Odd-frequency superconductivity describes a class of superconducting states where the superconducting gap is an odd function in relative time and Matsubara frequency. We present a group theoretical analysis based on the linearized gap equation in terms of Shubnikov groups of the second kind. By discussing systems with spin-orbit coupling and an interaction kernel which is symmetric under the reversal of relative time, we show that both even- and odd-frequency gaps are allowed to occur. Specific examples are discussed for the square lattice, the octahedral lattice, and the tetragonal lattice. For irreducible representations that are even under the reversal of relative time the common combinations of $s$- and $d$-wave spin singlet and $p$-wave spin triplet gaps are revealed, irreducible representations that are odd under reversal of relative time give rise to $s$- and $d$-wave spin triplet and $p$-wave spin singlet gaps. Furthermore, we discuss the construction of a generalized Ginzburg-Landau theory in terms of the associated irreducible representations. The result complements the established classification of superconducting states of matter.

Motivated in part by numerical simulations [H. G. Katzgraber and A. P. Young, Phys. Rev. B 66, 224507 (2002); J. M. Kosterlitz and N. Akino, Phys. Rev. Lett. 81, 4672 (1998); Phys. Rev. Lett. 81, 4672 (1998)] that reveal that the energy to create a defect in a gauge or phase glass scales as $L^{\theta }$ with $\theta <0$ for two dimensions, thereby implying a vanishing stiffness, we reexamine the relevance of these kinds of models to the Bose metal in light of the new experiments [N. P. Breznay and Kapitulnik (unpublished); Y. Wang, I. Tamir, D. Shahar, and N. P. Armitage, arXiv:1708.01908 [cond-mat.supr-con]], which reveal that the Hall conductance is zero in the metallic state that disrupts the transition from the superconductor to the insulator in two-dimensional (2D) samples. Because of the particle-hole symmetry in the phase-glass model, we find that bosonic excitations in a phase-glass background generate no Hall conductance at the Gaussian level. Furthermore, this result persists to any order in perturbation theory in the interactions. We show that when particle-hole symmetry is broken, the Hall conductance turns on with the same power law as does the longitudinal conductance. This prediction can be verified experimentally by applying a ground plane to the 2D samples.

We consider the nuclear spin-lattice relaxation rate $1/T_1$ in superconductors with accidental nodes, i.e., zeros of the order parameter that are not enforced by its symmetries. Such nodes in the superconducting gap are not constrained by symmetry to a particular position on the Fermi surface. We show, analytically and numerically, that a Hebel-Slichter-like peak occurs even in the absence of an isotropic component of the superconducting gap. For a gap with symmetry-required nodes the Fermi velocity at the node must point along the node. For accidental nodes this is not, in general, the case. This leads to additional terms in spectral function and hence the density of states. These terms lead to a logarithmic divergence in $1/T_{1}T$ at $T\to T_c^{-}$ in models neglecting disorder and interactions [except for those leading to superconductivity; here $T$ is temperature, $T_c^{-}={lim}_{\delta \to 0}(T_c-\delta )$, and $T_c$ is the critical temperature]. This contrasts with the usual Hebel-Slichter peak which arises from the coherence factors due to the isotropic component of the gap and leads to a divergence in $1/T_{1}T$ somewhat below $T_c$. The divergence in superconductors with accidental nodes is controlled by either disorder or additional electron-electron interactions. However, for reasonable parameters, neither of these effects removes the peak altogether. This provides a simple experimental method to distinguish between symmetry-required and accidental nodes.

