We propose a simple gradient-dependent bound for the exchange-correlation energy (sLL), based on the recent nonlocal bound derived by Lewin and Lieb. We show that sLL is equivalent to the original Lieb-Oxford bound in rapidly varying density cases, but it is tighter for slowly varying density systems. To show the utility of the sLL bound we apply it to the construction of simple semilocal and nonlocal exchange and correlation functionals. In both cases improved results, with respect to the use of Lieb-Oxford bound, are obtained, showing the power of the sLL bound.

Coupling of the spin and orbital degrees of freedom on the surface of a strong three-dimensional insulator, on the one hand, and textured magnetic configuration in an adjacent ferromagnetic film, on the other, is studied using a combination of transport and thermodynamic considerations. Expressing exchange coupling between the localized magnetic moments and Dirac electrons in terms of the electrons' out-of-plane orbital and spin magnetizations, we relate the thermodynamic properties of a general ferromagnetic spin texture to the physics in the zeroth Landau level. Persistent currents carried by Dirac electrons endow the magnetic texture with a Dzyaloshinski-Moriya interaction, which exhibits a universal scaling form as a function of electron temperature, chemical potential, and the time-reversal symmetry breaking gap. In addition, the orbital motion of electrons establishes a direct magnetoelectric coupling between the unscreened electric field and local magnetic order, which furnishes complex long-ranged interactions within the magnetic film.

We investigate the skyrmion formation process in nanostructured FeGe Hall-bar devices by measurements of the topological Hall effect, which extracts the winding number of a spin texture as an emergent magnetic field. Stepwise profiles of the topological Hall resistivity are observed in the course of varying the applied magnetic field, which arise from instantaneous changes in the magnetic nanostructure such as the creation, annihilation, and jittering motion of skyrmions. The discrete changes in the topological Hall resistivity demonstrate the quantized nature of an emergent magnetic flux inherent in each skyrmion, which had been indistinguishable in many-skyrmion systems on a macroscopic scale.

NMR measurements of spin-lattice relaxation of hydrogen nuclei in two prototype organic semiconducting solids, MEH-PPV and DOO-PPV, were carried out for temperatures between 4.2 K and room temperature, and for applied magnetic fields between 1.25 and 4.7 T. These $\pi$-conjugated polymers are of interest for use as the active semiconducting layer in spintronic devices. They typically exhibit weak spin-orbit coupling, and the interaction with inhomogeneous hyperfine fields generated by the nuclear spins plays a significant, if not dominant, role in the spin coherence and spin relaxation of electronic charge carriers. Our studies were conducted on unbiased bulk material with no photo-illumination. The characteristic ${}^1\mathrm{H}$ longitudinal relaxation times in these materials ranges from hundreds of milliseconds to $>1000$ s, and are predominantly nonmonoexponential. We present the data both in terms of a recovery time, $T_{1/2}$, corresponding to 50% recovery of thermal magnetization from saturation and in terms of a “$T_1$ spectrum” produced via a numerical Laplace transform of the time-domain data. The evidence best supports relaxation to paramagnetic centers (radicals) mediated by nuclear spin diffusion as the primary mechanism: the observed relaxation is predominantly nonmonoexponential, and a characteristic $T_1$ minimum as a function of temperature is apparent for both materials somewhere between 77 K and room temperature. The paramagnetic centers may be somewhat-delocalized charge-carrier pairs (i.e., polarons) along the polymer backbone, although the concentration in an unbiased sample (no carrier injection) should be very low. Alternatively, the centers may be localized defects, vacancies, or impurities. Our results may also be used to judge the feasibility of Overhauser-type dynamic nuclear polarization from polarized charge carriers or optically pumped exciton states.

Motivated by a recent experiment [F. Pei et al., Nat. Nanotechnol. 7, 630 (2012)], we theoretically study the Pauli blockade transport effect in a double quantum dot embedded in a bent carbon nanotube. We establish a model for the Pauli blockade, taking into account the strong $g$-factor anisotropy that is linked to the local orientation of the nanotube axis in each quantum dot. We provide a set of conditions under which our model is approximately mapped to the spin-blockade model of Jouravlev and Nazarov [O. N. Jouravlev and Y. V. Nazarov, Phys. Rev. Lett. 96, 176804 (2006)]. The results we obtain for the magnetic anisotropy of the leakage current, together with their qualitative geometrical explanation, provide a possible interpretation of previously unexplained experimental results. Furthermore, we find that in a certain parameter range, the leakage current becomes highly sensitive to the shape of the tube, and this sensitivity increases with increasing $g$-factor anisotropy. This mutual dependence of the electron transport and the tube shape allows for mechanical control of the leakage current, and for characterization of the tube shape via measuring the leakage current.

