We report on the crystal structure, physical properties, and electronic structure calculations for the ternary pnictide compound ${\text{EuCr}}_2$${\text{As}}_2$. X-ray diffraction studies confirmed that ${\text{EuCr}}_2$${\text{As}}_2$ crystalizes in the ${\text{ThCr}}_2$${\text{Si}}_2$-type tetragonal structure (space group $I4/mmm$). The Eu ions are in a stable divalent state in this compound. Eu moments in ${\text{EuCr}}_2$${\text{As}}_2$ order magnetically below $T_m$ = 21 K. A sharp increase in the magnetic susceptibility below $T_m$ and the positive value of the paramagnetic Curie temperature obtained from the Curie-Weiss fit suggest dominant ferromagnetic interactions. The heat capacity exhibits a sharp $\lambda$-shape anomaly at $T_m$, confirming the bulk nature of the magnetic transition. The extracted magnetic entropy at the magnetic transition temperature is consistent with the theoretical value $Rln(2S+1)$ for $S=7/2$ of the Eu${}^{2+}$ ion. The temperature dependence of the electrical resistivity $\rho \left(T\right)$ shows metallic behavior along with an anomaly at 21 K. In addition, we observe a reasonably large negative magnetoresistance ($\sim -24\%$) at lower temperature. Electronic structure calculations for ${\text{EuCr}}_2$${\text{As}}_2$ reveal a moderately high density of states of Cr-3$d$ orbitals at the Fermi energy, indicating that the nonmagnetic state of Cr is unstable against magnetic order. Our density functional calculations for ${\text{EuCr}}_2$${\text{As}}_2$ predict a G-type AFM order in the Cr sublattice. The electronic structure calculations suggest a weak interlayer coupling of the Eu moments.

Topological phases which host Majorana fermions can not be identified via local order parameters. We give simple nonlocal order parameters to distinguish quasi-one-dimensional (1D) topological superconductors of spinless fermions, for any interacting model in the absence of time reversal symmetry. These string or “brane” order parameters are natural for measurements in cold atom systems using quantum gas microscopy. We propose them as a way to identify symmetry-protected topological phases of Majorana fermions in cold atom experiments via bulk rather than edge degrees of freedom. Subsequently, we study two-dimensional (2D) topological superconductors via the quasi-1D limit of coupling $N$ identical chains on the cylinder. We classify the symmetric, interacting topological phases protected by the additional ${\mathbb{Z}}_N$ translation symmetry. The phases include quasi-1D analogs of (i) the $p+ip$ chiral topological superconductor, which can be distinguished up to the 2D Chern number mod 2, and (ii) the 2D weak topological superconductor. We devise general rules for constructing nonlocal order parameters which distinguish the phases. These rules encode the signature of the fermionic topological phase in the symmetry properties of the terminating operators of the nonlocal string or brane. The nonlocal order parameters for some of these phases simply involve a product of the string order parameters for the individual chains. Finally, we give a physical picture of one of the topological phases as a condensate of certain defects, which motivates the form of the nonlocal order parameter and is reminiscent of higher dimensional constructions of topological phases.

Graphene on Ir(111) is studied using scanning tunneling microscopy (STM) and x-ray standing waves (XSW). The graphene layer has a corrugated shape due to the moiré pattern formed as a result of a spatially varying interaction strength between graphene and its substrate. The coherent fraction $F^{\left(111\right)}$ determined in XSW allows us to determine the amplitude of this intrinsic corrugation when the incoherent contributions of wrinkles, step edges, graphene edges, and contaminations are taken into account. The corrugation is found to depend on the stress state of the carbon sheet. Using density functional theory (DFT) calculations, we show that graphene can compensate stress by increasing its corrugation rather than by a reduction of the C-C bond length.

Bin Shan et al. [Phys. Rev. B 80, 035404 (2009)] developed an embedded-atom-model potential for studying structural properties of Pd/Au alloy nanoparticles by means of Monte Carlo simulations. The parameters reported for the Pd-Au pairwise interaction appear to be erroneous as the Pd-Au interaction potential, Fig. 5(c) of that publication, cannot be reproduced with those parameters. In this Comment, we use the same procedure and reference systems for parametrization to provide a corrected set of parameters and we demonstrate, for selected results, that the previously published calculated properties of Pd/Au nanoparticles appear to be correct.

