The ab initio calculation of optical spectra of sheet crystals usually arranges them in a three-dimensional superlattice with a sufficiently large interlayer distance. We show how the resulting frequency-dependent dielectric tensor is related to the anisotropic optical conductivity of an individual sheet or to the dielectric tensor of a corresponding film with thickness $d$. Their out-of-plane component is taken into account, in contrast to usual treatments. We demonstrate that the generalized transfer-matrix method to model the optical properties of a layer system containing a sheet crystal accounts for all tensor components. As long as $d\ll \lambda$ ($\lambda$-wavelength of light) this generalized formulation of the optical properties for anisotropic two-dimensional (2D) systems of arbitrary thickness reproduces the limits found in literature that are based either on electromagnetic boundary conditions for a conducting surface or on an isotropic dielectric tensor. For $s$-polarized light, the results are independent of the sheet description. For oblique incidence of $p$-polarized light, the tensor nature of the optical conductivity (or the dielectric function) of the sheet crystal strongly impacts on reflectance, transmittance, and absorbance due to the out-of-plane optical conductivity. The limit $d\to 0$ should be taken in the final expressions. Example spectra are given for the group-IV honeycomb 2D crystals graphene and silicene.

Using first-principles spin-polarized density functional theory, we carried out an analysis on the atomic structure, stability, energetics, and mechanical and electronic properties of single-layer structures of arsenene. These are buckled honeycomb, symmetric, and asymmetric washboard arsenene structures. Our analysis is extended to include layered three-dimensional crystalline phase of arsenic, as well as bilayer and trilayer structures to reveal dimensionality effects. The buckled honeycomb and symmetric washboard structures are shown to maintain their stability at high temperatures even when they are freestanding. As a manifestation of the confinement effect, the large fundamental band gap of single-layer phases decreases with increasing number of layers and eventually is closed. Concomitantly, lattice constants partially increase, while interlayer distances decrease. The effects of hybrid functional or self-energy corrections together with the spin-orbit coupling on the electronic structure of arsenene are crucial. The responses of direct and indirect band gaps to biaxial or uniaxial strain are rather complex and directional; while the fundamental band gap decreases and changes from indirect to direct with the biaxial strain applied to buckled arsenene, these effects are strongly directional for washboard arsenene. The width and the indirect/direct character of the band gap can be tuned by the number of layers, as well as by applied uniaxial/biaxial strain.

An extensive investigation of the optical properties of single-layer buckled and washboard arsenene and their bilayers was performed, starting from layered three-dimensional crystalline phase of arsenic using density functional and many-body perturbation theories combined with random phase approximation. Electron-hole interactions were taken into account by solving the Bethe-Salpeter equation, suggesting first bound exciton energies on the order of 0.7 eV. Thus, many-body effects were found to be crucial for altering the optical properties of arsenene. The light absorption of single-layer and bilayer arsenene structures in general falls within the visible-ultraviolet spectral regime. Moreover, directional anisotropy, varying the number of layers, and applying homogeneous or uniaxial in-plane tensile strain were found to modify the optical properties of two-dimensional arsenene phases, which could be useful for diverse photovoltaic and optoelectronic applications.

We report the structural and magnetic properties of the $4d$ ($M$ = Rh) based and $5d$ ($M$ = Ir) based systems ${\mathrm{Ba}}_3{M}_x{\mathrm{Ti}}_{3-x}{\mathrm{O}}_9$ (nominally $x=0.5$, 1). The studied compositions were found to crystallize in a hexagonal structure with the centrosymmetric space group $P{6}_3/mmc$. The structures comprise of $A_2{\mathrm{O}}_9$ polyhedra [with the $A$ site (possibly) statistically occupied by $M$ and Ti] in which pairs of transition metal ions are stacked along the crystallographic $c$ axis. These pairs form triangular bilayers in the $ab$ plane. The magnetic Rh and Ir ions occupy these bilayers, diluted by Ti ions even for $x=1$. These bilayers are separated by a triangular layer which is dominantly occupied by Ti ions. From magnetization measurements we infer strong antiferromagnetic couplings for all of the materials but the absence of any spin-freezing or spin-ordering down to 2 K. Further, specific heat measurements down to 0.35 K show no sign of a phase transition for any of the compounds. Based on these thermodynamic measurements we propose the emergence of a quantum spin liquid ground state for ${\mathrm{Ba}}_3{\mathrm{Rh}}_{0.5}{\mathrm{Ti}}_{2.5}{\mathrm{O}}_9$, and ${\mathrm{Ba}}_3{\mathrm{Ir}}_{0.5}{\mathrm{Ti}}_{2.5}{\mathrm{O}}_9$, in addition to the already reported ${\mathrm{Ba}}_3{\mathrm{IrTi}}_2{\mathrm{O}}_9$.

