We study indirect exchange interaction between magnetic impurities in the (001) CdTe/HgTe/CdTe symmetric quantum well. We consider low temperatures and the case of the chemical potential placed in the energy gap of the two-dimensional quasiparticle spectrum. We find that the indirect exchange interaction is suppressed exponentially with the distance between magnetic impurities. The presence of inversion asymmetry results in oscillations of the indirect exchange interaction with the distance and generates additional terms which are noninvariant under rotations in the (001) plane. The indirect exchange interaction matrix has complicated structure with some terms proportional to the sign of the energy gap.

Epitaxial thin films of $\mathrm{C}{\mathrm{r}}_{2-x}\mathrm{T}{\mathrm{i}}_x{\mathrm{O}}_3$ were deposited by oxygen-plasma-assisted molecular beam epitaxy for $0.04\le x\le 0.26$. Ti valence is verified by both x-ray photoelectron spectroscopy (XPS) and Ti $K$-edge x-ray absorption near-edge spectroscopy (XANES) to be $\mathrm{T}{\mathrm{i}}^{4+}$. Substitution of Ti for Cr in the corundum lattice is verified by fitting the Ti $K$-edge extended x-ray absorption fine structure (EXAFS) data. Room temperature electrical transport measurements confirm the highly resistive nature of Ti-doped $\mathrm{C}{\mathrm{r}}_2{\mathrm{O}}_3$, despite the presence of aliovalent $\mathrm{T}{\mathrm{i}}^{4+}$. For comparison, the resistivity of very pure, undoped $\mathrm{C}{\mathrm{r}}_2{\mathrm{O}}_3$ was measured to be four orders of magnitude higher than for Ti-doped $\mathrm{C}{\mathrm{r}}_2{\mathrm{O}}_3$. Analysis of the XPS and EXAFS data reveal the presence of Cr vacancies at intermediate and high Ti concentrations. This conclusion is corroborated by the results of density functional modeling. At low Ti concentrations, a strong increase of the XPS $\mathrm{Ti}2p$ core level peak width is observed as the Ti concentration decreases. In this limit, the formation of Cr vacancies becomes less favorable due to the increased distance between Ti dopants, and compensation by O interstitials contributes to broadening of the $\mathrm{Ti}2p$ XPS peak. The differences in electronic structure which render $\mathrm{T}{\mathrm{i}}^{4+}$-doped $\mathrm{C}{\mathrm{r}}_2{\mathrm{O}}_3$ resistive due to the formation of compensating defects, but $\mathrm{T}{\mathrm{i}}^{4+}$-doped $\mathrm{F}{\mathrm{e}}_2{\mathrm{O}}_3$ conductive, are discussed. The defect compensation model developed here provides insight into previous, conflicting reports of $n$-type versus $p$-type conductivity in Ti-doped $\mathrm{C}{\mathrm{r}}_2{\mathrm{O}}_3$ at high temperature, and will inform future studies to exploit the wide variety of electronic and magnetic properties of corundum structure oxides.

We perform ultrahigh-resolution angle-resolved photoemission experiments at a temperature $T=0.8$ K on the type-II Weyl semimetal candidate ${\mathrm{WTe}}_2$. We find a surface Fermi arc connecting the bulk electron and hole pockets on the (001) surface. Our results show that the surface Fermi arc connectivity to the bulk bands is strongly mediated by distinct surface resonances dispersing near the border of the surface-projected bulk band gap. By comparing the experimental results to first-principles calculations, we argue that the coupling to these surface resonances, which are topologically trivial, is compatible with the classification of ${\mathrm{WTe}}_2$ as a type-II Weyl semimetal hosting topological Fermi arcs. We further support our conclusion by a systematic characterization of the bulk and surface character of the different bands and discuss the similarity of our findings to the case of topological insulators.