The antiferromagnetic ordered phase in ${\text{SmRu}}_4$${\text{P}}_{12}$ below the metal-insulator transition at $T_{\text{MI}}=16.5$ K with an unresolved transition at $T^{*}\sim 14$ K has been studied by resonant and nonresonant x-ray diffraction in magnetic fields. In the intermediate phase, a nonresonant Thomson scattering with $\mathit{q}=(1,0,0)$ is induced by applying a magnetic field, which is presumably caused by atomic displacements reflecting the charge order in the $p$ band, as predicted theoretically [R. Shiina, J. Phys. Soc. Jpn. 82, 083713 (2013)]. Simultaneously, the antiferromagnetic moment of Sm is enhanced along the field direction, which is considered to reflect the staggered ordering of the ${\Gamma }_7-{\Gamma }_8$ crystal-field states (scalar or hexadecapole order). The present results show that the orbital-dependent $p$-$f$ hybridization in association with the nesting instability in the $p$ band gives rise to the unconventional charge order similarly with ${\text{PrRu}}_4$${\text{P}}_{12}$ and ${\text{PrFe}}_4$${\text{P}}_{12}$.

Majorana fermions in a superconductor hybrid system are charge neutral zero-energy states. For the detection of this unique feature, we propose an interferometry of a chiral Majorana edge channel, formed along the interface between a superconductor and a topological insulator under an external magnetic field. The superconductor is of a ring shape and has a Josephson junction that allows the Majorana state to enclose continuously tunable magnetic flux. Zero-bias differential electron conductance between the Majorana state and a normal lead is found to be independent of the flux at zero temperature, manifesting the Majorana feature of a charge neutral zero-energy state. In contrast, the same setup on graphene has no Majorana state and shows Aharonov-Bohm effects.

The surfaces of three-dimensional topological insulators (3D TIs) are generally described as Dirac metals, with a single Dirac cone. It was previously believed that a gapped surface implied breaking of either time-reversal $\mathcal{T}$ or $\text{U}\left(1\right)$ charge conservation symmetry. Here, we discuss a possibility in the presence of interactions, a surface phase that preserves all symmetries but is nevertheless gapped and insulating. Then, the surface must develop topological order of a kind that can not be realized in a two-dimensional (2D) system with the same symmetries. We discuss candidate surface states, non-Abelian quantum Hall states which, when realized in 2D, have ${\sigma }_{xy}=\frac{1}{2}$ and hence break $\mathcal{T}$ symmetry. However, by constructing an exactly soluble 3D lattice model, we show they can be realized as $\mathcal{T}$-symmetric surface states. The corresponding 3D phases are confined, and have $\theta =\pi$ magnetoelectric response. Two candidate states have the same 12-particle topological order, the (Read-Moore) Pfaffian state with the neutral sector reversed, which we term T-Pfaffian topological order, but differ in their $\mathcal{T}$ transformation. Although we are unable to connect either of these states directly to the superconducting TI surface, we argue that one of them describes the 3D TI surface, while the other differs from it by a bosonic topological phase. We also discuss the 24-particle Pfaffian-antisemion topological order (which can be connected to the superconducting TI surface) and demonstrate that it can be realized as a $\mathcal{T}$-symmetric surface state.

Scaling behavior of the quantum phase transition from an insulator to a quantum Hall plateau state has often been examined within systems realizing Landau levels. We study the topological transition in an energy-band model with nonzero Chern number, which has the same topological property as a Landau level. We find that a topological band generally realizes the same universality class as the integer quantum Hall system under uniform magnetic flux for strong enough disorder scattering. Furthermore, the symmetry of the transition characterized by relations ${\sigma }_{xy}\left(\Delta E\right)=1-{\sigma }_{xy}(-\Delta E)$ for Hall conductance and ${\sigma }_T\left(\Delta E\right)={\sigma }_T(-\Delta E)$ for longitudinal Thouless conductance is observed near the transition region. We also establish that the finite-temperature dependence of Hall conductance is determined by inelastic-scattering relaxation time, while the localization exponent $\nu$ remains unchanged by such scattering.

We determined the phase diagram of magnesium oxide with finite-temperature density functional theory molecular dynamics simulations up to temperatures and pressures as relevant for the deep interior of super-Earths and in rocky cores of giant planets such as Jupiter. The equation of state data, the Hugoniot, and a ramp compression curve are computed and compared to earlier results from diamond anvil cell and (decaying) shock wave experiments. In addition, the dynamical electrical conductivity and the reflectivity along the experimental Hugoniot curve are calculated in order to characterize electronic structure changes under compression. The structural properties of MgO are identified using pair correlation functions and self-diffusion coefficients. The solid-solid coexistence line is calculated by comparing the free enthalpies of the B1 and the B2 phase. The free energy of the solid phases is determined via thermodynamic relations using the ab initio simulation results and phonon calculations in the harmonic approximation. Our results indicate that the solid B2 phase of MgO does not occur in the interior of the Earth but may play an important role in super-Earths and in rocky planetary cores.