We have investigated the magnetoresistance (MR) and Hall resistivity properties of the single crystals of tantalum sulfide, ${\mathrm{Ta}}_3{\mathrm{S}}_2$, which was recently predicted to be a new type-II Weyl semimetal. Large MR (up to $\sim 8000\%$ at 2 K and 16 T), field-induced metal-insulator-like transition, and nonlinear Hall resistivity are observed at low temperatures. The large MR shows a strong dependence on the field orientation, leading to a giant anisotropic magnetoresistance effect. For the field applied along the $b$ axis $\left(B\parallel b\right)$, MR exhibits quadratic field dependence at low fields and tends towards saturation at high fields; while for $B\parallel a$, MR presents quadratic field dependence at low fields and becomes linear at high fields without any trend towards saturation. The analysis of the Hall resistivity data indicates the coexistence of a large number of electrons with low mobility and a small number of holes with high mobility. Shubnikov-de Haas oscillation analysis reveals three fundamental frequencies originated from the three-dimensional Fermi surface pockets. We find that the semiclassical multiband model is sufficient to account for the experimentally observed MR in ${\mathrm{Ta}}_3{\mathrm{S}}_2$.

We present a mechanism for a spin blockade effect associated with a change in the type of magnetic anisotropy over oxidation state in a single molecule transistor, by taking an example of an individual ${\mathrm{Eu}}_2{\left({\mathrm{C}}_8{\mathrm{H}}_8\right)}_3$ molecule weakly coupled to nonmagnetic electrodes without linker groups. The molecule switches its magnetization direction from in-plane to out-of-plane when it is charged. In other words, the magnetic anisotropy of the molecule changes from easy plane to easy axis when the molecule is charged. By solving the master equation based on a model Hamiltonian, we find that current through the molecule is highly suppressed at low bias independently of gate voltage due to the interplay between spin selection rules and the change in the type of magnetic anisotropy. Transitions between the lowest magnetic levels in successive charge states are forbidden because the magnetic levels differ by $\left|\mathrm{\Delta }M\right|>1/2$ due to the change in the type of magnetic anisotropy, although the total spins differ by $\left|\mathrm{\Delta }S\right|=1/2$. This current suppression can be lifted by significant $\mathbf{B}$ field, and the threshold $\mathbf{B}$ field varies as a function of the field direction and the strength of magnetic anisotropy. The spin blockade effect sheds light on switching the magnetization direction by non-spin-polarized current and on exploring effects of this property coupled to other molecular degrees of freedom.

The $1/4$-filled organic compound, $\delta$-(EDT-TTF-${\mathrm{CONMe}}_2$)${}_2{\mathrm{AsF}}_6$ is a frustrated two-dimensional triangular magnetic system as shown by high-frequency (111.2 and 222.4 GHz) electron spin resonance (ESR) and structural data in the literature. The material gradually orders antiferromagnetically below 40 K, but some magnetically disordered domains persist down to 4 K. We propose that in defect free regions frustration prevents true magnetic order down to at least 4 K in spite of the large first- and second-neighbor exchange interactions along chains and between chains, respectively. The antiferromagnetic (AFM) order gradually developing below 40 K nucleates around structural defects that locally cancel frustration. Two antiferromagnetic resonance modes mapped in the principal planes at 4 K are assigned to the very weakly interacting one-dimensional molecular chains in antiferromagnetic regions.

