Energy gaps are crucial aspects of the electronic structure of finite and extended systems. Whereas much is known about how to define and calculate charge gaps in density-functional theory (DFT), and about the relation between these gaps and derivative discontinuities of the exchange-correlation functional, much less is known about spin gaps. In this paper we give density-functional definitions of spin-conserving gaps, spin-flip gaps and the spin stiffness in terms of many-body energies and in terms of single-particle (Kohn-Sham) energies. Our definitions are as analogous as possible to those commonly made in the charge case, but important differences between spin and charge gaps emerge already on the single-particle level because unlike the fundamental charge gap spin gaps involve excited-state energies. Kohn-Sham and many-body spin gaps are predicted to differ, and the difference is related to derivative discontinuities that are similar to, but distinct from, those usually considered in the case of charge gaps. Both ensemble DFT and time-dependent DFT (TDDFT) can be used to calculate these spin discontinuities from a suitable functional. We illustrate our findings by evaluating our definitions for the Lithium atom, for which we calculate spin gaps and spin discontinuities by making use of near-exact Kohn-Sham eigenvalues and, independently, from the single-pole approximation to TDDFT. The many-body corrections to the Kohn-Sham spin gaps are found to be negative, i.e., single-particle calculations tend to overestimate spin gaps while they underestimate charge gaps.

We study the spectral function of a two-dimensional superconductor in a regime of strong phase fluctuations. Although the developed approach is valid for any symmetry, we concentrate on $d$-wave superconductors. We obtain analytical expressions for the single electron Green’s function below the transition temperature and have worked out a way to extrapolate it for a finite temperatures above $T_c$. The suggested approach is easily generalizable for other models with critical fluctuations.

A mechanism for relaxing the nuclear magnetic moments, in which a pair of spin-polarized BCS quasiparticles is emitted or absorbed, and which dominates at low temperature, is identified in type-II $d$-wave superconductors in an external magnetic field above $H_{c1}$. The results of the theory are compared with the NMR experiments on YBCO in high magnetic fields and found to agree without invoking antiferromagnetic order in the vortex core.

The experimental realization of Majorana fermions presents an important problem due to their non-Abelian nature and potential exploitation for topological quantum computation. Very recently Sau et al. [Phys. Rev. Lett. 104, 040502 (2010)] demonstrated that a topological superconducting phase supporting Majorana fermions can be realized using surprisingly conventional building blocks: a semiconductor quantum well coupled to an $s$-wave superconductor and a ferromagnetic insulator. Here we propose an alternative setup, wherein a topological superconducting phase is driven by applying an in-plane magnetic field to a (110)-grown semiconductor coupled only to an $s$-wave superconductor. This device offers a number of advantages, notably a simpler architecture and the ability to tune across a quantum phase transition into the topological superconducting state while still largely avoiding unwanted orbital effects. Experimental feasibility of both setups is discussed in some detail.

A combination of spectroscopic probes was used to develop a detailed experimental description of the transport and magnetic properties of superlattices composed of the paramagnetic metal ${\text{CaRuO}}_3$ and the antiferromagnetic insulator ${\text{CaMnO}}_3$. The charge-carrier density and Ru valence state in the superlattices are not significantly different from those of bulk ${\text{CaRuO}}_3$. The small charge transfer across the interface implied by these observations confirms predictions derived from density-functional calculations. However, a ferromagnetic polarization due to canted Mn spins penetrates 3–4 unit cells into ${\text{CaMnO}}_3$, far exceeding the corresponding predictions. The discrepancy may indicate the formation of magnetic polarons at the interface.

We study the concept of spin heat accumulation in excited spin valves, more precisely the effective electron temperature that may become spin dependent, both in linear response and far from equilibrium. A temperature or voltage gradient create nonequilibrium energy distributions of the two spin ensembles in the normal-metal spacer, which approach Fermi-Dirac functions through energy relaxation mediated by electron-electron and electron-phonon coupling. Both mechanisms also exchange energy between the spin subsystems. This interspin energy exchange may strongly affect thermoelectric properties of spin valves, leading, e.g., to violations of the Wiedemann-Franz law.