We study the phase diagram of a topological string-net-type lattice model in the presence of geometrically frustrated interactions. These interactions drive several phase transitions that reduce the topological order, leading to a rich phase diagram including both Abelian $\left({\mathbb{Z}}_2\right)$ and non-Abelian $\left(\text{Ising}\times \overline{\text{Ising}}\right)$ topologically ordered phases, as well as phases with broken translational symmetry. Interestingly, one of these phases simultaneously exhibits (Abelian) topological order and long-ranged order due to translational symmetry breaking, with nontrivial interactions between excitations in the topological order and defects in the long-ranged order. We introduce a variety of effective models, valid along certain lines in the phase diagram, which can be used to characterize both topological and symmetry-breaking order in these phases and in many cases allow us to characterize the phase transitions that separate them. We use exact diagonalization and high-order series expansion to study areas of the phase diagram where these models break down and to approximate the location of the phase boundaries.

Interfacing $s$-wave superconductors and quantum spin Hall edges produces time-reversal-invariant topological superconductivity of a type that can not arise in strictly one-dimensional systems. With the aim of establishing sharp fingerprints of this phase, we use renormalization-group methods to extract universal transport characteristics of superconductor/quantum spin Hall heterostructures where the native edge states serve as leads. We determine scaling forms for the conductance through a grounded superconductor and show that the results depend sensitively on the interaction strength in the leads, the size of the superconducting region, and the presence or absence of time-reversal-breaking perturbations. We also study transport across a floating superconducting island isolated by magnetic barriers. Here, we predict $e$-periodic Coulomb-blockade peaks, as recently observed in nanowire devices [S. M. Albrecht et al., Nature (London) 531, 206 (2016)], with the added feature that the island can support fractional charge tunable via the relative orientation of the barrier magnetizations. As an interesting corollary, when the magnetic barriers arise from strong interactions at the edge that spontaneously break time-reversal symmetry, the Coulomb-blockade periodicity changes from $e$ to $e/2$. These findings suggest several future experiments that probe unique characteristics of topological superconductivity at the quantum spin Hall edge.

We report unusual physics associated with wave scattering in pseudospin-1 systems whose band structure consists of a conventional Dirac cone and a topologically flat band. First, for small scatterer size, we find a surprising revival resonant scattering phenomenon and identify a peculiar type of boundary trapping profile through the formation of unusual vortices as the physical mechanism. Second, for larger scatterer size, a perfect caustic phenomenon arises as a manifestation of the super-Klein tunneling effect, leading to the scatterer's being effectively as a Veselago lens. Third, in the far scattering field, an unexpected isotropic behavior emerges at low energies, which can be attributed to the vanishing Berry phase for massless pseudospin-1 particles and, consequently, to constructive interference between the time-reversed backscattering paths. We develop an analytic theory based on the generalized Dirac-Weyl equation to fully explain these phenomena and articulate experimental schemes with photonic or electronic systems.

Precipitation of anion nanocrystals (NCs) in initially stoichiometric II-VI crystals under hydrostatic pressure and light exposure is explored by Raman spectroscopy, and the mechanism for this effect is analyzed by model calculations. ZnSe, ZnTe, and CdSe crystals are studied in bulk and/or epitaxial-film forms. Se and Te NCs in the trigonal (t) phase precipitate in ZnSe and ZnTe, but the effect is absent or minimal in CdSe. The precipitation is induced by pressure and assisted by sub-band-gap light. In ZnSe, t-Se NCs appear for pressure exceeding 4.8 GPa and light flux above $50–70\mathrm{W}/\mathrm{m}{\mathrm{m}}^2$. In ZnTe, the precipitation of t-Te NCs requires less pressure to initiate, and there is a clear upper-pressure limit for t-Te nuclei to form. We find also that ZnTe samples with cleavage damage or elevated zinc-vacancy content are more prone to form t-Te NCs at lower pressures (even 1 atm in some cases) and lower flux. The precipitation seen in ZnSe and ZnTe occurs at pressures far below their phase transitions, and cannot be due to those transitions. Rather, we propose that the NCs nucleate on dislocations that arise from hydrostatic-pressure induced plastic flow triggered by noncubic defect sites. Calculations of the kinetic barrier for growth of an optimally shaped nucleus are performed, including hydrostatic pressure in the energy minimization scheme. Using sensible values for the model parameters related to the cohesive energies of Se and Te, the calculations account for our main observations, including the existence of an upper pressure limit for precipitation, and the absence of precipitation in CdSe. We consider the effects of pressure-induced precipitate formation on the I-II phase transitions in a variety of binary semiconductors and make predictions of when this effect should be important.