We show that a heavy fermion superconductor ${\mathrm{UPt}}_3$ is a topological Weyl superconductor with tunable Weyl nodes. Adopting a generic order parameter in the $E_{2u}$ representation allowed by nonsymmorphic crystal symmetry, we clarify unusual gap structure and associated topological properties. The pair creation, pair annihilation, and coalescence of Weyl nodes are demonstrated in the time-reversal symmetry broken B-phase. At most 98 point nodes compatible with Blount's theorem give rise to line-node-like behaviors in low-energy excitations, consistent with experimental results. We also show an arc node protected by the nonsymmorphic crystal symmetry on the Brillouin zone face, which is a counterexample of Blount's theorem.

Entropy is a critical, but often overlooked, factor in determining the relative stabilities of crystal phases. The importance of entropy is most pronounced in softer materials, where small changes in free energy can drive phase transitions, which has recently been demonstrated in the case of organic-inorganic hybrid-formate perovskites. In this Rapid Communication we demonstrate the interplay between composition and crystal structure that is responsible for the particularly pronounced role of entropy in determining polymorphism in hybrid organic-inorganic materials. Using ab initio based lattice dynamics, we probe the origins and effects of vibrational entropy of four archetype perovskite $\left(AB{X}_3\right)$ structures. We consider an inorganic material $\left({\mathrm{SrTiO}}_3\right)$, an $A$-site hybrid-halide material $\left({\mathrm{CH}}_3{\mathrm{NH}}_3\right){\mathrm{PbI}}_3$, a $X$-site hybrid material $\mathrm{KSr}{\left({\mathrm{BH}}_4\right)}_3$, and a mixed $A$- and $X$-site hybrid-formate material $\left({\mathrm{N}}_2{\mathrm{H}}_5\right)\mathrm{Zn}{\left({\mathrm{HCO}}_2\right)}_3$, comparing the differences in entropy between two common polymorphs. The results demonstrate the importance of low-frequency intermolecular modes in determining the phase stability in these materials. The understanding gained allows us to propose a general principle for the relative stability of different polymorphs of hybrid materials as temperature is increased.

We observe anisotropic Hanle line shape with unequal in-plane and out-of-plane nonlocal signals for spin precession measurements carried out on lateral metallic spin valves with transparent interfaces. The conventional interpretation for this anisotropy corresponds to unequal spin relaxation times for in-plane and out-of-plane spin orientations as for the case of two-dimensional materials like graphene, but it is unexpected in a polycrystalline metallic channel. Systematic measurements as a function of temperature and channel length, combined with both analytical and numerical thermoelectric transport models, demonstrate that the anisotropy in the Hanle line shape is magnetothermal in origin, caused by the anisotropic modulation of the Peltier and Seebeck coefficients of the ferromagnetic electrodes. Our results call for the consideration of such magnetothermoelectric effects in the study of anisotropic spin relaxation.

We present a comprehensive quasiclassical approach for studying transport properties of superconducting diffusive hybrid structures in the presence of extrinsic spin-orbit coupling. We derive a generalized Usadel equation and boundary conditions that in the normal state reduce to the drift-diffusion theory governing the spin-Hall effect in inversion symmetric materials. These equations predict the nondissipative spin-galvanic effect, that is the generation of supercurrents by a spin-splitting field, and its inverse—the creation of magnetic moment by a supercurrent. These effects can be seen as counterparts of the spin-Hall, anomalous Hall, and their inverse effects in the superconducting state. Our theory opens numerous possibilities for using superconducting structures in magnetoelectronics.