Band splittings, chiral spin polarization, and topological surface states generated by spin-orbit interactions at crystal surfaces are receiving a lot of attention for their potential device applications as well as fascinating physical properties. Most studies have focused on $sp$ states near the Fermi energy, which are relevant for transport and have long lifetimes. Far less explored, though in principle stronger, are spin-orbit interaction effects within $d$ states, including those deep below the Fermi energy. Here, we report a joint photoemission and ab initio study of spin-orbit effects in the deep $d$-orbital surface states of a 24-layer Au film grown on Ag(111) and a 24-layer Ag film grown on Au(111), singling out a conical intersection (Dirac cone) between two surface states in a large surface-projected gap at the time-reversal symmetric $\overline{M}$ points. Unlike the often isotropic dispersion at $\overline{\Gamma }$ point Dirac cones, the $\overline{M}$ point cones are strongly anisotropic. An effective $\mathbf{k}·\mathbf{p}$ Hamiltonian is derived to describe the anisotropic band splitting and spin polarization near the Dirac cone.

Using hybrid density functional theory combined with a semiempirical van der Waals dispersion correction, we have investigated the structural and electronic properties of vacancies and self-interstitials in defective few-layer phosphorene. We find that both a vacancy and a self-interstitial defect are more stable in the outer layer than in the inner layer. The formation energy and transition energy of both a vacancy and a self-interstitial $P$ defect decrease with increasing film thickness, mainly due to the upward shift of the host valence band maximum in reference to the vacuum level. Consequently, both vacancies and self-interstitials could act as shallow acceptors, and this well explains the experimentally observed $p$-type conductivity in few-layer phosphorene. On the other hand, since these native point defects have moderate formation energies and are stable in negatively charged states, they could also serve as electron compensating centers in $n$-type few-layer phosphorene.

Thin Bi(110) films deposited on highly oriented pyrolytic graphite (HOPG) exhibit a pronounced moiré pattern; here the origin of the moiré pattern is investigated using scanning tunneling microscopy (STM) and spectroscopy (STS), high-resolution transmission electron microscopy (HR-TEM), and density functional theory (DFT). It is shown that the moiré pattern forms only on islands which are misoriented by $\sim {30}^{\circ }$ with respect to the usual substrate symmetry direction. Two models of the moiré pattern are presented: (i) a commensurate monolayer construction (CMC) for rectangular overlayer symmetry on hexagonal substrates and (ii) a qualitative model based on simple superposition of a Bi overlayer on graphene. The CMC model has previously been applied only to systems with pure hexagonal symmetry. Both models generate moiré patterns with key parameters (period, angles of the pattern measured with respect to the main HOPG and Bi crystal directions) that are consistent with the experimental results, but development of a fully predictive/quantitative model remains an outstanding challenge. The electronic structure of the moiré pattern is investigated using STS and DFT, and it is found that the local density of states (LDOS) is modulated by the moiré pattern. These results are consistent with a picture in which a small distortion of Bi atomic positions at the film-substrate interface results in periodic modulation of the LDOS, hence allowing observation of the moiré pattern in STM images.

We analyze the electronic properties of bilayer graphene with Bernal stacking and a low concentration of adatoms. Assuming that the host bilayer lies on top of a substrate, we consider the case where impurities are adsorbed only on the upper layer. We describe nonmagnetic impurities as a single orbital hybridized with carbon's ${\mathrm{p}}_z$ states. The effect of impurity doping on the local density of states with and without a gated electric field perpendicular to the layers is analyzed. We look for Anderson localization in the different regimes and estimate the localization length. In the biased system, the field-induced gap is partially filled by strongly localized impurity states. Interestingly, the structure, distribution, and localization length of these states depend on the field polarization.

Recent angle-resolved photoemission reveals that the doping level in some ${\mathrm{BiS}}_2$-based superconductors is much lower than the nominal one. Here we determine the pairing function at such a realistic low doping level by a functional renormalization group (FRG) and study the resulting physical properties by an FRG-based effective mean field theory. We find that the pairing is a mixture of singlets and triplets due to spin-orbital coupling, and the triplet components dominate. The gap function transforms as a $d_{x^2-y^2}^{*}$ wave under simultaneous rotation of spin and lattice, but is nodeless on the Fermi pockets which avoid the nodal lines. The specific heat, superfluid density, and Knight shift are similar to that in a fully gapped conventional $s$-wave superconductor, in agreement with available experiments. However, the absence of the Hebel-Slichter peak in spin-lattice relaxation rate (in the dirty limit), the impurity induced in-gap states, and the gapless edge states (due to the weak topological nature of the pairing) are defining properties of the nodeless $d_{x^2-y^2}^{*}$-wave pairing to be measured in future experiments.