We study how low-energy charge carriers scatter off periodic and linear graphene grain boundaries oriented along the zigzag direction with a periodicity three times greater than that of pristine graphene. These defects map the two Dirac points into the same position, and thus allow for intervalley scattering to occur. Starting from graphene's first-neighbor tight-binding model we show how we can compute the boundary condition seen by graphene's massless Dirac fermions at such grain boundaries. We illustrate this procedure for the 3-periodic pentagon-only grain boundary, and then work out the low-energy electronic scattering off this linear defect. We also compute the effective generalized potential seen by the Dirac fermions at the grain boundary region.

The spin Hall effect and the magnetic proximity effect are two main sources of the magnetoresistance (MR) effects in heavy metal/ferromagnet bilayers, where they play isolated roles but are usually contaminated by each other. In $\mathrm{T}{{\mathrm{a}}_1}_{-x}\mathrm{P}{\mathrm{t}}_x/\mathrm{YIG}(={\mathrm{Y}}_3\mathrm{F}{\mathrm{e}}_5{\mathrm{O}}_{12})$ bilayers consisting of Ta and Pt nanograins, these effects are intrinsically coupled to generate new MR with 360° direction sensitivity to the magnetic field and proportionality to the out-of-plane magnetization of YIG. Due to the opposite spin Hall angle of Ta and Pt, vertical spin accumulation is generated via the spin Hall effect at the transverse boundaries between Ta and Pt grains. The spin-dependent scattering by the proximity-induced Pt magnetization finally leads to the MR, which is named as vertical spin Hall MR taking the role of spin Hall angle into account. Besides fundamental insight to spin transport physics, our work provides an approach to detecting perpendicular magnetization in a variety of magnets.

We study the role of the anomalous $E=0$ state in dynamical properties of noninteracting fermionic chains with chiral symmetry and correlated bond disorder in one dimension. These models possess a diverging density of states at zero energy leading to a divergent localization length at the band center. By analytically calculating the localization length for a finite system, we show that correlations in the disorder modify the spatial decay of the $E=0$ state from being quasilocalized to extended. We numerically simulate charge and entanglement propagation and provide evidence that states close to $E=0$ dominate the dynamical properties. Remarkably, we find that correlations lead to subdiffusive charge propagation, whereas the growth of entanglement is logarithmically slow. A logarithmic scaling of entanglement saturation with system size is also observed, which indicates a behavior akin to quantum critical glasses.

Studies of superconductivity in multiband correlated electronic systems have become one of the central topics in condensed-matter and materials physics. In this paper, we present the results of thermodynamic measurements on the superconducting filled skutterudite system ${\mathrm{Pr}}_{1-x}{\mathrm{Ce}}_x{\mathrm{Pt}}_4{\mathrm{Ge}}_{12}$ $\left(0\le x\le 0.2\right)$ to investigate how substitution of Ce at Pr sites affects superconductivity. We find that an increase in Ce concentration leads to a suppression of the superconducting transition temperature from $T_c\sim 7.9$ K for $x=0$ to $T_c\sim 0.6$ K for $x=0.14$. Our analysis of the specific-heat data for $x\le 0.07$ reveals that superconductivity must develop in at least two bands: the superconducting order parameter has nodes on one Fermi pocket and remains fully gapped on the other. Both the nodal and nodeless gaps decrease, with the nodal gap being suppressed more strongly upon Ce substitution. Ultimately, the higher-Ce-concentration samples $(x>0.07)$ display a nodeless gap only.

