Magnetically doped semiconductors are well known for their giant Zeeman splittings which can reach several meV even in relatively small external magnetic fields. After preparing a nonequilibrium exciton distribution via optical excitation, the spin dynamics in diluted magnetic semiconductor quantum wells is typically governed by spin-flip scattering processes due to the exciton-impurity exchange interaction. Our theoretical calculations show that the giant Zeeman splitting in these materials in combination with the influence of longitudinal acoustic phonons lead to a quantum ratchet-type dynamics, resulting in an almost complete reversal of the carrier spin polarization at very low temperatures. Furthermore, we find that the predictions of a much simpler rate-equation approach qualitatively agree with a more advanced and numerically demanding quantum-kinetic description of the spin dynamics for a wide range of temperatures, although quantitative differences are noticeable.

We develop a microscopic theory of an unconventional photogalvanic effect in two-dimensional materials with the Dirac energy spectrum of the carriers of charge under strong driving. As a test bed, we consider a layer of a transition metal dichalcogenide, exposed to two different electromagnetic fields. The first pumping field is circularly polarized, and its frequency exceeds the material band gap. It creates an extremely nonequilibrium distribution of electrons and holes in one valley (K) and opens dynamical gaps, whereas the other valley (${\mathrm{K}}^{\prime }$) remains empty due to the valley-dependent interband selection rules. The second probe field has the frequency much smaller than the material band gap. It generates intraband perturbations of the nonequilibrium carriers density, resulting in the photogalvanic current due to the trigonal asymmetry of the dispersions. This current shows thresholdlike behavior due to the dynamical gap opening and renormalizations of the density of states and velocity of quasiparticles.

Two-dimensional Floquet systems consisting of irradiated valley-polarized metal are investigated. For the corresponding static systems, we consider two graphene models of valley-polarized metal with either a staggered sublattice or uniform intrinsic spin-orbital coupling, whose Dirac point energies are different from the intrinsic Fermi level. If the frequency of irradiation is appropriately designed, the largest dynamical gap (first-order dynamical gap) opens around the intrinsic Fermi level. In the presence of the irradiation, two types of edge states appear at the zigzag edge of the semi-infinite sheet with energy within the first-order dynamical gap: the Floquet edge states and the strongly localized edge states. In narrow zigzag nanoribbons, the Floquet edge states are gapped out by the finite-size effect and the strongly localized edge states remain gapless. As a result, the conducting channels of the nanoribbons consist of the strongly localized edge states. Under the first and second model, the strongly localized edge states carry one-way spin-polarized and one-way charge current around the intrinsic Fermi level, respectively. Thus, the narrow zigzag nanoribbons of the first and second model have asymmetric spin and charge transmission rates, respectively. Quantum-transport calculations predict sizable pumped currents of charge and spin, which could be controlled by the Fermi level.

We investigate the properties of an impurity particle interacting with a Fermi gas in a Chern-insulating state. The interaction leads to the formation of an exotic polaron, which consists of a coherent superposition of the topologically trivial impurity and the surrounding topological cloud. We characterize this intriguing topologically composite object by calculating its transverse (Hall) conductivity, using diagrammatic as well as variational methods. The “polaronic Hall conductivity,” i.e., the transverse drag exerted by the dressing cloud on the impurity, is shown to exhibit a sharp jump from zero to a finite value whenever the surrounding cloud enters a topologically nontrivial state. In this way, the polaron partially inherits the topological properties of the Chern insulator through genuine interaction effects. This is also analyzed at the microscopic level of wave functions, by identifying a “composite Berry curvature” for the polaron, which closely mimics the Berry curvature of the Chern insulator's band structure. Finally, we discuss how this interplay between topology and many-body correlations can be studied in cold-atom experiments, using available technologies.

Recent theoretical and experimental results from quasi-one-dimensional heavy-hole systems have suggested that heavy-hole gases have a strongly anisotropic $g$ factor. In this theoretical work, we propose a method for measuring this anisotropy using transverse magnetic focusing (TMF). We demonstrate that for experimentally accessible fields, the $g$-factor anisotropy leads to a relative variation in the characteristic of spin splitting of the TMF spectrum which allows for the measurement of the anisotropy of the $g$ factor. We show that this variation is insensitive to additional spin-orbit interactions, and is resolvable with current devices.