We theoretically study the quantum Hall effect (QHE) in graphene with an ac electric field. Based on the tight-binding model, the structure of the half-integer Hall plateaus at ${\sigma }_{\mathrm{xy}}=\pm (n+1/2)4e^2/h$ ($n$ is an integer) gets qualitatively changed with the addition of new integer Hall plateaus at ${\sigma }_{\mathrm{xy}}=\pm n(4e^2/h)$ starting from the edges of the band center regime towards the band center with an increasing ac field. Beyond a critical field strength, a Hall plateau with ${\sigma }_{\mathrm{xy}}=0$ can be realized at the band center, hence fully restoring a conventional integer QHE with particle-hole symmetry. Within a low-energy Hamiltonian for Dirac cones merging, we show a very good agreement with the tight-binding calculations for the Hall plateau transitions. We also obtain the band structure for driven graphene ribbons to provide a further understanding on the appearance of the new Hall plateaus, showing a trivial insulator behavior for the ${\sigma }_{\mathrm{xy}}=0$ state. In the presence of disorder, we numerically study the disorder-induced destruction of the quantum Hall states in a finite driven sample and find that qualitative features known in the undriven disordered case are maintained.

${\mathrm{Bi}}_2{\mathrm{Te}}_3$ is a topological insulator whose unique properties result from topological surface states in the band gap. The neutralization of scattered low-energy ${\mathrm{Na}}^{+}$, which is sensitive to dipoles that induce inhomogeneities in the local surface potential, is larger when scattered from Te than from Bi, indicating an upwards dipole at the Te sites and a downwards dipole above Bi. These dipoles are caused by the spatial distribution of the conductive electrons in the topological surface states. This result demonstrates how this alkali ion scattering method can be applied to provide direct experimental evidence of the spatial distribution of electrons in filled surface states.

The excitation spectrum of graphene on Cu(111), probed by momentum-resolved electron-energy-loss spectroscopy, exhibits multiple acoustic surface plasmons (ASP), arising from both the graphene overlayer and the Cu(111) substrate. We have investigated the mutual interaction between the ASP of the graphene overlayer and that of the underlying Cu(111) substrate. The weak interaction between graphene and Cu(111) implies that the ASP of Cu(111) survives, with only slight changes in its group velocity. Remarkably, we find that the damping processes of ASP are mitigated as compared to the cases of other graphene/metal interfaces. Therefore, this interface is an ideal graphene/metal contact for graphene-based plasmonics. Moreover, the presence of graphene coating protects the ASP of Cu(111) from quenching in an ambient atmosphere.

The frequency-dependent transport through a nanodevice containing a large-spin magnetic molecule is studied theoretically in the Kondo regime. Specifically, the effect of magnetic anisotropy on dynamical spin accumulation is of primary interest. Such accumulation arises due to finite components of frequency-dependent conductance that are off diagonal in spin. Here, employing the Kubo formalism and the numerical renormalization group method, we demonstrate that the dynamical transport properties strongly depend on the relative orientation of spin moments in electrodes of the device, as well as on intrinsic parameters of the molecule. In particular, the effect of dynamical spin accumulation is found to be greatly affected by the type of magnetic anisotropy exhibited by the molecule, and it develops for frequencies corresponding to the Kondo temperature. For the parallel magnetic configuration of the device, the presence of dynamical spin accumulation is conditioned by the interplay of ferromagnetic-lead-induced exchange field and the Kondo correlations.

We demonstrate theoretically that a strong high-frequency circularly polarized electromagnetic field can turn a two-dimensional periodic array of interconnected quantum rings into a topological insulator. The elaborated approach is applicable to calculate and analyze the electron energy spectrum of the array, the energy spectrum of the edge states, and the corresponding electronic densities. As a result, the present theory paves the way to optical control of the topological phases in ring-based mesoscopic structures.

We calculate the spectral level-level correlation function of Anderson insulating wires for all three Wigner-Dyson classes. A measurement of its Fourier transform, the spectral form factor, is within reach of state-of-the-art cold atom quantum quench experiments, and we find good agreement with recent numerical simulations of the latter. Our derivation builds on a representation of the level-level correlation function in terms of a local generating function which may prove useful in other contexts.