The noninteracting electronic structures of tight-binding models on bipartite lattices with unequal numbers of sites in the two sublattices have a number of unique features, including the presence of spatially localized eigenstates and flat bands. When a uniform on-site Hubbard interaction $U$ is turned on, Lieb proved rigorously that at half-filling ($\rho =1$) the ground state has a nonzero spin. In this paper we consider a “${\mathrm{CuO}}_2$ lattice” (also known as “Lieb lattice,” or as a decorated square lattice), in which “$d$ orbitals” occupy the vertices of the squares, while “$p$ orbitals” lie halfway between two $d$ orbitals; both $d$ and $p$ orbitals can accommodate only up to two electrons. We use exact determinant quantum Monte Carlo (DQMC) simulations to quantify the nature of magnetic order through the behavior of correlation functions and sublattice magnetizations in the different orbitals as a function of $U$ and temperature; we have also calculated the projected density of states, and the compressibility. We study both the homogeneous (H) case, $U_d=U_p$, originally considered by Lieb, and the inhomogeneous (IH) case, $U_d\ne U_p$. For the H case at half-filling, we found that the global magnetization rises sharply at weak coupling, and then stabilizes towards the strong-coupling (Heisenberg) value, as a result of the interplay between the ferromagnetism of like sites and the antiferromagnetism between unlike sites; we verified that the system is an insulator for all $U$. For the IH system at half-filling, we argue that the case $U_p\ne U_d$ falls under Lieb's theorem, provided they are positive definite, so we used DQMC to probe the cases $U_p=0,U_d=U$ and $U_p=U,U_d=0$. We found that the different environments of $d$ and $p$ sites lead to a ferromagnetic insulator when $U_d=0$; by contrast, $U_p=0$ leads to to a metal without any magnetic ordering. In addition, we have also established that at density $\rho =1/3$, strong antiferromagnetic correlations set in, caused by the presence of one fermion on each $d$ site.

We develop a theory for the analytic computation of the free energy of band insulators in the presence of a uniform and constant electric field. The two key ingredients are a perturbation-like expression of the Wannier-Stark energy spectrum of electrons and a modified statistical mechanics approach involving a local chemical potential in order to deal with the unbounded spectrum and impose the physically relevant electronic filling. At first order in the field, we recover the result of King-Smith, Vanderbilt, and Resta for the electric polarization in terms of a Zak phase—albeit at finite temperature—and, at second order, deduce a general formula for the electric susceptibility, or equivalently for the dielectric constant. Advantages of our method are the validity of the formalism both at zero and finite temperature and the easy computation of higher order derivatives of the free energy. We verify our findings on two different one-dimensional tight-binding models.

We investigate numerically the inverse participation ratios in a spin-1/2 XXZ chain, computed in the “Ising” basis (i.e., eigenstates of ${\sigma }_i^z)$. We consider in particular a quantity $T$, defined by summing the inverse participation ratios of all the eigenstates in the zero-magnetization sector of a finite chain of length $N$, with open boundary conditions. From a dynamical point of view, $T$ is proportional to the stationary return probability to an initial basis state, averaged over all the basis states (initial conditions). We find that $T$ exhibits an exponential growth, $T\sim exp\left(aN\right)$, in the gapped phase of the model and a linear scaling, $T\sim N$, in the gapless phase. These two different behaviors are analyzed in terms of the distribution of the participation ratios of individual eigenstates. We also investigate the effect of next-nearest-neighbor interactions, which break the integrability of the model. Although the massive phase of the nonintegrable model also has $T\sim exp\left(aN\right)$, in the gapless phase $T$ appears to saturate to a constant value.

