, which greatly improves over the Arrhenius (single-exponential) scaling found in typical quantum memories.

We investigate the average structure, local structure, and magnetic behavior of Heusler alloys of the composition ${\mathrm{Mn}}_{1-x}{\mathrm{Fe}}_x{\mathrm{Ru}}_2\mathrm{Sn}$, between antiferromagnetic (AFM) ${\mathrm{MnRu}}_2\mathrm{Sn}$ and ferromagnetic (FM) ${\mathrm{FeRu}}_2\mathrm{Sn}$ (often written ${\mathrm{Ru}}_2\mathrm{MnSn}$ and ${\mathrm{Ru}}_2\mathrm{FeSn}$). Using a combination of neutron total scattering, electron microscopy, and ${}^{57}\mathrm{Fe}$ Mössbauer spectroscopy, we conclude that true solid solutions are formed across the compositional space investigated, with Fe substituting for Mn on the Heusler lattice, with little or no antisite disorder. Despite the lack of chemical phase separation, magnetic phase separation is present in compositions near $x=0.50$, where the coexistence of AFM and FM domains is confirmed by 15 K neutron diffraction. At these intermediate compositions a large increase in magnetic coercivity is observed, in excess of 1 kOe, attributed to local exchange interactions.

We numerically examine driven skyrmions interacting with a periodic quasi-one-dimensional substrate where the driving force is applied either parallel or perpendicular to the substrate periodicity direction. For perpendicular driving, the particles in a purely overdamped system simply slide along the substrate minima; however, for skyrmions where the Magnus force is relevant, we find that a rich variety of dynamics can arise. In the single skyrmion limit, the skyrmion motion is locked along the driving or longitudinal direction for low drives, while at higher drives a transition occurs to a state in which the skyrmion moves both transverse and longitudinal to the driving direction. Within the longitudinally locked phase we find a pronounced speedup effect that occurs when the Magnus force aligns with the external driving force, while at the transition to transverse and longitudinal motion, the skyrmion velocity drops, producing negative differential conductivity. For collectively interacting skyrmion assemblies, the speedup effect is still present and we observe a number of distinct dynamical phases, including a sliding smectic phase, a disordered or moving liquid phase, a moving hexatic phase, and a moving crystal phase. The transitions between the dynamic phases produce distinct features in the structure of the skyrmion lattice and in the velocity-force curves. We map these different phases as a function of the ratio of the Magnus term to the dissipative term, the substrate strength, the commensurability ratio, and the magnitude of the driving force.

The rules that govern spin exchange interaction in pristine graphene nanostructures are constrained by the bipartite character of the lattice, so that the sign of the exchange is determined by whether magnetic moments are on the same sublattice or not. The synthesis of graphene ribbons with perfect zigzag edges and a fluoranthene group with a pentagon ring, a defect that breaks the bipartite nature of the honeycomb lattice, has been recently demonstrated. Here we address how the electronic and spin properties of these structures are modified by such defects, both for indirect exchange interactions as well as the emergent edge magnetism, studied both with density functional theory and mean-field Hubbard model calculations. In all instances we find that the local breakdown of the bipartite nature at the defect reverts the sign of the otherwise ferromagnetic correlations along the edge, introducing a locally antiferromagnetic intraedge coupling and, for narrow ribbons, also revert the antiferromagnetic interedge interactions that are normally found in pristine ribbons. Our findings show that these pentagon defects are a resource that permits us to engineer the spin exchange interactions in graphene-based nanostructures.

Point contact Andreev reflection spectroscopy is employed to extract the effective Fermi-level spin polarization of three distinct compositions from the (${\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x$)${}_2{\mathrm{Te}}_3$ topological insulator family. The end members, ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and ${\mathrm{Sb}}_2{\mathrm{Te}}_3$, exhibit high polarization of 70(4)% and 57(3)%, respectively. High-field $({\mu }_{0}H=14\mathrm{T})$ point contact spectroscopy shows carrier depletion close to the Fermi level for these two compositions with small activation gaps of 0.40(4) and 0.28(2) meV, respectively. The almost fully suppressed bulk conductivity in the (${\mathrm{Bi}}_{0.18}{\mathrm{Sb}}_{0.82}$)${}_2{\mathrm{Te}}_3$ results in an even higher spin polarization of 83(9)%. Further, it is demonstrated that magnetic doping with Cr and V tends to reduce the spin-polarization values with respect to the ones of the pure compositions. ${\mathrm{Bi}}_{1.97}{\mathrm{Cr}}_{0.03}{\mathrm{Te}}_3, {\mathrm{Sb}}_{1.975}{\mathrm{Cr}}_{0.025}{\mathrm{Te}}_3, {\mathrm{Bi}}_{1.975}{\mathrm{V}}_{0.025}{\mathrm{Te}}_3$, and ${\mathrm{Sb}}_{1.97}{\mathrm{V}}_{0.03}{\mathrm{Te}}_3$ exhibit spin polarization of 52%, 52%, 58%, and 50%, respectively. In view of the rather high effective polarization, nonmagnetic topological insulators close to (${\mathrm{Bi}}_{0.18}{\mathrm{Sb}}_{0.82}$)${}_2{\mathrm{Te}}_3$ may provide a path towards the characterization of pair-breaking mechanisms in spin-triplet superconductors.

When charge current passes through a normal metal that exhibits the spin Hall effect, spin accumulates at the edge of the sample in the transverse direction. We predict that this spin accumulation, or spin voltage, enables quantum tunneling of spin through an insulator or vacuum to reach a ferromagnet without transferring charge. In a normal metal/insulator/ferromagnetic insulator trilayer (such as Pt/oxide/YIG), the quantum tunneling explains the spin-transfer torque and spin pumping that exponentially decay with the thickness of the insulator. In a normal metal/insulator/ferromagnetic metal trilayer (such as Pt/oxide/Co), the spin transfer in general does not decay monotonically with the thickness of the insulator. Combining with the spin Hall magnetoresistance, this tunneling mechanism points to the possibility of a tunneling spectroscopy that can probe the magnon density of states of a ferromagnetic insulator in an all-electrical and noninvasive manner.