We demonstrate a topological classification of vortices in three-dimensional time-reversal invariant topological superconductors based on superconducting Dirac semimetals with an $s$-wave superconducting order parameter by means of a pair of numbers $(N_{\mathrm{\Phi }},N)$, accounting how many units $N_{\mathrm{\Phi }}$ of magnetic fluxes $hc/4e$ and how many $N$ chiral Majorana modes the vortex carries. From these quantities, we introduce a topological invariant, which further classifies the properties of such vortices under linking processes. While such processes are known to be related to instanton processes in a field theoretic description, we demonstrate here that they are, in fact, also equivalent to the fractional Josephson effect on junctions based at the edges of quantum spin Hall systems. This allows one to consider microscopically the effects of interactions in the linking problem. We therefore demonstrate that associated to links between vortices, one has the exchange of quasiparticles, either Majorana zero modes, or $e/2$ quasiparticles, which allows for a topological classification of vortices in these systems, seen to be ${\mathbb{Z}}_8$ classified. While $N_{\mathrm{\Phi }}$ and $N$ are shown to be both even or odd in the weakly interacting limit, in the strongly interacting scenario one loosens this constraint. In this case, one may have further fractionalization possibilities for the vortices, whose excitations are described by $\text{SO}{\left(3\right)}_3$-like conformal field theories with quasiparticle exchanges of more exotic types.

High-field magnetization of the spin-$1/2$ antiferromagnet $\alpha \text{−}{\mathrm{Cu}}_2{\mathrm{V}}_2{\mathrm{O}}_7$ was measured in pulsed magnetic fields of up to 56 T in order to study its magnetic phase diagram. When the field was applied along the easy axis (the $a$ axis), two distinct transitions were observed at $H_{c1}=6.5$ T and $H_{c2}=18.0$ T. The former is a spin-flop transition typical for a collinear antiferromagnet and the latter is believed to be a spin-flip transition of canted moments. The canted moments, which are induced by the Dzyaloshinskii-Moriya interactions, anti-align for $H_{c1}<H<H_{c2}$ due to the anisotropic exchange interaction that favors the antiferromagnetic arrangement along the $a$ axis. Above $H_{c2}$, the Zeeman energy of the applied field overcomes the antiferromagnetic anisotropic interaction and the canted moments are aligned along the field direction. Density functional theory was employed to compute the exchange interactions, which were used as inputs for quantum Monte Carlo calculations and then further refined by fitting to the magnetic susceptibility data. Contrary to our previous report in Phys. Rev. B 92, 024423 (2015), the dominant exchange interaction is between the third nearest-neighbor spins, which form zigzag spin chains that are coupled with one another through an intertwining network of the nonnegligible nearest and second nearest-neighbor interactions. In addition, elastic neutron scattering under the applied magnetic fields of up to 10 T reveals the incommensurate helical spin structure in the spin-flop state.

Density functional theory calculations reveal the existence of different correlated-electron ground states in (111)-oriented $n$-type ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ symmetric superlattices. They can be tuned by selecting the ${\mathrm{SrTiO}}_3$ thickness, and range from a trivial metal for thick ${\mathrm{SrTiO}}_3$ slabs to a Mott-type antiferromagnet in the ultrathin limit. An itinerant ferromagnet and a half-metal phase are also stable in the intermediate region. This remarkable property is a distinct characteristic of (111) perovskite heterostructures and originates from the combined effect of polar discontinuity at the interface, trigonal lattice symmetry, and quantum confinement. While the polar discontinuity promotes the filling of the empty $d$ states of the ${\mathrm{SrTiO}}_3$ with one electron, the trigonal symmetry dictates that the wave function of the occupied bands spreads over the entire ${\mathrm{SrTiO}}_3$ slab. Thus, the electron density can be chosen by selecting the number of ${\mathrm{SrTiO}}_3$ layers. For high densities, symmetry breaking and on-site Coulomb interaction drive the occurrence of correlated-electron ground states. Our results show that low dimensionality can lead to unconventional behavior of oxide heterostructures formed by electronically fairly simple nonmagnetic band insulators, and can open perspectives for the use of ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ superlattices grown along the [111] direction to explore quantum phase transitions.