We perform infrared conductivity measurements on a series of ${\mathrm{CaCuO}}_2\text{/}{\mathrm{SrTiO}}_3$ heterostructures made by the insulating cuprate ${\mathrm{CaCuO}}_2$ (CCO) and the insulating perovskite ${\mathrm{SrTiO}}_3$ (STO). We estimate the carrier density of various heterostructures with different levels of hole doping from the integral of the optical conductivity, and we measure the corresponding degree of correlation by estimating the ratio between the Drude weight and the integral of the infrared spectrum. The analysis demonstrates a large degree of correlation, which increases as the doping is reduced. The experimental results can be reproduced by dynamical mean-field theory calculations, which strongly support the role of correlations in the CCO/STO heterostructures and their similarities with the most common cuprate superconductors. Our results suggest that cuprate superconductors can be looked at as natural superlattices, where the peculiar characteristics of the native interfaces between the conducting block (containing the ${\mathrm{CuO}}_2$ planes) and the charge reservoir block are mainly responsible for the electrodynamic properties of these systems.

Helicoidal magnetic order breaks inversion symmetry in quadruple perovskite ${\mathrm{CaMn}}_7{\mathrm{O}}_{12}$, generating one of the largest spin-induced ferroelectric polarizations measured to date. Here, the microscopic origin of the polarization, including exchange interactions, coupling to the spin helicity, and charge density redistribution, is explored via first-principles calculations. The $B$-site ${\mathrm{Mn}}^{4+}$ (Mn3) spin adopts a noncentrosymmetric configuration, stabilized not only by spin-orbit coupling (SOC), but also by the fully anisotropic Hubbard $J$ parameter in the absence of SOC, to break inversion symmetry and generate polarization. Berry phase computed polarization $\left(P_{\mathrm{elec}}=2169\mu \mathrm{C}/{\mathrm{m}}^2\right)$ exhibits nearly pure electronic behavior, with negligible Mn displacements $\left(\approx 0.7\mathrm{m}\AA \right)$. Orbital-resolved density of states shows that $p\text{−}d$ orbital mixing is microscopically driven by nonrelativistic exchange striction within the commensurate ionic structure. Persistent electronic polarization induced by helical spin order in the nearly inversion-symmetric ionic crystal lattice suggests opportunities for ultrafast magnetoelectric response.

Heat sources whose characteristic dimension $R$ is comparable to phonon mean free paths display thermal resistances that exceed conventional diffusive predictions. This has direct implications to (opto)electronics thermal management and phonon spectroscopy. Theoretical analyses have so far limited themselves to particular experimental configurations. Here, we build upon the multidimensional Boltzmann transport equation (BTE) to derive universal expressions for the apparent conductivity suppression $S\left(R\right)={\kappa }_{\text{eff}}\left(R\right)/{\kappa }_{\text{bulk}}$ experienced by radially symmetric 2D and 3D sources. In striking analogy to cross-plane heat conduction in thin films, a distinct quasiballistic regime emerges between ballistic (${\kappa }_{\text{eff}}\sim R$) and diffusive (${\kappa }_{\text{eff}}\simeq {\kappa }_{\text{bulk}}$) asymptotes that displays a logarithmic dependence ${\kappa }_{\text{eff}}\sim ln\left(R\right)$ in single crystals and fractional power dependence ${\kappa }_{\text{eff}}\sim R^{2-\alpha }$ in alloys (with $\alpha$ the Lévy superdiffusion exponent). Analytical solutions and Monte Carlo simulations for spherical and circular heat sources in Si, GaAs, ${\mathrm{Si}}_{0.99}{\mathrm{Ge}}_{0.01}$, and ${\mathrm{Si}}_{0.82}{\mathrm{Ge}}_{0.18}$, all carried out from first principles, confirm the predicted generic tendencies. Contrary to the thin film case, common approximations like kinetic theory estimates ${\kappa }_{\text{eff}}\simeq \sum S_{\omega }^{\text{grey}}{\kappa }_{\omega }$ and modified Fourier temperature curves perform relatively poorly. Up to threefold deviations from the BTE solutions for sub-$100\mathrm{nm}$ sources underline the need for rigorous treatment of multidimensional nondiffusive transport.

