We study the thermoelectric response of a device containing a pair of helical edge states contacted at the same temperature $T$ and chemical potential $\mu$ and connected to an external reservoir, with different chemical potential and temperature, through a side quantum dot. Different operational modes can be induced by applying a magnetic field $B$ and a gate voltage $V_g$ at the quantum dot. At finite $B$, the quantum dot acts simultaneously as a charge and a spin filter. Charge and spin currents are induced, not only through the quantum dot, but also along the edge states. We focus on linear response and analyze the regimes, which we identify as charge heat engines or refrigerator, spin heat engine, and spin refrigerator.

Motivated by experiments confirming that the optical transparency of graphene is defined through the fine structure constant and that it could be fully explained within the relativistic Dirac fermions in a two-dimensional picture, we investigate in this article how this property is affected by next-to-nearest-neighbor coupling in the low-energy continuum description of graphene. A detailed calculation within the linear response regime allows us to conclude that, somewhat surprisingly, the optical conductivity at zero temperature that determines the transparency remains robust up to this correction.

Constructing an effective field theory in terms of doped magnetic impurities [described by an O(3) vector model with a random mass term], itinerant electrons of spin-orbit coupled semiconductors (given by a Dirac theory with a relatively large mass term), and effective interactions between doped magnetic ions and itinerant electrons (assumed by an effective Zeeman coupling term), we perform the perturbative renormalization group analysis in the one-loop level based on the dimensional regularization technique. As a result, we find that the mass renormalization in dynamics of itinerant electrons acquires negative feedback effects due to quantum fluctuations involved with the Zeeman coupling term, in contrast with that of the conventional problem of quantum electrodynamics, where such interaction effects enhance the fermion mass more rapidly. Recalling that the applied magnetic field decreases the band gap in the presence of spin-orbit coupling, this renormalization group analysis shows that the external magnetic field overcomes the renormalized band gap, allowed by doped magnetic impurities even without ferromagnetic ordering. In other words, the Weyl metal physics can be controlled by doping magnetic impurities into spin-orbit coupled semiconductors, even if the external magnetic field alone cannot realize the Weyl metal phase due to relatively large band gaps of semiconductors. Furthermore, we emphasize that quasiparticles do not exist in this emergent disordered Weyl metal phase due to correlations with strong magnetic fluctuations. This non-Fermi-liquid type Weyl metal state may be regarded to be a anomalous metallic phase in the respect that a topologically nontrivial band structure appears in the vicinity of quantum criticality.

In this work we address the physics of individual three-dimensional Weyl nodes subject to a moderate concentration of disorder. Previous analysis indicates the presence of a quantum phase transition below which disorder becomes irrelevant and the integrity of sharp nodal points of vanishing spectral density is preserved in this system. This statement appears to be at variance with the inevitable presence of statistically rare fluctuations which cannot be considered as weak and must have strong influence on the system's spectrum, no matter how small the average concentration. We here reconcile the two pictures by demonstrating that rare fluctuation potentials in the Weyl system generate a peculiar type of resonances which carry spectral density in any neighborhood of zero energy, but never at zero. In this way, the vanishing of the DoS for weak disorder survives the inclusion of rare events. We demonstrate this feature by considering three different models of disorder, each emphasizing specific aspects of the problem: a simplistic box potential model, a model with Gaussian distributed disorder, and one with a finite number of $s$-wave scatterers. Our analysis also explains why the protection of the nodal DoS may be difficult to see in simulations of finite size lattices.

Defects play crucial roles in the photonic and chemical activities of ${\mathrm{TiO}}_2$. The origin of the deep band-gap defect state $S_{bg}$ in the rutile ${\mathrm{TiO}}_2$(110) surface has remained controversial for quite a long time. Using many-body Green's function theory, we believe that $S_{bg}$ can be attributed only to $\sigma$ bonds formed between $3d$ orbitals at the Ti interstitial, while the nonbonded Ti $3d$ defect states from the oxygen vacancy and polaron, which are held to be responsible for $S_{bg}$ by the present prevailing view, are shallow regardless of their spatial distribution. Especially, we discover the defect-induced appreciable downshift of unoccupied Ti $3d$ bands which should be the key for accurately describing the electronic structure of ${\mathrm{TiO}}_2$ but was missed in previous studies based on density functional theory. Our model could more consistently and more reasonably account for various experimental phenomena on rutile (110) than the current model based on the oxygen vacancy and polaron.