The strong interplay of fundamental order parameters in complex oxides is known to give rise to exotic physical phenomena. The $4d$ transition-metal oxide $\mathrm{SrRh}{\mathrm{O}}_3$ has generated much interest, but advances have been hindered by difficulties in preparing single-crystalline phases. Here we epitaxially stabilize high-quality single-crystalline $\mathrm{SrRh}{\mathrm{O}}_3$ films and investigate their structural, electronic, and magnetic properties. We determine that their properties significantly differ from the paramagnetic metallic ground state that governs bulk samples and are strongly related to rotations of $\mathrm{Rh}{\mathrm{O}}_6$ octahedra.

Unidirectional evanescent-wave coupling from circularly polarized dipole sources is one of the most striking types of evidence of spin-orbit interactions of light and an inherent property of circularly polarized dipoles. Polarization handedness self-determines propagation direction of guided modes. In this paper, we compare two different approaches currently used to describe this phenomenon: the first requires the evaluation of the coupling amplitude between dipole and waveguide modes, while the second is based on the calculation of the angular spectrum of the dipole. We present an analytical expression of the angular spectrum of dipole radiation, unifying the description for both electric and magnetic dipoles. The symmetries unraveled by the implemented formalism show the existence of specific terms in the dipole spectrum which can be recognized as being directly responsible for directional evanescent-wave coupling. This provides a versatile tool for both a comprehensive understanding of the phenomenon and a fully controllable engineering of directionality of guided modes.

We present the results of classical molecular dynamics simulations to assess the relative contributions to interfacial thermal conductance from inelastic phonon processes at the interface and in the adjacent bulk materials. The simulated system is the prototypical interface between argon and “heavy argon” crystals, which enables comparison with many past computational studies. We run simulations interchanging the Lennard-Jones potential with its harmonic approximation to test the effect of anharmonicity on conductance. The results confirm that the presence of anharmonicity is correlated with increasing thermal conductance with temperature, which supports conclusions from prior experimental and theoretical work. However, in the model Ar/heavy-Ar system, anharmonic effects at the interface itself contribute a surprisingly small part of the total thermal conductance. The larger fraction of the thermal conductance at high temperatures arises from anharmonic effects away from the interface. These observations are supported by comparisons of the spectral energy density, which suggest that bulk anharmonic processes increase the interfacial conductance by thermalizing energy from modes with low transmission to modes with high transmission.

Infrared reflectance spectra of the polar optic phonons in a ${[{\left({\mathrm{BaTiO}}_3\right)}_8/{\left({\mathrm{SrTiO}}_3\right)}_4]}_{50}$ superlattice over the temperature range 8 to 650 K are reported. The spectra exhibit lattice vibration features typical of the perovskite constituents, ${\mathrm{BaTiO}}_3$ and ${\mathrm{SrTiO}}_3$. Using the effective medium approximation for multilayer systems and a fitting procedure, we were able to successfully simulate the infrared reflectivity of the superlattice structures and extract the parameters and dielectric functions of the phonons. When applied at varying temperatures, this approach provides the parameters of the zone-center polar phonons and their temperature dependence. Comparing these results with x–ray diffraction we identified some anomalies in phonon behavior related to the phase transitions that the superlattice undergoes.

The prediction for the stability of glassy material is a key challenge in physical science. Here, we report a theoretical framework to predict the glass stability based on stochastic surface walking global optimization and reaction pathway sampling. This is demonstrated by revealing for the first time the global potential energy surface (PES) of two systems, CuZr binary metallic glass and nonglassy pure Cu systems, and establishing the lowest energy pathways linking glassy/amorphous structures with crystalline structures. The CuZr system has a significant number of glassy structures on PES that are $\sim 0.045\mathrm{eV}/\mathrm{atom}$ above the crystal structure. Two clear trends are identified from global PES in the glass-to-crystal transition of the CuZr system: (i) the local Zr-Cu coordination (nearest neighbor) increases, and (ii) the local Zr bonding environment becomes homogeneous. This allows us to introduce quantitative structural and energetics conditions to distinguish the glassy structures from the crystalline structures. Because of the local Zr-Cu exchange in the glass-to-crystal transition, a high reaction barrier $\left(>0.048\mathrm{eV}/\mathrm{atom}\right)$ is present to separate the glassy structures and the crystals in CuZr. By contrast, the Cu system, although it does possess amorphous structures that appear at much higher energy $\left(\sim 0.075\mathrm{eV}/\mathrm{atom}\right)$ with respect to the crystal structure, has very low reaction barriers for the crystallization of amorphous structures, i.e. $<0.011\mathrm{eV}/\mathrm{atom}$. The quantitative data on PES now available from global optimization techniques deepens our understanding on the microscopic nature of glassy material and might eventually facilitate the design of stable glassy materials.