Core hole resonance is used in x-ray spectroscopy to incisively probe the local electronic states of many-body systems. Here, resonant inelastic x-ray scattering (RIXS) is studied as a function of incident photon energy on Mott insulators ${\mathrm{SrCuO}}_2$ and NiO to examine how resonance states decay into different excitation symmetries at the transition-metal $M$, $L$, and $K$ edges. Quantum interference patterns characteristic of the two major RIXS mechanisms are identified within the data, and used to distinguish the attosecond scale scattering dynamics by which fundamental excitations of a many-body system are created. A function is proposed to experimentally evaluate whether a particular excitation has constructive or destructive interference in the RIXS cross section, and corroborates other evidence that an anomalous excitation is present at the leading edge of the Mott gap in quasi-one-dimensional ${\mathrm{SrCuO}}_2$.

The magnetic susceptibilities of nanoparticle assemblies of two Bechgaard salts ${\left(\mathrm{TMTSF}\right)}_2{\text{PF}}_6$ and ${\left(\mathrm{TMTSF}\right)}_2{\text{ClO}}_4$, have been studied vs temperature and magnetic field. In the bulk these materials exhibit a spin density wave formation $(T_{\text{SDW}}=12\mathrm{K})$ and superconductivity $(T_{\text{c}}=1.2\mathrm{K})$, respectively. We show from inductive (susceptibility) measurements that the nanoparticle assemblies exhibit ground-state phase transitions similar to those of randomly oriented polycrystalline samples of the parent materials. Resistivity and diamagnetic shielding measurements yield additional information on the functional nanoparticle structure in terms of stoichiometric and nonstoichiometric composition.

We use quantum Monte Carlo simulations to study a finite-temperature dimensional-crossover-driven evolution of spin and charge dynamics in an anisotropic two-dimensional system of weakly coupled Hubbard chains with a half-filled band. The low-temperature behavior of the charge gap indicates a crossover between two distinct energy scales: a high-energy one-dimensional (1D) Mott gap due to the umklapp process and a low-energy gap which stems from long-range antiferromagnetic (AF) spin fluctuations. Away from the 1D regime and at temperature scales above the charge gap, the emergence of a zero-frequency Drude-like feature in the interchain optical conductivity ${\sigma }_{\perp }\left(\omega \right)$ implies the onset of a higher-dimensional metal. In this metallic phase, enhanced quasiparticle scattering off finite-range AF spin fluctuations results in incoherent single-particle dynamics. The coupling between spin and charge fluctuations is also seen in the spin dynamical structure factor $S(q,\omega )$ displaying damped spin excitations (paramagnons) close to the AF wave vector $q=(\pi ,\pi )$ and particle-hole continua near 1D momentum transfers spanning quasiparticles at the Fermi surface. We relate our results to the charge deconfinement in quasi-1D organic Bechgaard-Fabre salts.

Noncentrosymmetric superconductors with strong spin-orbit coupling and the B phase of ${}^3\mathrm{He}$ are possible realizations of topological superconductors with time-reversal symmetry. The nontrivial topology of these time-reversal invariant superconductors manifests itself at the material surface in the form of helical Majorana modes. In this paper, using extensive numerical simulations, we investigate the stability and properties of these Majorana states under strong surface disorder, which influences both bulk and surface states. To characterize the effects of strong disorder, we compute the level spacing statistics and the local density of states of both two- and three-dimensional topological superconductors. The Majorana surface states, which are located in the outermost layers of the superconductor, are protected against weak disorder due to their topological characteristic. Sufficiently strong disorder, on the other hand, partially localizes the surface layers, with a more pronounced effect on states with energies close to the gap than on those with energies close to zero. In particular, we observe that for all disorder strengths and configurations there always exist two extended states at zero energy that can carry thermal current. At the crossover from weak to strong disorder the surface state wave functions and the local density of states show signs of critical delocalization. We find that at this crossover the edge density of states of two-dimensional topological superconductors exhibits a zero-energy divergence, reminiscent of the Dyson singularity of quasi-one-dimensional dirty superconductors.

We employ a combination of density functional theory (DFT), molecular dynamics (MD), and a variety of advanced postprocessing methods to construct an analytic thermodynamic potential (free energy) for ices VII and X. In particular, the temperature-dependent part of the free energy function is constructed using entropy data obtained via the spectrum of vibrational modes from the MD simulations. Conceptional challenges due to the partial absence of stable zero-temperature states and proton disorder are overcome by performing calculations of representative crystalline states combined with a three-stage fitting procedure of data from MD simulations and static DFT calculations. The influence of the exchange-correlation functional is extensively discussed, and a comparison with available experiments is made as well and generally shows good agreement. This work is of significant importance for astrophysical applications, such as the interior modeling of dense icy planets and moons.