Based on hybrid density-functional calculations, we propose that ferromagnetism in the prototypical bixbyite sesquioxide ${\text{In}}_2$${\text{O}}_3$ doped with Cr is due to Cr-oxygen vacancy complexes, while isolated Cr cannot support carrier-mediated magnetic coupling. Our proposal is consistent with experimental facts such as the onset of ferromagnetism in O-lean conditions only, the low or vanishing net moment in unintentionally doped material, and its increase upon intentional doping.

We report ${}^{31}\mathrm{P}$ and ${}^7\mathrm{Li}$ nuclear magnetic resonance (NMR) studies in new non-olivine LiZnPO${}_4$-type LiCoPO${}_4^{\mathrm{tetra}}$ microcrystals, where the Co${}^{2+}$ ions are tetrahedrally coordinated. Olivine LiCoPO${}_4$, which was directly transformed from LiCoPO${}_4^{\mathrm{tetra}}$ by an annealing process, was also studied and compared. The uniform bulk magnetic susceptibility and the ${}^{31}\mathrm{P}$ Knight shift obey the Curie-Weiss law for both materials with a high spin Co${}^{2+}$ ($3d^7$, $S=3/2$), but the Weiss temperature $\Theta$ and the effective magnetic moment ${\mu }_{\mathrm{eff}}$ are considerably smaller in LiCoPO${}_4^{\mathrm{tetra}}$. The spin-lattice relaxation rate $T_1^{-1}$ reveals a quite different nature of the spin dynamics in the paramagnetic state of both materials. Our NMR results imply that strong geometrical spin frustration occurs in tetrahedrally coordinated LiCoPO${}_4$, which may lead to the incommensurate magnetic ordering.

We provide a derivation of a spin Skyrmion number classification for two-dimensional topological superconductors constructed from ferromagnetic and Rashba spin-orbit coupled semiconductor–superconductor heterostructures. We show that in the nontrivial topological phase, characterized by a nonzero Chern number, there is always a topological spin texture in the occupied bands represented by a Skyrmion number. The Skyrmion number has the advantage of being both physically intuitive and directly measurable using spin-sensitive band structure imaging techniques. In addition, we show that the Skyrmion classification can be extended to the equivalent one-dimensional topological superconductors.

We show from detailed magnetometry across 2–300 K that the ${\mathrm{BiFeO}}_3$-${\mathrm{Bi}}_2$${\mathrm{Fe}}_4$${\mathrm{O}}_9$ nanocomposite offers a unique spin morphology where superspin glass (SSG) and dilute antiferromagnet in a field (DAFF) coexist at the interface between ferromagnetic ${\mathrm{Bi}}_2$${\mathrm{Fe}}_4$${\mathrm{O}}_9$ and antiferromagnetic ${\mathrm{BiFeO}}_3$. The coexisting SSG and DAFF combine to form a local spin texture, which gives rise to a path-dependent exchange bias below the spin freezing temperature ($\sim$29 K). The exchange bias varies depending on the protocol or path followed in tracing the hysteresis loop. The exchange bias has been observed below the blocking temperature ($T_B$) 60 K of the superparamagnetic ${\mathrm{Bi}}_2$${\mathrm{Fe}}_4$${\mathrm{O}}_9$. The conventional exchange bias (CEB) increases nonmonotonically as temperature decreases. The magnitude of both exchange bias ($H_E$) and coercivity ($H_C$) increase with decrease in temperature and are found to be asymmetric below 20 K depending on the path followed in tracing the hysteresis loop and bias field. The local spin texture at the interface between ferromagnetic and antiferromagnetic particles generates a nonswitchable unidirectional anisotropy along the negative direction of the applied field. The influence of this texture also shows up in “asymmetric” jumps in the hysteresis loop at 2 K, which smears off at higher temperature. The role of the interface spin texture in yielding the path dependency of exchange bias is thus clearly delineated.

We investigated the transport properties of ${\text{Fe}}_{1+y}$${\text{Te}}_{0.6}$${\text{Se}}_{0.4}$ single crystals with different amounts of excess Fe prepared by ${\text{O}}_2$ annealing. The ${\text{O}}_2$ annealing remarkably improved transport properties. In particular, a strongly nonlinear Hall resistivity was observed only in the fully annealed crystal, and the magnetoresistance (MR) was drastically enhanced after annealing, reaching a value larger than 17% at 16 K and 14 T. The obvious change of transport properties after the annealing indicates that the band structure of ${\text{Fe}}_{1+y}$${\text{Te}}_{0.6}$${\text{Se}}_{0.4}$ is affected by the excess Fe. The nonlinear Hall resistivity and violation of (modified) Kohler's scaling of the large MR prove the multiband effects in the ${\text{Fe}}_{1+y}$${\text{Te}}_{0.6}$${\text{Se}}_{0.4}$ single crystal. The MR for the fully annealed crystal develops linearly against the magnetic field from the intermediate field (e.g., 2 T at 16 K) to the measurement limit of 14 T. This phenomenon is interpreted by the existence of the Dirac cone state, in which all the Dirac fermions occupy only the lowest Landau level in the quantum limit.