Motivated by recent scanning tunneling microscopy and spectroscopy experiments on probing single vacancies in black phosphorus, we present a theory for Fano antiresonances induced by coupling between vacancy states and edge states of zigzag phosphorene nanoribbons (zPNRs). To this end, in the first step, using the tight-binding Hamiltonian, we obtain an analytic solution on the lattice for the state associated with a single vacancy located in the bulk phosphorene which shows a highly anisotropic localization in real space. For a finite zigzag ribbon, in the absence of particle-hole symmetry, the localized state induced by vacancies can couple with the wave functions of the edge states, which results in the formation of a new bound state. The energy of the vacancy bound state lies inside the quasiflat band composed of edge states when the vacancy locates sufficiently far away from the edge. Then, we employ the $T$-matrix Lippmann-Schwinger approach to obtain an explicit analytical expression for the scattering amplitude of the edge electrons of a zPNR through the presence of a single vacancy which shows a Fano resonance profile with a tunable dip. We demonstrate that varying the position of the vacancy produces substantially different effects on the resonance width, the resonance energy position, and the asymmetry parameter of the Fano line shape. Furthermore, the validity of the theoretical descriptions is verified numerically by using the Landauer approach.

Fundamental upper bounds are given for the plasmonic multipole absorption and scattering of a rotationally invariant dielectric sphere embedded in a lossy surrounding medium. A specialized Mie theory is developed for this purpose and when combined with the corresponding generalized optical theorem, an optimization problem is obtained which is explicitly solved by straightforward analysis. In particular, the absorption cross section is a concave quadratic form in the related Mie (scattering) parameters and the convex scattering cross section can be maximized by using a Lagrange multiplier constraining the absorption to be non-negative. For the homogeneous sphere, the Weierstrass preparation theorem is used to establish the existence and the uniqueness of the plasmonic singularities and explicit asymptotic expressions are given for the dipole and the quadrupole. It is shown that the optimal passive material for multipole absorption and scattering of a small homogeneous dielectric sphere embedded in a dispersive medium is given approximately as the complex conjugate and the real part of the corresponding pole positions, respectively. Numerical examples are given to illustrate the theory, including a comparison with the plasmonic dipole and quadrupole resonances obtained in gold, silver, and aluminum nanospheres based on some specific Brendel-Bormann (BB) dielectric models for these metals. Based on these BB models, it is interesting to note that the metal spheres can be tuned to optimal absorption at a particular size at a particular frequency.

Both $\alpha \text{−}\mathrm{PdB}{\mathrm{i}}_2$ and $\beta \text{−}\mathrm{PdB}{\mathrm{i}}_2$ are superconductors with topological nontrivial signs. Here we report that the $\alpha \text{−}\mathrm{PdB}{\mathrm{i}}_2$ superconductor is converted by pressure into the β-phase superconducting polymorph, with the superconductivity being further enhanced upon decompression. Through high-pressure resistance and synchrotron x-ray-diffraction experiments, we show that the α phase transforms into the β phase at $P_c\sim 8$ GPa, above which the superconductivity is robust up to the maximum pressure investigated in this work. More interestingly, when the applied pressure is gradually released from 42.9 down to 1.7 GPa, the $T_c$ increases monotonously from 2.5 to 4.0 K. We argue that the observed unusual evolution of superconductivity can be explained by combination of pressure-manipulated crystal quality and the pressure dependence of $T_c$ of the $\beta \text{−}\mathrm{PdB}{\mathrm{i}}_2$ superconductor.