The correlation between magnetic properties and microscopic structural aspects in the diluted magnetic semiconductor ${\mathrm{Ge}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ is investigated by x-ray diffraction and magnetization as a function of the Mn concentration $x$. The occurrence of high ferromagnetic-transition temperatures in the rhombohedrally distorted phase of slowly cooled ${\mathrm{Ge}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ is shown to be directly correlated with the formation and coexistence of strongly distorted Mn-poor and weakly distorted Mn-rich regions. It is demonstrated that the weakly distorted phase fraction is responsible for the occurrence of high-transition temperatures in ${\mathrm{Ge}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$. When the Mn concentration becomes larger, the Mn-rich regions start to switch into the undistorted cubic structure, and the transition temperature is suppressed concurrently. By identifying suitable annealing conditions, we successfully increased the transition temperature to above 200 K for Mn concentrations close to the cubic phase. Structural data indicate that the weakly distorted phase fraction can be restored at the expense of the cubic regions upon the enhancement of the transition temperature, clearly establishing the direct link between high-transition temperatures and the weakly distorted Mn-rich phase fraction.

We report a study on the thermal conductivity of ${\mathrm{CuFe}}_{1-x}{\mathrm{Ga}}_x{\mathrm{O}}_2$ $\left(x=0–0.12\right)$ single crystals at temperatures down to 0.3 K and in magnetic fields up to 14 T. ${\mathrm{CuFeO}}_2$ is a well-known geometrically frustrated triangular lattice antiferromagnet and can be made to display multiferroicity either by applying magnetic field along the $c$ axis or by doping nonmagnetic impurities, accompanied by rich behaviors of magnetic phase transitions. The main experimental findings of this work are as follows: (i) the thermal conductivities $({\kappa }_a$ and ${\kappa }_c)$ show drastic anomalies at temperature- or field-induced magnetic transitions, (ii) the low-$T\kappa \left(H\right)$ isotherms exhibit irreversibility in a broad region of magnetic fields, and (iii) a phonon scattering effect is caused by magnetic fluctuations at very low temperatures. These results demonstrate strong spin-phonon coupling in this material and reveal the non-negligible magnetic fluctuations in the “ground state” of pure and Ga-doped samples.

Recently, nonsymmorphic symmetry was found to be able to protect various exotic surface fermions. One example is the hourglass fermions predicted and realized in the (010) surface of KHgSb. In this work, we investigate the finite-size effects of hourglass fermions in KHgSb (010) thin films by careful first-principles calculations and thorough group analyses. We find that in thin films, although most hourglasses open up a gap due to the finite-size effects, some hourglasses remain intact. The surviving hourglass fermions are protected by certain nonsymmorphic symmetries at certain high-symmetry lines. We propose that a feasible external electric field can recover all the gapless hourglasses. Also, we notice that hourglass fermions can hold a large-scale spin texture featuring Dirac points with the two constituting bands having the same spin polarization. Our findings may pave the way for thickness-engineered manipulation and application of hourglass fermions.

A spin-1 atomic gas in an optical lattice, in the unit-filling Mott insulator (MI) phase and in the presence of disordered spin-dependent interaction, is considered. In this regime, at zero temperature, the system is well described by a disordered rotationally invariant spin-1 bilinear-biquadratic model. We study, via the density matrix renormalization group algorithm, a bounded disorder model such that the spin interactions can be locally either ferromagnetic or antiferromagnetic. Random interactions induce the appearance of a disordered ferromagnetic phase characterized by a nonvanishing value of the spin glass order parameter across the boundary between a ferromagnetic phase and a dimer phase exhibiting random singlet order. We also study the distribution of the block entanglement entropy in the different regions.