We perform a numerical simulation of quantum turbulence produced by thermal counterflow in superfluid ${}^4\text{H}\text{e}$ by using the vortex filament model with the full Biot-Savart law. The pioneering work of Schwarz has two shortcomings: it neglects the nonlocal terms of the Biot-Savart integral [known as the localized induction approximation (LIA)] and it employs an unphysical mixing procedure to sustain the statistically steady state of turbulence. We have succeeded in generating the statistically steady state under periodic boundary conditions without using the LIA or the mixing procedure. This state exhibits the characteristic relation $L={\gamma }^2{v}_{ns}^2$ between the line-length density $L$ and the counterflow relative velocity $v_{ns}$ and there is quantitative agreement between the coefficient $\gamma$ and some measured values. The parameter $\gamma$ and some anisotropy parameters are calculated as functions of temperature and the counterflow relative velocity. The numerical results obtained using the full Biot-Savart law are compared with those obtained using the LIA. The LIA calculation constructs a layered structure of vortices and does not proceed to a turbulent state but rather to another anisotropic vortex state; thus, the LIA is not suitable for simulations of turbulence.

Ferroelectric perovskite solid solutions with morphotropic phase boundary (MPB) have been studied extensively as best candidates for electromechanical transduction due to their exceptionally high piezoelectric coefficients. However, despite the high number of publications about these oxides, there is still ambiguity about the actual symmetry of the phases at the MPBs. Here, we present a detailed analysis of the crystalline structure of $0.39{\text{BiScO}}_3\text{−}0.61{\text{PbTiO}}_3$ twin free nanocrystals, using the combination of aberration-corrected high-resolution electron microscopy and multislice simulations. Our study indicates the presence of a monoclinic symmetry for crystals with an average size of 15 nm. This is strong evidence in favor of the actual existence of this polymorph at the MPB, which has been recently questioned. It also shows that perovskite distortion is still present in nanocrystals, which is important from the point of view of the size limit of ferroelectricity and consistent with previous electrical measurements in nanostructured ceramics.

The lateral Casimir force, which arises between aligned sinusoidally corrugated surfaces of a sphere and a plate, was measured for the case of a small corrugation period beyond the applicability region of the proximity force approximation (PFA). The increased amplitudes of the corrugations on both the sphere and the plate allowed observation of an asymmetry of the lateral Casimir force, i.e., deviation of its profile from a perfect sine function. The dependences of the lateral force on the phase shift between the corrugations on both test bodies were measured at different separations in two sets of measurements with different amplitudes of corrugations on the sphere. The maximum magnitude of the lateral force as a function of separation was also measured in two successive experiments. All measurement data were compared with the theoretical approach using the proximity force approximation and with the exact theory based on Rayleigh expansions with no fitting parameters. In both cases real material properties of the test bodies and nonzero temperature were taken into account. The data were found to be in a good agreement with the exact theory but deviate significantly from the predictions of the proximity force approximation approach. This provides the quantitative confirmation for the observation of diffraction-type effects that are disregarded within the PFA approach. Possible applications of the phenomenon of the lateral Casimir force in nanotechnology for the operation of micromachines are discussed.

We present a method for obtaining quantum transport properties in graphene that uniquely combines three crucial features: microscopic treatment of charge disorder, fully quantum-mechanical analysis of transport, and the ability to model experimentally relevant system sizes. As a pertinent application we study the disorder dependence of Klein tunneling dominated transport in $p\text{−}n\text{−}p$ junctions. Both the resistance and the Fano factor show broad resonance peaks due to the presence of quasi-bound-states. This feature is washed out by the disorder when the mean free path becomes of the order of the distance between the two $p\text{−}n$ interfaces.

We study the impact of spin-active scattering on Andreev spectra of point contacts between superconductors (SC) and strongly spin-polarized ferromagnets (FM) using recently derived boundary conditions for the quasiclassical theory of superconductivity. We describe the interface region by a microscopic model for the interface scattering matrix. Our model includes both spin filtering and spin mixing and is nonperturbative in both transmission and spin polarization. We emphasize the importance of spin-mixing caused by interface scattering, which has been shown to be crucial for the creation of exotic pairing correlations in such structures. We provide estimates for the magnitude of this effect in different scenarios and discuss its dependence on various physical parameters. Our main finding is that the shape of the interface potential has a tremendous impact on the magnitude of the spin-mixing effect. Thus, all previous calculations, being based on delta-function or box-shaped interface potentials, underestimate this effect gravely. As a consequence, we find that with realistic interface potentials the spin-mixing effect can easily be large enough to cause spin-polarized subgap Andreev bound states in SC/FM point contacts. In addition, we show that our theory generalizes earlier models based on the Blonder-Tinkham-Klapwijk approach.