Optical and transport properties of materials depend heavily upon features of electronic band structures in proximity of energy extrema in the Brillouin zone (BZ). Such features are generally described in terms of multidimensional quadratic expansions and corresponding definitions of effective masses. Multidimensional quadratic expansions, however, are permissible only under strict conditions that are typically violated when energy bands become degenerate at extrema in the BZ. Even for energy bands that are nondegenerate at critical points in the BZ there are instances in which multidimensional quadratic expansions cannot be correctly performed. Suggestive terms such as “band warping,” “fluted energy surfaces,” or “corrugated energy surfaces” have been used to refer to such situations and ad hoc methods have been developed to treat them. While numerical calculations may reflect such features, a complete theory of band warping has not hitherto been developed. We define band warping as referring to band structures that do not admit second-order differentiability at critical points in $\mathbf{k}$ space and we develop a generally applicable theory, based on radial expansions, and a corresponding definition of angular effective mass. Our theory also accounts for effects of band nonparabolicity and anisotropy, which hitherto have not been precisely distinguished from, if not utterly confused with, band warping. Based on our theory, we develop precise procedures to evaluate band warping quantitatively. As a benchmark demonstration, we analyze the warping features of valence bands in silicon using first-principles calculations and we compare those with previous semiempirical models. As an application of major significance to thermoelectricity, we use our theory and angular effective masses to generalize derivations of tensorial transport coefficients for cases of either single or multiple electronic bands, with either quadratically expansible or warped energy surfaces. From that theory we discover the formal existence at critical points of transport-equivalent ellipsoidal bands that yield identical results from the standpoint of any transport property. Additionally, we illustrate with some basic multiband models the drastic effects that band warping and anisotropy can induce on thermoelectric properties such as electronic conductivity and thermopower tensors.

We demonstrate how to control the spectra and current flow of Dirac electrons in both a graphene sheet and a topological insulator (TI) by applying either two linearly polarized laser fields with frequencies $\omega$ and $2\omega$ or a monochromatic (one-frequency) laser field together with a spatially periodic static potential (graphene/TI superlattice). Using the Floquet theory and the resonance approximation, we show that a Dirac point in the electron spectrum can be split into several Dirac points whose relative location in momentum space can be efficiently manipulated by changing the characteristics of the laser fields. In addition, the laser-field-controlled Dirac fermion band structure—a Dirac fermion time-Floquet crystal—allows the manipulation of the electron currents in graphene and topological insulators. Furthermore, the generation of dc currents of desirable intensity in a chosen direction occurs when the biharmonic laser field is applied, which can provide a straightforward experimental test of the predicted phenomena.

We consider the steady-state thermoelectric transport through a vibrating molecular quantum dot that is contacted to macroscopic leads. For moderate electron-phonon interaction strength and comparable electronic and phononic timescales, we investigate the impact of the formation of a local polaron on the thermoelectric properties of the junction. We apply a variational Lang-Firsov transformation and solve the equations of motion in the Kadanoff-Baym formalism up to second order in the dot-lead coupling parameter. We calculate the thermoelectric current and voltage for finite temperature differences in the resonant and inelastic tunneling regimes. For a near resonant dot level, the formation of a local polaron can boost the thermoelectric effect because of the Franck-Condon blockade. The line shape of the thermoelectric voltage signal becomes asymmetrical due to the varying polaronic character of the dot state and in the nonlinear transport regime, vibrational signatures arise.

We analyze spin density waves (SDWs) in the Hubbard model on a square lattice within the framework of inhomogeneous dynamical mean field theory (IDMFT). Doping the half-filled Hubbard model results in a change of the antiferromagnetic Néel state, which exists exactly at half filling, to a phase of incommensurate SDWs. Previous studies of this phase mainly rely on static mean field calculations. In this paper, we will use large-scale IDMFT calculations to study properties of SDWs in the Hubbard model. A great advantage of IDMFT over static mean field approaches is the inclusion of local screening effects and the easy access to dynamical correlation functions. Furthermore, this technique is not restricted to the Hubbard model, but can be easily used to study incommensurate phases in various strongly correlated materials.