We show that delaminations in bilayer graphene (BLG) with electrostatically induced interlayer symmetry can provide one with ballistic channels for electrons with energies inside the electrostatically induced BLG gap. These channels are formed by a combination of valley-polarized evanescent states propagating along the delamination edges (which persist in the presence of a strong magnetic field) and standing waves bouncing between them inside the delaminated region (in a strong magnetic field, these transform into Landau levels in the monolayers). For inverted stackings in BLGs on the left and right of the delamination (AB-2ML-BA or BA-2ML-AB, where 2ML indicates two decoupled monolayers of graphene), the lowest-energy ballistic channels are gapless, have linear dispersion, and appear to be weakly topologically protected. When BLG stackings on both sides of the delamination are the same (AB-2ML-AB or BA-2ML-BA), the lowest-energy ballistic channels are gapped, with a gap ${\varepsilon }_g$ scaling as ${\varepsilon }_g\propto W^{-1}$ with delamination width and ${\varepsilon }_g\propto {\delta }^{-1}$ with the on-layer energy difference in the delaminated part of the structure. Depending on the width, delaminations may also support several “higher-energy” waveguide modes. Our results are based on both the analytical study of the wave matching of Dirac states and tight-binding model calculations, and we analyze in detail the dependence of the delamination spectrum on the electrostatic conditions in the structure, such as the vertical displacement field.

We develop fluctuational electrodynamics for media with nonlinear optical response in and out of thermal equilibrium. Starting from the stochastic nonlinear Helmholtz equation and using the fluctuation dissipation theorem, we obtain perturbatively a deterministic nonlinear Helmholtz equation for the average field, the physical linear response, as well as the fluctuations and Rytov currents. We show that the effects of nonlinear optics, in or out of thermal equilibrium, can be taken into account with an effective dielectric function. We discuss the heat radiation of a planar, nonlinear surface, showing that Kirchhoff's law must be applied carefully. We find that the spectral emissivity of a nonlinear nanosphere can in principle be negative, implying the possibility of heat-flow reversal for specific frequencies.

Understanding the underlying mechanism of the nanostructure-mediated high diffusivity of H in Pd is of recent scientific interest and also crucial for industrial applications. Here, we present a decisive scenario explaining the emergence of the fast lattice-diffusion mode of interstitial H in face-centered cubic Pd, based on the quantum mechanical natures of both electrons and nuclei under finite strains. Ab initio path-integral molecular dynamics was applied to predict the temperature- and strain-dependent free energy profiles for H migration in Pd over a temperature range of 150–600 K and under hydrostatic tensile strains of 0.0%–2.4%; such strain conditions are likely to occur in real systems, especially around the elastic fields induced by nanostructured defects. The simulated results revealed that, for preferential H location at octahedral sites, as in unstrained Pd, the activation barrier for H migration ($Q$) was drastically increased with decreasing temperature owing to nuclear quantum effects. In contrast, as tetrahedral sites increased in stability with lattice expansion, nuclear quantum effects became less prominent and ceased impeding H migration. This implies that the nature of the diffusion mechanism gradually changes from quantum- to classical-like as the strain is increased. For H atoms in Pd at the hydrostatic strain of $\sim 2.4\%$, we determined that the mechanism promoted fast lattice diffusion ($Q=0.11$ eV) of approximately 20 times the rate of conventional H diffusion ($Q=0.23$ eV) in unstrained Pd at a room temperature of 300 K.