We introduce and explore a one-dimensional “hybrid” quantum circuit model consisting of both unitary gates and projective measurements. While the unitary gates are drawn from a random distribution and act uniformly in the circuit, the measurements are made at random positions and times throughout the system. By varying the measurement rate we can tune between the volume law entangled phase for the random unitary circuit model (no measurements) and a “quantum Zeno phase” where strong measurements suppress the entanglement growth to saturate in an area law. Extensive numerical simulations of the quantum trajectories of the many-particle wave functions (exploiting Clifford circuitry to access systems up to 512 qubits) provide evidence for a stable “weak measurement phase” that exhibits volume-law entanglement entropy, with a coefficient decreasing with increasing measurement rate. We also present evidence for a continuous quantum dynamical phase transition between the “weak measurement phase” and the “quantum Zeno phase,” driven by a competition between the entangling tendencies of unitary evolution and the disentangling tendencies of projective measurements. Detailed steady-state and dynamic critical properties of this quantum entanglement transition are accessed.

Spin-orbit interactions often are taken into account via pseudopotentials or related treatments of core electrons. In this case, the commonly employed Kohn-Sham methods with noncollinear spin are not applicable from a formal point of view. Instead, more general methods in the framework of spin-current density-functional theory (SCDFT) have to be employed. Here, we first review the derivation of SCDFT as a unifying theory that encompasses density-functional theory (DFT) with noncollinear spin, current DFT, and a DFT treatment of currents of the spin. We discuss which parts of SCDFT necessarily have to be taken into account in which physical situation and which parts can be considered on an optional basis. Then, an exact-exchange-only (EXX) SCDFT method (SCEXX) is used to investigate pressure-driven topological phase transition in SnTe and AlBi as representative systems. An estimate of the effect of correlation is obtained by a screening of exchange in the EXX methods. SnTe undergoes a transition from a trivial to a topological insulator, while AlBi is transformed from a topological metal with inverted band edges to a trivial insulator. We show that there is a sizable range of lattice parameters for which electronic structures obtained with noncollinear spin EXX (NCSEXX) and SCEXX belong to different topological classes. Thus, differences between results obtained with NCSEXX and SCEXX, which are due to the consideration of spin currents in SCEXX, are of practical importance in situations when a material simultaneously is characterized by strong spin-orbit interactions and a band ordering governed by small energy differences, e.g., narrow band gaps in semiconductors or small negative gaps in metals with inverted band edges. This is a typical situation for topological materials suggesting to use SCDFT methods for such materials.

The effect of electronic correlation on $\mathrm{WT}{\mathrm{e}}_2$ has been investigated by means of angle-resolved photoemission spectroscopy (ARPES) and band-structure calculation. In the ARPES results, the valence band top with Te $5p$ character reaches the Fermi level and forms complicated hole pockets around the zone center. In addition, two electron pockets are observed besides the hole pockets. The position of the electron pockets is inconsistent with the prediction of band calculation, suggesting the importance of electronic correlation in $\mathrm{WT}{\mathrm{e}}_2$. The present analysis indicates the correlation effect is associated with the excitonic coupling between the W $5d$ electron and Te $5p$ hole bands.