The mixed $\mathrm{B}{\mathrm{a}}_2\mathrm{C}{\mathrm{o}}_9{\mathrm{O}}_{14}\mathrm{C}{\mathrm{o}}^{2+}/\mathrm{C}{\mathrm{o}}^{3+}$ system undergoes an insulator-insulator transition at $T_{\mathrm{SS}}\sim 567\mathrm{K}$ that arises from a spin-state transition at trivalent cobalt sites. Below this temperature, Co1, Co2, and Co4 are nonmagnetic ($S=0$, low spin). Ferromagnetically aligned Co5 spins are sandwiched between antiparallel planes of Co3 spins below $T_{\mathrm{N}}\approx 41\mathrm{K}$. The successive antiferromagnetic trilayers are inverted along the $c$ axis (compatible with $C_{c}2/c,C_{c}2/m$, or $P_S\text{−}1$ magnetic space groups, depending on the moment orientation in the $ab$ plane). The origin of the resistivity drop on warming was investigated by means of neutron and x-ray diffraction, x-ray absorption and emission spectroscopies, and x-ray magnetic circular dichroism. Charge-transfer multiplet calculations confirm that the divalent Co sites are both in an $S=3/2$ high spin state. Independently, the analysis of measured Co Kβ x-ray emission spectroscopy spectra agrees with this model. The magnetic moment from divalent Co5 ions is not fully ordered, likely due to the competition between magnetic anisotropy and weak supersuperexchange interactions, but not to covalency effects. Results agree with the spin blockade of electronic transport being partially removed at the octahedral trimers and also at the $\mathrm{Co}4{\mathrm{O}}_6$ units within the $\mathrm{Cd}{\mathrm{I}}_2$-type layer.

Particle-hole symmetry in the lowest Landau level of the two-dimensional electron gas requires the electrical Hall conductivity to equal $\pm e^2/2h$ at half filling. We study the consequences of weakly broken particle-hole symmetry for magnetoresistance oscillations about half filling in the presence of an applied periodic one-dimensional electrostatic potential using the Dirac composite fermion theory proposed by Son [Son, Phys. Rev. X 5, 031027 (2015)]. At fixed electron density, the oscillation minima are asymmetrically biased towards higher magnetic fields, while at fixed magnetic field the oscillations occur symmetrically as the electron density is varied about half filling. We find an approximate “sum rule” obeyed for all pairs of oscillation minima that can be tested in experiment. The locations of the magnetoresistance oscillation minima for the composite fermion theory of Halperin, Lee, and Read (HLR) and its particle-hole conjugate agree exactly. Within the current experimental resolution, the locations of the oscillation minima produced by the Dirac composite fermion coincide with those of HLR. These results may indicate that all three composite fermion theories describe the same long-wavelength physics.

We have used scanning tunneling microscopy and spectroscopy to resolve the spatial variation of the density of states of twisted graphene layers on top of a highly oriented pyrolytic graphite substrate. Owing to the twist a moiré pattern develops with a periodicity that is substantially larger than the periodicity of a single layer graphene. The twisted graphene layer has electronic properties that are distinctly different from that of a single layer graphene due to the nonzero interlayer coupling. For small twist angles $(\sim 1^{\circ }–3.5^{\circ })$ the integrated differential conductivity spectrum exhibits two well-defined Van Hove singularities. Spatial maps of the differential conductivity that are recorded at energies near the Fermi level exhibit a honeycomb structure that is comprised of two inequivalent hexagonal sublattices. For energies $|E-E_F|>0.3\mathrm{eV}$ the hexagonal structure in the differential conductivity maps vanishes. We have performed tight-binding calculations of the twisted graphene system using the propagation method, in which a third graphene layer is added to mimic the substrate. This third layer lowers the symmetry and explains the development of the two hexagonal sublattices in the moiré pattern. Our experimental results are in excellent agreement with the tight-binding calculations.