We have used neutron powder diffraction to solve the magnetic structure of orthorhombic ${\mathrm{CoTi}}_2{\mathrm{O}}_5$, showing that the long-range ordered state below 26 K identified in our muon-spin rotation experiments is antiferromagnetic with propagation vector $\mathbf{k}=(\pm \frac{1}{2},\frac{1}{2},0)$ and moment of $2.72\left(1\right){\mu }_{\mathrm{B}}$ per ${\mathrm{Co}}^{2+}$ ion. This long-range magnetic order is incompatible with the experimentally determined crystal structure because the imposed symmetry completely frustrates the exchange coupling. We conclude that the magnetic transition must therefore be accompanied by a spin Jahn-Teller effect which lowers the structural symmetry and thereby relieves the frustration. These results show that ${\mathrm{CoTi}}_2{\mathrm{O}}_5$ is a highly unusual low-symmetry material exhibiting a purely spin-driven lattice distortion critical to the establishment of an ordered magnetic ground state.

We use density-matrix renormalization group to study the first-order quantum phase transition induced by a magnetic field $h$ in a frustrated ferrimagnetic chain. The magnetization ($m$) curve as a function of $h$ presents a macroscopic jump and the energy curve as a function of $m$ has two global minima. We characterize the two competing phases and study the phase-separated states in the coexistence region. Also, we observe that the transition is accompanied by an increase in the number of itinerant singlet pairs between sites in the unit cells of the chain. Finally, we identify the critical point at the end of the first-order transition line and a crossover line.

Weyl semimetals are characterized by unconventional electromagnetic response. We present analytical expressions for all components of the frequency- and wave-vector-dependent charge-spin linear-response tensor of Weyl fermions. The spin-momentum locking of the Weyl Hamiltonian leads to a coupling between charge and longitudinal spin fluctuations, while transverse spin fluctuations remain decoupled from the charge. A real Weyl semimetal with multiple Weyl nodes can show this charge-spin coupling in equilibrium if its crystal symmetry is sufficiently low. All Weyl semimetals are expected to show this coupling if they are driven into a nonequilibrium stationary state with different occupations of Weyl nodes, for example, by exploiting the chiral anomaly. Based on the response tensor, we investigate the low-energy collective excitations of interacting Weyl fermions. For a local Hubbard interaction, the charge-spin coupling leads to a dramatic change of the zero-sound dispersion: its velocity becomes independent of the interaction strength and the chemical potential and is given solely by the Fermi velocity. In the presence of long-range Coulomb interactions, the coupling transforms the plasmon modes into spin plasmons. For real Weyl semimetals with multiple Weyl nodes, the collective modes are strongly affected by the presence of parallel static electric and magnetic fields, due to the chiral anomaly. In particular, the zero-sound frequency at fixed momentum and the spin content of the spin plasmons go through cusp singularities as the chemical potential of one of the Weyl cones is tuned through the Weyl node. We discuss possible experiments that could provide smoking-gun evidence for Weyl physics.

Crystalline topological phases have recently attracted a lot of experimental and theoretical attention. Key advances include the complete elementary band representation analyses of crystalline matter by symmetry indicators and the discovery of higher-order hinge and corner states. However, current classification schemes of such phases are either implicit or limited in scope. We present a scheme for the explicit classification of crystalline topological insulators and superconductors. These phases are protected by crystallographic point group symmetries and are characterized by bulk topological invariants. The classification paradigm generalizes the Clifford algebra extension process of each Altland-Zirnbauer symmetry class and utilizes algebras which incorporate the point group symmetry. Explicit results for all point group symmetries of three-dimensional crystals are presented as well as for all symmorphic layer groups of two-dimensional crystals. We discuss future extensions for treatment of magnetic crystals and defected or higher-dimensional systems as well as weak and fragile invariants.

We theoretically investigate intersubband plasmon excitations in doped single-wall carbon nanotubes (SWNTs) by examining the dependence of plasmon frequency on the nanotube diameter, chirality, and Fermi energy. The intersubband plasmons can be excited by light with polarization perpendicular to the nanotube axis and thus the plasmon excitations correspond to optical transitions between the two different subbands, which are sensitive to the Fermi energy. In every SWNT, this mechanism leads to the emergence of the optical absorption peak at the plasmon frequency for a given Fermi energy, $E_F$. The plasmon frequencies calculated for many SWNTs with diameter $d_t<2\mathrm{nm}$ exhibit a dependence on ${(1/d_t)}^{0.7}$ and the frequencies are further affected by Fermi energy as $E_F^{0.25}$. With this knowledge, it is possible to develop a map of intersubband plasmon excitations in doped SWNTs that could be useful to quickly estimate the doping level and also be an alternative way to characterize nanotube chirality.