We fabricated bilayer photonic crystal (PhC) as large as $20\times 30\mu \text{m}$ possessing 200-nm-thick slabs and a 200-nm-thick air gap. Input power dependence of reflectance spectra indicates air gap reduction by 3.6 nm. Combining it with finite element method calculation we estimate optomechanically generated force per unit stored energy as $0.4\mu \text{N}/\text{pJ}$, exhibiting strong optomechanical coupling. RF spectrum of reflected light reveals intensity modulation by thermal vibration of bilayer PhC, which also shows strong interaction of optical resonance mode and mechanical mode of bilayer PhC

Low-temperature magnetoconductance measurements were made in the vicinity of the charge neutrality point (CNP). Two origins for the fluctuations were identified close to the CNP. At very low magnetic fields there exist only mesoscopic magnetoconductance quantum interference features which develop rapidly as a function of density. At slightly higher fields $\left(>0.5\text{T}\right)$, close to the CNP, additional fluctuations track the quantum Hall (QH) sequence expected for monolayer graphene. These additional features are attributed to effects of locally charging individual QH localized states. These effects reveal a precursor to the quantum Hall effect since, unlike previous transport observations of QH dot charging effects, they occur in the absence of quantum Hall plateaus or Shubnikov-de Haas oscillations. From our transport data we are able to extract parameters that characterize the inhomogeneities in our device.

Using high-quality graphene $pnp$ junctions, we observe prominent conductance fluctuations on transitions between quantum Hall (QH) plateaus as the top gate voltage $V_{tg}$ is varied. In the $V_{tg}\text{−}B$ plane, the fluctuations form crisscrossing lines that are parallel to those of the adjacent plateaus, with different temperature dependences for the conductance peaks and valleys. These fluctuations arise from Coulomb-induced charging of electron- or hole-doped localized states when the device bulk is delocalized, underscoring the importance of electronic interactions in graphene in the QH regime.

Recently, fractional-quantized Hall effect was observed in suspended graphene (SG), a free-standing monolayer of carbon, where it was found to persist up to $T=10\text{K}$. The best results in those experiments were obtained on micron-size flakes, on which only two-terminal transport measurements could be performed. Here we address the problem of extracting transport coefficients of a fractional quantum Hall state from the two-terminal conductance. We develop a general method, based on the conformal invariance of two-dimensional magnetotransport, and employ it to analyze the measurements on SG. From the temperature dependence of longitudinal conductivity, extracted from the measured two-terminal conductance, we estimate the energy gap of quasiparticle excitations in the fractional-quantized $\nu =1/3$ state. The gap is found to be significantly larger than in GaAs-based structures, signaling much stronger electron interactions in suspended graphene. Our approach provides a tool for the studies of quantum transport in suspended graphene and other nanoscale systems.

The critical current of a niobium type II superconducting loop has been measured far below the critical temperature using contacts applied symmetrically or asymmetrically around the loop. The magnetic field dependence of the critical current allows a direct observation of the circulating current resulting from the fluxoid quantization and presents a saw-tooth behavior. The periodicity is given by a flux quantum through the outer area of the loop. Despite the presence of many vortices at high magnetic fields, the circulating current finds its way in between them and still has an impact on the total critical current of the loop. Macroscopic quantum coherence effects in such a niobium loop allow observing single quanta changes of the fluxoid up to a magnetic field of 1.2 T.

We study the transport properties of graphene nanoribbons of standardized 30 nm width and varying lengths. We find that the extent of the gap observed in transport as a function of Fermi energy in these ribbons (the “transport gap”) does not have a strong dependence on ribbon length, while the extent of the gap as a function of source-drain voltage (the “source-drain gap”) increases with increasing ribbon length. We anneal the ribbons to reduce the amplitude of the disorder potential and find that the transport gap both shrinks and moves closer to zero gate voltage. In contrast, annealing does not systematically affect the source-drain gap. We conclude that the transport gap reflects the overall strength of the background disorder potential, while the source-drain gap is sensitively dependent on its details. Our results support the model that transport in graphene nanoribbons occurs through quantum dots forming along the ribbon due to a disorder potential induced by charged impurities.