Three-dimensional Weyl semimetals have been observed to have negative magnetoresistance (MR) with the magnetic field parallel to the electric field and positive MR with the magnetic field perpendicular to the electric field. It is understood that the negative MR is due to a Berry phase that causes the chiral anomaly, while the positive MR can be understood from a semiclassical transport theory. We solve a semiclassical Boltzmann equation with both the Berry phase and Lorentz force terms present for an arbitrary angle of the applied magnetic field relative to the electric field within the relaxation-time approximation. The plots of the magnetoconductivity show both the Berry phase and Lorentz force effects. For some angles between the electric and magnetic fields, the conductivity has a minimum, where the forces balance each other. The standard semiclassical theory does not show the linear increase in the transverse MR with the magnetic field seen experimentally. By assuming a magnetic-field-dependent transport time, we find the transverse MR increases linearly with the magnetic field. The low-field MR does change from negative to positive as one rotates the magnetic field away from the direction of the electric field. As the magnetic field is increased, we find in some cases the MR starts out negative and then becomes positive. This is consistent with recent experimental data in ${\text{Cd}}_3{\text{As}}_2$.

Three-particle complexes consisting of two holes in the completely filled zero-electron Landau level and an excited electron in the unoccupied first Landau level are investigated in a quantum Hall insulator. The distinctive features of these three-particle complexes are an electron-hole mass symmetry and the small energy gap of the quantum Hall insulator itself. Theoretical calculations of the trion energy spectrum in a quantizing magnetic field predict that, besides the ground state, trions feature a hierarchy of excited bound states. In agreement with the theoretical simulations, we observe new photoluminescence lines related to the excited trion states. A relatively small energy gap allows the binding of three-particle complexes with magnetoplasma oscillations and the formation of plasmarons. The plasmaron properties are investigated experimentally.

Shockley surface states of a bulk crystal with both time reversal and space inversion symmetries exhibit the Rashba spin splitting due to the broken space inversion symmetry at the surface. Since the evanescent states in the bulk region are doubly degenerate with respect to spin degrees of freedom even in the presence of spin-orbit interaction (SOI), one might think that the entire spin splitting occurs via the SOI in the surface region where the potential energy deviates from the bulk one. In the present work, we elucidate why this is not the case. Namely, in the presence of SOI, the complex energy bands are modified such that a pair of evanescent states having the same energy and the same complex wave number become two distinct solutions of the Schrödinger equation that do not satisfy the same boundary condition. Since the tail of the surface-state wave function is expressed as a superposition of these evanescent waves, the bulk region also contributes to the Rashba spin splitting. We illustrate this effect by a first-principles calculation for Au(111) and by a simplified $sp$-band model Hamiltonian on a square lattice.

All-optical modulation of light relies on exploiting intrinsic material nonlinearities [V. R. Almeida et al., Nature 431, 1081 (2004)]. However, this optical control is rather challenging due to the weak dependence of the refractive index and absorption coefficients on the concentration of free carriers in standard semiconductors [R. A. Soref and B. R. Bennett, Proc. SPIE 704, 32 (1987)]. To overcome this limitation, resonant structures with high spatial and spectral confinement are carefully designed to enhance the stored electromagnetic energy, thereby requiring lower excitation power to achieve significant nonlinear effects [K. Nozaki et al., Nat. Photonics 4, 477 (2010)]. Small mode-volume and high-quality ($Q$)-factor cavities also offer an efficient coherent control of the light field and the targeted optical properties. Here, we report on optical resonances reaching $Q\sim {10}^5$ induced by disorder on photonic/phononic-crystal waveguides. At relatively low excitation powers (below $1\text{mW}$), these cavities exhibit nonlinear effects leading to periodic (up to $\sim 35$ MHz) oscillations of their resonant wavelength. Our system represents a test bed to study the interplay between structural complexity and material nonlinearities and their impact on localization phenomena and introduces a different functionality to the toolset of disordered photonics.