The electrical transport of $p$-type monolayer ${\mathrm{MoS}}_2$ from acoustic phonon scattering at low temperature ($T<100$ K) is theoretically analyzed. The formalism of conductivity is systemically derived through the standard Green's functions technique (a full quantum-mechanical treatment) by taking into account the realistic band structure of ${\mathrm{MoS}}_2$. It is found that the main contribution to resistivity is from piezoelectric scattering in the transverse direction. Analogous to graphene, the conductivity exhibits a transition from $\sigma \sim T^{-4}$ temperature dependence in the Bloch-Grüneisen temperature regime to weaker $\sigma \sim T^{-1}$ dependence at high temperature. It is remarkable that we observe the derivation of Matthiessen's rule in the presence of both disorder scattering and phonon scattering due to the abrupt variation of phonon-induced transport scattering rates.

We report results of the Raman measurements for ${\mathrm{SrRu}}_2{\mathrm{O}}_6$ having extraordinary high Néel temperature for a layered material. No additional phonon modes were detected at the temperature of magnetic transition thus excluding lowering of the symmetry in the magnetically ordered phase. An unusual increase in softening and damping of some phonons as the temperature approaches $T_N$ indicates the appearance of a continuum of interacting electronic excitations at $T\ge 300\text{K}$. We also observe an intensive Raman response at 2050 ${\mathrm{cm}}^{-1}$. Analysis of the polarization dependence and comparison with available theoretical data shows that this peak likely originates from the transitions between molecular orbitals previously proposed to explain the magnetic properties of ${\mathrm{SrRu}}_2{\mathrm{O}}_6$. It can be explained by two magnon excitations only if the magnon bandwidth is $\sim 140$ meV.

We consider in depth the applicability of the Wiedemann-Franz (WF) law, namely that the electronic thermal conductivity $\left(\kappa \right)$ is proportional to the product of the absolute temperature $\left(T\right)$ and the electrical conductivity $\left(\sigma \right)$ in a metal with the constant of proportionality, the so-called Lorenz number $L_0$, being a materials-independent universal constant in all systems obeying the Fermi liquid (FL) paradigm. It has been often stated that the validity (invalidity) of the WF law is the hallmark of an FL [non-Fermi liquid (NFL)]. We consider, both in two (2D) and three (3D) dimensions, a system of conduction electrons at a finite temperature $T$ coupled to a bath of acoustic phonons and quenched impurities, ignoring effects of electron-electron interactions. We find that the WF law is violated arbitrarily strongly with the effective Lorenz number vanishing at low temperatures as long as phonon scattering is stronger than impurity scattering. This happens both in 2D and in 3D for $T<T_{\text{BG}}$, where $T_{\text{BG}}$ is the Bloch-Grüneisen temperature of the system. In the absence of phonon scattering (or equivalently, when impurity scattering is much stronger than the phonon scattering), however, the WF law is restored at low temperatures even if the impurity scattering is mostly small angle forward scattering. Thus, strictly at $T=0$ the WF law is always valid in a FL in the presence of infinitesimal impurity scattering. For strong phonon scattering, the WF law is restored for $T>T_{\text{BG}}$ (or the Debye temperature $T_D$, whichever is lower) as in usual metals. At very high temperatures, thermal smearing of the Fermi surface causes the effective Lorenz number to go below $L_0$, manifesting a quantitative deviation from the WF law. Our paper establishes definitively that the uncritical association of an NFL behavior with the failure of the WF law is incorrect.