Ferroelectric polymorphic phase coexistence, associated with either the presence of a morphotropic phase boundary or a temperature-driven polymorphic phase transition, is currently acknowledged as the key to high piezoelectric activity and is searched when new perovskite materials are developed, like lead-free alternatives to state-of-the-art $\mathrm{Pb}(\mathrm{Zr},\mathrm{Ti}){\mathrm{O}}_3$. This requires characterization tools that allow phase coexistence and transitions to be readily identified, among which measurements of the temperature dependences of Young's modulus and mechanical losses by dynamical mechanical analysis stand out as a powerful technique to complement standard electrical characterizations. We report here the application of this technique to $\left({\mathrm{K}}_{1-x}{\mathrm{Na}}_x\right){\mathrm{NbO}}_3$-based materials, which are under extensive investigation as environmentally friendly high sensitivity piezoelectrics. The elastic anomalies associated with the different phase transitions are identified and are shown to be distinctively shifted in relation to the dielectric ones. The origin of this discrepancy is discussed with the help of temperature-dependent Raman spectroscopy and is proposed to be a characteristic of diffuse phase transitions.

Heusler compounds offer potential as spintronic devices due to their spin polarization and half-metallicity properties, where electron spin-majority (minority) manifold exhibits states (band gap) at the electronic chemical potential, yielding full spin polarization in a single manifold. Yet, Heuslers often exhibit intrinsic disorder that degrades its half-metallicity and spin polarization. Using density-functional theory, we analyze the electronic and magnetic properties of equiatomic Heusler $\left(L{2}_1\right)$ CoMnCrAl and CoFeCrGe alloys for effects of hydrostatic pressure and intrinsic disorder (thermal antisites, binary swaps, and vacancies). Under pressure, CoMnCrAl undergoes a metallic transition, while half-metallicity in CoFeCrGe is retained for a limited range. Antisite disorder between Cr-Al pair in CoMnCrAl alloy is energetically the most favorable, and retains half-metallic character in Cr-excess regime. However, Co-deficient samples in both alloys undergo a transition from half-metallic to metallic, with a discontinuity in the saturation magnetization. For binary swaps, configurations that compete with the ground state are identified and show no loss of half-metallicity; however, the minority-spin band gap and magnetic moments vary depending on the atoms swapped. For single binary swaps, there is a significant energy cost in CoMnCrAl but with no loss of half-metallicity. Although a few configurations in CoFeCrGe energetically compete with the ground state, the minority-spin band gap and magnetic moments vary depending on the atoms swapped. This information should help in controlling these potential spintronic materials.

We consider a film of a normal-state Fermi liquid on a planar substrate. Landau's Fermi liquid theory is applied to calculate the linear response of the film to transverse oscillation of the substrate. The response consists of a collective transverse zero-sound mode, as well as incoherent quasiparticle excitations of the degenerate fermions. We calculate numerically the acoustic impedance of the film under a wide range of conditions relevant to normal-state ${}^3\mathrm{He}$ at millikelvin temperatures. Some cases of known experiments are studied but most of the parameter range has not yet been tested experimentally.

The structure of binary $\mathrm{T}{\mathrm{i}}_{62}\mathrm{C}{\mathrm{u}}_{38}$ metallic glass is investigated under pressures up to 33.8 GPa using the pair distribution function analysis based on high-energy x-ray scattering and reverse Monte Carlo (RMC) simulations. At a global scale, its relative volume shows a continuously smooth curve as a function of pressure. The isothermal bulk modulus of $\mathrm{T}{\mathrm{i}}_{62}\mathrm{C}{\mathrm{u}}_{38}$ metallic glass is estimated as $B_0=132\left(3\right)\mathrm{GPa}$ with $B_0^{\prime }=5.8\left(0.4\right)$. At a local scale, the atomic packing structure under compression conditions, which is extracted from RMC simulations, shows that the topological short-range order is dominated by the deformed icosahedron polyhedra and basically maintains stable. From the relationship between the relative volume and changing ratio of the atomic separation distances, the real-space fractal dimensionality of this metallic glass is determined as about 2.5 for all of the first four peaks. This experimental result reveals the consistent nature of the fractal feature on the degree of self-similarity in this sample within the entire experimental pressure range.