We use above-band-gap optical excitation, via a 1047-nm laser, to hyperpolarize the ${}^{31}\mathrm{P}$ spins in low-doped ($N_D=6\times {10}^{15}{\mathrm{cm}}^{-3}$) natural abundance silicon at 4.2 K and 6.7 T, and inductively detect the resulting NMR signal. The 30-kHz spectral linewidth observed is dramatically larger than the 600-Hz linewidth observed from a ${}^{28}\mathrm{Si}$-enriched silicon crystal. We show that the broadening is consistent with previous electron-nuclear double-resonance results showing discrete isotope mass effect contributions to the donor hyperfine coupling. A secondary source of broadening is likely due to variations in the local strain, induced by the random distribution of different isotopes in natural silicon. The nuclear spin $T_1$ and the buildup time for the optically induced ${}^{31}\mathrm{P}$ hyperpolarization in the natural abundance silicon sample were observed to be $178\pm 47$ and $69\pm 6$ s, respectively, significantly shorter than the values previously measured in ${}^{28}\mathrm{Si}$-enriched samples under the same conditions. We measured the $T_1$ and hyperpolarization buildup time for the ${}^{31}\mathrm{P}$ signal in natural abundance silicon at 9.4 T to be $54\pm 31$ and $13\pm 2$ s, respectively. The shorter buildup and nuclear spin $T_1$ times at high field are likely due to the shorter electron spin $T_1$, which drives nuclear spin relaxation via nonsecular hyperfine interactions. At 6.7 T, the phosphorus nuclear spin $T_2$ was $16.7\pm 1.6$ ms at 4.2 K, a factor of 4 shorter than in ${}^{28}\mathrm{Si}$-enriched crystals. This was observed to shorten to $1.9\pm 0.4$ ms in the presence of the infrared laser.

Negative Poisson's ratio (NPR) is a counterintuitive material elastic constant that can lead to many unusual auxetic properties. Here, using first-principles calculations, we report tunable negative Poisson's ratio in the out-of-plane direction in group-IV monochalcogenide monolayers $MX$ ($M=\text{Sn}$, Ge and $X=\text{S}$, Se). SnSe, GeS, and SnS monolayers have intrinsic NPR ${\nu }_{zx}$ ranging from $-0.004$ to $-0.210$ in armchair ($x$) tension, whereas GeSe monolayer possesses a much larger NPR ${\nu }_{zy}$ of $-0.433$ in zigzag ($y$) tension. Our analysis attributes the NPR effects to the relative position of $M$ and $X$ in the puckered structure and the smaller bending stiffness of $M\text{−}X\text{−}M$ bond angle. We further established the correlation between electronic structures of materials and their crystal structures. It allows us to fine tune GeSe structure via electron doping, leading to a reversible and continuous change of ${\nu }_{zy}$ from $-0.821$ up to 0.895. We also demonstrate the concept of strain engineering GeSe monolayer to switch its Poisson's ratio ${\nu }_{zx}$ between two different values: 0.583 and $-0.433$. Our in-depth study provides not only fundamental knowledge but also practical routes for designing 2D smart materials with tunable negative Poisson's ratio, which are desirable for smart devices at small scale.

We investigate large deviations of the work performed in a quantum quench across two different phases separated by a quantum critical point, using as an example the Dicke model quenched from its superradiant to its normal phase. We extract the distribution of the work from the Loschmidt amplitude and compute for both the corresponding large-deviation forms. Comparing these findings with the predictions of the classification scheme put forward in Gambassi and Silva [Phys. Rev. Lett. 109, 250602 (2012)], we are able to identify a regime which is in fact distinct to the ones identified so far: here the rate function exhibits a nonanalytical point which is a strong indication of the existence of an out-of-equilibrium phase transition in the rare fluctuations of the work.

In this work we report detailed experimental results and band structure calculations to establish a subtle link between the crystal structure and Griffiths phase (GP) behavior for the geometrically frustrated intermetallic $\mathrm{Gd}{\mathit{M}}_x{\mathrm{Sn}}_{2-\delta }$ (M = Co, Ni, Cu; $0<\mathit{x}<1,0\le \delta \le 0.22$) compounds. The crystal structure analysis through powder x-ray diffraction patterns reveals that the atomic positions of the M atoms in the GP analogs are slightly displaced in comparison to those of non-GP members of this series. Further, the band structure calculation shows that this slightly differing atomic position of M atoms results in narrowing in M d bands and the ferromagnetic clusters centered on the T atoms are responsible for GP behavior. This effect is insignificant in non-GP members.