We consider a short-range deformation-potential scattering model of electron-acoustic phonon interaction to calculate the resistivity of an ideal metal (i.e., no other scattering mechanism except acoustic phonon scattering) as a function of temperature $\left(T\right)$ and electron density $\left(n\right)$. The resistivity calculation is based on the Boltzmann transport theory within the relaxation-time approximation in the nearly-free-electron single-band approximation. We consider both 3D metals and 2D metals and focus on the dilute limit, i.e., low effective metallic carrier density (and hence low effective Fermi wave number $k_F)$ of the system. The main findings are (1) a phonon-scattering-induced linear-in-$T$ resistivity could persist to arbitrarily low temperatures in the dilute limit independent of the Debye temperature $\left(T_D\right)$, although, eventually, the low-$T$ resistivity turns over to the expected Bloch-Grüneisen (BG) behavior with $T^5\left(T^4\right)$ dependence, in 3D (2D), respectively, with the crossover temperature, $T_{\text{BG}}$, from the linear-in-$T$ to the BG behavior, being proportional to the Fermi momentum, is small in the dilute limit; (2) because of low values of $n$, the phonon-induced resistivity could be very high in the system, orders of magnitude above the corresponding room temperature resistivity of ordinary metals; and (3) the resistivity shows an intrinsic saturation effect at very high temperatures (for $T>T_D)$ and, in fact, weakly decreases with increasing $T$ above a high crossover temperature with this crossover being dependent on both $T_D$ and $n$ in a nonuniversal manner—this high-temperature crossover is not directly connected with the Mott-Ioffe-Regel limit and is a reflection of phonon phase-space restriction. We discuss the qualitative trends in the resistivity as a function of temperature, density, phonon velocity, and system dimensionality. We also provide “high-temperature” linear-in-$T$ resistivity results for 2D and 3D Dirac materials. Our work brings out the universal features of phonon-induced transport in dilute metals, and we comment on possible implications of our results for strange metals, emphasizing that the mere observation of a linear-in-$T$ metallic resistivity at low temperatures or a very high metallic resistivity at high temperatures is not necessarily a reason to invoke an underlying quantum critical strange-metal behavior. Dilute metals may very well have highly unusual (compared with normal metals) transport properties arising from quantitative, but not qualitatively new, underlying physics. We discuss the temperature variation of the effective transport scattering rate showing that, for reasonable parameters, the scattering rate could be below or above $k_{B}T$ and, in particular, purely coincidentally, the calculated scattering rate happens to be $k_{B}T$ in normal metals with no implications whatsoever for the so-called Planckian behavior. Our work manifestly establishes that an apparent Planckian dissipative behavior could arise from the usual electron-phonon interaction without implying any strange metallicity or a failure of the quasiparticle paradigm in contrast to recent claims.

We study the effect of inhomogeneous strain on transition-metal dichalcogenides with a large intrinsic gap in their spectrum. It is found that, by tuning the chemical potential, superconductivity can preserve within the strain-induced discrete pseudo Landau levels (LLs), which introduce interesting topological properties to these systems. As we show, the superconductivity for integer fillings is quantum critical, and the quantum critical coupling strength is determined by the spacing between the two LLs closest to the Fermi level. For partial fillings, the superconducting gap is scaled linearly with the coupling strength and decreases rapidly when the chemical potential shifts away from the middle of each LL. In the presence of a Zeeman field, a pair of Majorana modes emerges simultaneously in the two valleys of strained dichalcogenides. When valley symmetry is further destroyed, a single Majorana mode can be expected to emerge at the edges of the strained monolayer dichalcogenides.

The magnetotransport in phase-separated (Ga,Fe)N containing ${\gamma }^{\prime }\text{−}{\mathrm{Ga}}_y{\mathrm{Fe}}_{4-y}\mathrm{N}$ ($0<y<1$) nanocrystals (NCs) is studied in the temperature range between 2 and 300 K. The evolution of the resistivity and of the magnetoresistance (MR) as a function of temperature points to two conduction mechanisms, namely, a conventional Arrhenius-type one down to 50 K and Mott variable range hopping at lower temperatures, where the spin-polarized current is transported between NCs in a regime in which phonon-scattering effects are not dominant. Below 25 K, the MR shows a hysteretic contribution at magnetic fields $<1\mathrm{T}$ and proportional to the coercive field. Anisotropic magnetoresistance with values one order of magnitude greater than those previously reported for ${\gamma }^{\prime }\text{−}{\mathrm{Fe}}_4\mathrm{N}$ thin films over the whole considered temperature range confirms that the observed MR in these layers is determined by the embedded nanocrystals.