At room temperature, PbTe and SnTe are efficient thermoelectrics with a cubic structure. At low temperature, SnTe undergoes a ferroelectric transition with a critical temperature strongly dependent on the hole concentration, while PbTe is an incipient ferroelectric. By using the stochastic self-consistent harmonic approximation, we investigate the anharmonic phonon spectra and the occurrence of a ferroelectric transition in both systems. We find that vibrational spectra strongly depend on the approximation used for the exchange-correlation kernel in density-functional theory. If gradient corrections and the theoretical volume are employed, then the calculation of the phonon frequencies as obtained from the diagonalization of the free-energy Hessian leads to phonon spectra in good agreement with experimental data for both systems. In PbTe we evaluate the linear thermal expansion coefficient $\gamma =2.3\times {10}^{-5}{\text{K}}^{-1}$, finding it to be in good agreement with experimental value of $\gamma =2.04\times {10}^{-5}{\text{K}}^{-1}$. Furthermore, we study the phonon spectrum and we do reproduce the transverse optical mode phonon satellite detected in inelastic neutron scattering and the crossing between the transverse optical and the longitudinal acoustic modes along the $\mathrm{\Gamma }\mathrm{X}$ direction. The phonon satellite becomes broader at high temperatures but its energy is essentially temperature independent, in agreement with experiments. We decompose the self-consistent harmonic free energy in second-, third-, and fourth-order anharmonic terms. We find that the third- and fourth-order terms are small. However, treating the third-order term perturbatively on top of the second-order self-consistent harmonic free energy overestimates the energy of the satellite associated with the transverse optical mode. On the contrary, a perturbative treatment on top of the harmonic Hamiltonian breaks down and leads to imaginary phonon frequencies already at 300 K. In the case of SnTe, we describe the occurrence of a ferroelectric transition from the high-temperature $Fm\overline{3}m$ structure to the low-temperature $R3m$ one. The transition temperature is, however, underestimated with respect to the experimental one. No satellites are present in the SnTe phonon spectra despite a not negligible anharmonic broadening of the zone-center TO mode.

Quasiballistic heat conduction, in which some phonons propagate ballistically over a thermal gradient, has recently become of intense interest. Most works report that the thermal resistance associated with nanoscale heat sources is far larger than predicted by Fourier's law; however, recent experiments show that in certain cases the difference is negligible despite the heaters being far smaller than phonon mean-free paths. In this work, we examine how thermal resistance depends on the heater geometry using analytical solutions of the Boltzmann equation. We show that the spatial frequencies of the heater pattern play the key role in setting the thermal resistance rather than any single geometric parameter, and that for many geometries the thermal resistance in the quasiballistic regime is no different than the Fourier prediction. We also demonstrate that the spectral distribution of the heat source also plays a major role in the resulting transport, unlike in the diffusion regime. Our work provides an intuitive link between the heater geometry, spectral heating distribution, and the effective thermal resistance in the quasiballistic regime, a finding that could impact strategies for thermal management in electronics and other applications.

We calculate Aslamazov-Larkin (AL) paraconductity ${\sigma }_{\text{AL}}\left(T\right)$ for a model of strongly disordered superconductors (dimensions $d=2,3$) with a large pseudogap whose magnitude strongly exceeds transition temperature $T_c$. We show that, within Gaussian approximation over Cooper-pair fluctuations, paraconductivity is just twice larger that the classical AL result at the same $\epsilon =(T-T_c)/T_c$. Upon decreasing $\epsilon$, Gaussian approximation is violated due to local fluctuations of pairing fields that become relevant at $\epsilon \le {\epsilon }_1\ll 1$. Characteristic scale ${\epsilon }_1$ is much larger than the width ${\epsilon }_2$ of the thermodynamical critical region, that is determined via the Ginzburg criterion, ${\epsilon }_2\approx {\epsilon }_1^d$. We argue that in the intermediate region ${\epsilon }_2\le \epsilon \le {\epsilon }_1$, paraconductivity follows the same AL power law, albeit with another (yet unknown) numerical prefactor. At further decrease of the temperature, all kinds of fluctuational corrections become strong at $\epsilon \le {\epsilon }_2$; in particular, conductivity occurs to be strongly inhomogeneous in real space.