We investigate the entanglement entropy (EE) and entanglement spectra (ES) of critical $\mathrm{SU}\left(N\right) \left(2\le N\le 4\right)$ spin chains and other integrable models of finite length with the density matrix renormalization group method. For all models under investigation, we find a remarkable agreement of the level spacings and the degeneracy structure of the ES with the spectrum of the corner Hamiltonian (CS), defined as the generator of the associated corner transfer matrix. The correspondence holds between ${\mathrm{ES}}^{\left(n\right)}$ at the $n\mathrm{th}$ cut position from the edge of the spin model, and the spectrum ${\mathrm{CS}}^{\left(n\right)}$ of the corner Hamiltonian of length $n$, for all values of $n$ that we have checked. The cut position dependence of the ES shows a period-$N$ oscillatory behavior for a given $\mathrm{SU}\left(N\right)$ chain, reminiscent of the oscillatory part of the entanglement entropy observed in the past for the same models. However, the oscillations of the ES do not die out in the bulk of the chain, in contrast to the asymptotically vanishing oscillation of the entanglement entropy. We present a heuristic argument based on Young tableaux construction that can explain the period-$N$ structure of the ES qualitatively.

Spontaneous charge ordering occurring in correlated systems may be considered as a possible route to generate effective lattice structures with unconventional couplings. For this purpose we investigate the phase diagram of doped extended Hubbard models on two lattices: (i) the honeycomb lattice with on-site $U$ and nearest-neighbor $V$ Coulomb interactions at $3/4$ filling $\left(n=3/2\right)$ and (ii) the triangular lattice with on-site $U$, nearest-neighbor $V$, and next-nearest-neighbor $V^{\prime }$ Coulomb interactions at $3/8$ filling ($n=3/4$). We consider various approaches including mean-field approximations, perturbation theory, and variational Monte Carlo. For the honeycomb case (i), charge order induces an effective triangular lattice at large values of $U/t$ and $V/t$, where $t$ is the nearest-neighbor hopping integral. The nearest-neighbor spin exchange interactions on this effective triangular lattice are antiferromagnetic in most of the phase diagram, while they become ferromagnetic when $U$ is much larger than $V$. At $U/t\sim {(V/t)}^3$, ferromagnetic and antiferromagnetic exchange interactions nearly cancel out, leading to a system with four-spin ring-exchange interactions. On the other hand, for the triangular case (ii) at large $U$ and finite $V^{\prime }$, we find no charge order for small $V$, an effective kagome lattice for intermediate $V$, and one-dimensional charge order for large $V$. These results indicate that Coulomb interactions induce [case (i)] or enhance [case(ii)] emergent geometrical frustration of the spin degrees of freedom in the system, by forming charge order.

We investigate the unconventional quantum phases in Weyl semimetals. The emergent boson fields, coupling with the Weyl fermion bilinears, contain a Wess-Zumino-Witten term or topological $\mathrm{\Theta }$ term inherited from the momentum space monopoles carried by Weyl points. Three types of unconventional quantum critical points will be studied in the following order. (1) The transition between two distinct symmetry breaking phases whose criticality is beyond Landau's paradigm. (2) The transition between a symmetry breaking state to a topological ordered state. (3) The transition between $3d$ topological order phase to trivial disordered phase whose criticality could be traced back to a $Z_2$ symmetry breaking transition in $4d$. The essence of these unconventional critical points lies in the fact that the topological defect of an order parameter carries either a nontrivial quantum number or a topological term so the condensation of the defects would either break some symmetry or give rise to a topological order phase with nontrivial braiding statistics.

We study finite-temperature properties of metals close to an Ising-nematic quantum critical point in two spatial dimensions. In particular we show that at any finite temperature there is a regime where order parameter fluctuations are characterized by a dynamical critical exponent $z=2$, in contrast to $z=3$ found at zero temperature. Our results are based on a simple Eliashberg-type approach, which gives rise to a boson self-energy proportional to $\mathrm{\Omega }/\gamma \left(T\right)$ at small momenta, where $\gamma \left(T\right)$ is the temperature dependent fermion scattering rate. These findings might shed some light on recent Monte Carlo simulations at finite temperature, where results consistent with $z=2$ were found.