We study a model fractional quantum Hall (FQH) wave function called the Gaffnian state, which is believed to represent a gapless, strongly correlated state that is very different from conventional metals. To understand this exotic gapless state better, we provide a representation based on work of Halperin in which the pairing structure of the Gaffnian state becomes more explicit. We employ the single-mode approximation introduced by Girvin, MacDonald, and Platzman, here extended to three-body interactions, in order to treat a neutral collective excitation mode in order to clarify the physical origin of the gaplessness of the Gaffnian state. We discuss approaches to extract systematically the relevant physics in the long-distance, large-electron-number limit of FQH states using numerical calculations with relatively few electrons. In Appendices, we provide second-quantized expressions for many-body Haldane pseudopotentials in various geometries including the plane, sphere, cylinder, and torus based on the proper definition of the relative angular momentum.

Nodal surfaces of orbitals, in particular of the highest occupied one, play a special role in Kohn-Sham density-functional theory. The exact Kohn-Sham exchange potential, for example, shows a protruding ridge along such nodal surfaces, leading to the counterintuitive feature of a potential that goes to different asymptotic limits in different directions. We show here that nodal surfaces can heavily affect the potential of semilocal density-functional approximations. For the functional derivatives of the Armiento-Kümmel (AK13) [Phys. Rev. Lett. 111, 036402 (2013)] and Becke88 [Phys. Rev. A 38, 3098 (1988)] energy functionals, i.e., the corresponding semilocal exchange potentials, as well as the Becke-Johnson [J. Chem. Phys. 124, 221101 (2006)] and van Leeuwen–Baerends (LB94) [Phys. Rev. A 49, 2421 (1994)] model potentials, we explicitly demonstrate exponential divergences in the vicinity of nodal surfaces. We further point out that many other semilocal potentials have similar features. Such divergences pose a challenge for the convergence of numerical solutions of the Kohn-Sham equations. We prove that for exchange functionals of the generalized gradient approximation (GGA) form, enforcing correct asymptotic behavior of the potential or energy density necessarily leads to irregular behavior on or near orbital nodal surfaces. We formulate constraints on the GGA exchange enhancement factor for avoiding such divergences.

Field-effect transistors (FETs) were fabricated using exfoliated single crystals of $\mathrm{Mo}{\left(\mathrm{S}{\mathrm{e}}_{1-x}\mathrm{T}{\mathrm{e}}_x\right)}_2$ with an $x$ range of 0 to 1, and the transistor properties fully investigated at 295 K in four-terminal measurement mode. The chemical composition and crystal structure of exfoliated single crystals were identified by energy-dispersive x-ray spectroscopy (EDX), single-crystal x-ray diffraction, and Raman scattering, suggesting the $2H$- structure in all $\mathrm{Mo}{\left(\mathrm{S}{\mathrm{e}}_{1-x}\mathrm{T}{\mathrm{e}}_x\right)}_2$. The lattice constants of $a$ and $c$ increase monotonically with increasing $x$, indicating the substitution of Se by Te. When $x<0.4$ in a FET with a thin single crystal of $\mathrm{Mo}{\left(\mathrm{S}{\mathrm{e}}_{1-x}\mathrm{T}{\mathrm{e}}_x\right)}_2$, $n$-channel FET properties were observed, changing to $p$-channel or ambipolar operation for $x>0.4$. In contrast, the polarity of a thick single-crystal $\mathrm{Mo}{\left(\mathrm{S}{\mathrm{e}}_{1-x}\mathrm{T}{\mathrm{e}}_x\right)}_2$ FET did not change despite an increase in $x$. The change of polarity in a thin single-crystal FET was well explained by the variation of electronic structure. The absence of such change in the thick single-crystal FET can be reasonably interpreted based on the large bulk conduction due to naturally accumulated electrons. The $\mu$ value in the thin single-crystal FET showed a parabolic variation, with a minimum $\mu$ at around $x=0.4$, which probably originates from the disorder of the single crystal caused by the partial replacement of Se by Te, i.e., a disorder that may be due to ionic size difference of Se and Te.