The ${}^{57}\text{F}\text{e}$-specific phonon density of states (DOS) of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ single crystals $\left(x=0.0,0.08\right)$ was measured at cryogenic temperatures and at high pressures with nuclear-resonant inelastic x-ray scattering. Measurements were conducted for two different orientations of the single crystals, yielding the orientation-projected ${}^{57}\text{F}\text{e}$-phonon density of states for phonon polarizations in-plane and out-of-plane with respect to the basal plane of the crystal structure. In the tetragonal phase at 300 K, a clear stiffening was observed upon doping with Co. Increasing pressure to 4 GPa caused a marked increase of phonon frequencies, with the doped material still stiffer than the parent compound. Upon cooling, both the doped and undoped samples showed a stiffening and the parent compound exhibited a discontinuity across the magnetic and structural phase transitions. These findings are generally compatible with the changes in volume of the system upon doping, increasing pressure, or increasing temperature, but an extra softening of high-energy modes occurs with increasing temperature. First-principles computations of the phonon DOS were performed and showed an overall agreement with the experimental results, but underestimate the Grüneisen parameter. This discrepancy is explained in terms of a magnetic Grüneisen parameter, causing an extra phonon stiffening as magnetism is suppressed under pressure.

A study of the antiferromagnet ${\text{CeRh}}_2{\text{Si}}_2$ by torque, magnetostriction, and transport in pulsed magnetic fields up to 50 T and by thermal expansion in static fields up to 13 T is presented. The magnetic field temperature phase diagram of ${\text{CeRh}}_2{\text{Si}}_2$, where the magnetic field is applied along the easy axis $\mathbf{c}$, is deduced from these measurements. The second-order phase transition temperature $T_N$ and the first-order phase transition temperature $T_{1,2}$ ($=36\text{K}$ and 26 K at zero field, respectively) decrease with increasing field. The field-induced antiferromagnetic-to-paramagnetic borderline $H_c$, which equals 26 T at 1.5 K, goes from first order at low temperature to second order at high temperature. The magnetic field temperature phase diagram is found to be composed of (at least) three different antiferromagnetic phases. These are separated by the first-order lines $H_{1,2}$, corresponding to $T_{1,2}$ at $H=0$, and $H_{2,3}$, which equals 25.5 T at 1.5 K. A maximum of the $T^2$-coefficient $A$ of the resistivity is observed at the onset of the high-field polarized regime, which is interpreted as the signature of an enhanced effective mass at the field-induced quantum instability. The magnetic field dependence of the $A$ coefficient in ${\text{CeRh}}_2{\text{Si}}_2$ is compared with its pressure dependence, and also with the field dependence of $A$ in the prototypal heavy-fermion system ${\text{CeRu}}_2{\text{Si}}_2$.

We present an implementation of the $GW$ approximation for the electronic self-energy within the full-potential linearized augmented-plane-wave (FLAPW) method. The algorithm uses an all-electron mixed product basis for the representation of response matrices and related quantities. This basis is derived from the FLAPW basis and is exact for wave-function products. The correlation part of the self-energy is calculated on the imaginary-frequency axis with a subsequent analytic continuation to the real axis. As an alternative we can perform the frequency convolution of the Green function $G$ and the dynamically screened Coulomb interaction $W$ explicitly by a contour integration. The singularity of the bare and screened interaction potentials gives rise to a numerically important self-energy contribution, which we treat analytically to achieve good convergence with respect to the $\mathbf{k}$-point sampling. As numerical realizations of the $GW$ approximation typically suffer from the high computational expense required for the evaluation of the nonlocal and frequency-dependent self-energy, we demonstrate how the algorithm can be made very efficient by exploiting spatial and time-reversal symmetry as well as by applying an optimization of the mixed product basis that retains only the numerically important contributions of the electron-electron interaction. This optimization step reduces the basis size without compromising the accuracy and accelerates the code considerably. Furthermore, we demonstrate that one can employ an extrapolar approximation for high-lying states to reduce the number of empty states that must be taken into account explicitly in the construction of the polarization function and the self-energy. We show convergence tests, CPU timings, and results for prototype semiconductors and insulators as well as ferromagnetic nickel.