We develop an analytical model to describe sub-band-gap optical absorption in two-dimensional semiconducting transition metal dichalcogenide (s-TMD) nanoflakes. The material system represents an array of few-layer molybdenum disulfide crystals, randomly orientated in a polymer matrix. We propose that optical absorption involves direct transitions between electronic edge states and bulk bands, depends strongly on the carrier population, and is saturable with sufficient fluence. For excitation energies above half the band gap, the excess energy is absorbed by the edge-state electrons, elevating their effective temperature. Our analytical expressions for the linear and nonlinear absorption could prove useful tools in the design of practical photonic devices based on s-TMDs.

Calculating the quasiparticle (QP) band structure of two-dimensional (2D) materials within the GW self-energy approximation has proven to be a rather demanding computational task. The main reason is the strong $q$ dependence of the 2D dielectric function around $q=0$ that calls for a much denser sampling of the Brillouin zone (BZ) than is necessary for similar three-dimensional solids. Here, we use an analytical expression for the small $q$ limit of the 2D response function to perform the BZ integral over the critical region around $q=0$. This drastically reduces the requirements on the $q$-point mesh and implies a significant computational speedup. For example, in the case of monolayer ${\mathrm{MoS}}_2$, convergence of the ${\text{G}}_0{\text{W}}_0$ band gap to within $\sim 0.1$ eV is achieved with $12\times 12 q$ points rather than the $36\times 36$ mesh required with discrete BZ sampling techniques. We perform a critical assessment of the band gap of the three prototypical 2D semiconductors, ${\mathrm{MoS}}_2, h$-BN, and phosphorene, including the effect of self-consistency at the ${\mathrm{GW}}_0$ level. The method is implemented in the open source code gpaw.

We propose an all-electrically controlled nanodevice—a gated semiconductor nanowire—capable of generating a coherent state of a single electron trapped in a harmonic oscillator or superposition of such coherent states—the Schrödinger cat state. In the proposed scheme, the electron in the ground state of the harmonic potential is driven by resonantly oscillating Rashba spin-orbit coupling. This allows for the creation of the Schrödinger cat state with superposition amplitudes depending on the initial electron spin state. Such a method can be used for initialization of a single-spin qubit defined in a coherent state. The harmonic confinement potential along the InSb nanowire and the modulation of the Rashba spin-orbit coupling is obtained by proper gating. The results are supported by realistic three-dimensional time-dependent self-consistent Poisson-Schrödinger calculations.

$\alpha -{\mathrm{RuCl}}_3$ has been hinted to be a spin-orbital-assisted Mott insulator in proximity to a Kitaev spin liquid state. Here we present angle-resolved photoemission measurements on single-crystal $\alpha -{\mathrm{RuCl}}_3$ in both the pristine and electron-doped states, and combine them with Local Density Approximation (LDA)+Spin Orbital Coupling (SOC)+U calculations performed for several low-energy competing magnetically ordered states as well as the paramagnetic state. A large Mott gap is found in the measured band structure of the pristine compound that persists to more than 30 times beyond the magnetic ordering temperature, though the paramagnetic calculation shows almost no gap. Upon electron doping, spectral weight is transferred into the gap but the new states still maintain a sizable gap from the Fermi edge. These findings are most consistent with a Mott insulator with a somewhat exotic evolution out of the Mott state with both temperature and doping, likely related to unusually strong spin fluctuations.

The Hofstadter butterfly of lattice electrons in a strong magnetic field is a cornerstone of condensed matter physics, exploring the competition between periodicities imposed by the lattice and the field. Here, we introduce and characterize the Weyl butterfly, which emerges when a large magnetic field is applied to a three-dimensional Weyl semimetal. Using an experimentally motivated lattice model for cold-atomic systems, we solve this problem numerically. We find that Weyl nodes reemerge at commensurate fluxes and propose using wave-packet dynamics to reveal their chirality and location. Moreover, we show that the chiral anomaly—a hallmark of the topological Weyl semimetal—does not remain proportional to the magnetic field at large fields, but rather inherits a fractal structure of linear regimes as a function of the external field. The slope of each linear regime is determined by the difference of two Chern numbers in the gaps of the Weyl butterfly and can be measured experimentally in time of flight.