We report on a highly efficient spin diode effect in exchange-biased spin-valve giant-magnetoresistance (GMR) strips. In such multilayer structures, the symmetry of the current distribution along the vertical direction is broken and, as a result, a noncompensated Oersted field acting on the magnetic free layer appears. This field in turn is a driving force of magnetization precessions. Due to the GMR effect, the resistance of the strip oscillates following the magnetization dynamics. This leads to rectification of the applied radio-frequency current and induces a direct-current voltage $V_{\text{dc}}$. We present a theoretical description of this phenomenon and calculate the spin diode signal $V_{\text{dc}}$ as a function of frequency, external magnetic field, and angle at which the external field is applied. Satisfactory quantitative agreement between theoretical predictions and experimental data has been achieved. Finally, we show that the spin diode signal in GMR devices is significantly stronger than in the anisotropic magnetoresistance permalloy-based devices.

In many materials it remains a challenge to reveal the nature of magnetic correlations, including antiferromagnetism and spin disorder. Revealing the spin structure in magnetic nanoparticles is further complicated by the large incoherent neutron scattering cross section from water adsorbed at the particle surfaces and by the broadening of diffraction peaks due to the finite crystallite size. Moreover, the spin structure in magnetic nanoparticles may deviate significantly from that of the corresponding bulk material because of the low-symmetry surroundings of surface atoms and the large relative surface contribution to the magnetic anisotropy. Here we explore the potential use of polarized neutron diffraction to reveal the magnetic structure in NiO bulk and nanoparticle powders by applying the $XYZ$-polarization analysis method. Our investigations address in particular the spin orientation in bulk NiO and platelet-shaped NiO nanoparticles with thickness from greater than 200 nm down to 2.0 nm. The advantage of the applied method is that it is able to clearly separate the structural, the magnetic, and the spin-incoherent scattering signals for all particle sizes. For platelet-shaped particles with thickness from greater than 200 nm down to 2.2 nm we find that the spin orientation deviates about ${16}^{\circ }$ from the primary (111) plane of the platelet-shaped particles. In the smallest particles (2.0 nm thick) we find the spins are oriented with a ${30}^{\circ }$ average angle to the primary (111) plane of the particles. The results show that polarization analyzed neutron powder diffraction is a viable method to investigate magnetic order in powders of antiferromagnetic nanoparticles.

Inelastic neutron scattering techniques have been used to study the field-induced multiferroic transition and the temperature dependence of magnetic excitations in ${\text{TbMnO}}_3$. The significant changes in the spin-wave spectra across the field-induced transition perfectly agree with a rotation of the cycloidal spiral plane and with efficient pinning in the commensurate high-field phase. Further analysis of the $\mathbf{Q}$ dependence allows the identification of an electromagnon in the multiferroic high-field phase whose energy and polarization precisely matches previous infrared data. This and the zero-field temperature dependence of a zone-center magnon, which exactly agrees with that of an optically detected excitation, document that the inverse Dzyaloshinskii-Moriya interaction induces an electromagnon hybrid excitation in ${\text{TbMnO}}_3$.

We study numerically Majorana fermions (MFs) induced by a charged impurity in topological superconductors. It is revealed from the relevant Bogoliubov–de Gennes equations that (i) for quasi-one-dimensional systems, a pair of MFs are bounded at the two sides of one charged impurity and are well-separated; and (ii) for a two-dimensional square lattice, the charged-impurity-induced MFs are similar to the known pair of vortex-induced MFs, in which one MF is bounded by the impurity while the other appears at the boundary. Moreover, the corresponding local density of states is explored, demonstrating that the presence of MF states may be tested experimentally.

Lattice structures have long fascinated physicists and engineers not only because of their outstanding functionalities, but also for their ability to control the propagation of elastic waves. While the study of the relation between the connectivity of these systems and their static properties has a long history that goes back to Maxwell, rules that connect the dynamic response to the network topology have not been established. Here, we demonstrate that by tuning the average connectivity of a beam network $\left(\overline{z}\right)$, locally resonant band gaps can be generated in the structures without embedding additional resonating units. In particular, a critical threshold for $\overline{z}$ is identified, far from which the band gap size is purely dictated by the global lattice topology. By contrast, near this critical value, the detailed local geometry of the lattice also has strong effects. Moreover, in stark contrast to the static case, we find that the nature of the joints is irrelevant to the dynamic response of the lattices. Our results not only shed new light on the rich dynamic properties of periodic lattices, but also outline a new strategy to manipulate mechanical waves in elastic systems.