We report a complete analytical expression for the one-loop correction to the ac conductivity $σ(ω)$ of a disordered two-dimensional electron system in the diffusive regime. The obtained expression includes the weak localization and Altshuler-Aronov corrections as well as the corrections due to superconducting fluctuations above superconducting transition temperature. The derived expression has no $1/(iω)$ divergency in the static limit, $ω\to 0$, in agreement with general expectations for the normal state conductivity of a disordered electron system.
We study differential shot noise in mesoscopic diffusive normal-superconducting (NS) heterostructures at finite voltages where nonlinear effects due to the superconducting proximity effect arise. A numerical scattering-matrix approach is adopted. Through an NS contact, we observe that the shot noise shows a reentrant dependence on voltage due to the superconducting proximity effect but the differential Fano factor stays approximately constant. Furthermore, we consider differential shot noise in the structures where an insulating barrier is formed between normal and superconducting regions and …
We calculate the density of states (DOS) in a diffusive superconducting/ferromagnetic bilayer with a spin-active interface. We use a self-consistent numerical treatment to make a systematic study of the effects of the Spin-Dependence of Interfacial Phase Shifts (SDIPS) on the self-consistent superconducting gap and the DOS. Strikingly, we find that the SDIPS can induce a double gap structure (DGS) in the DOS of the ferromagnet, even when the superconducing layer is much thicker than the superconducting coherence lenght. We thus obtain DOS curves which have interesting similarities with those o…
We reconsider the problem of the superconducting proximity effect in a diffusive ferromagnet bounded by tunneling interfaces, using spin-dependent boundary conditions. This introduces for each interface a phase-shifting conductance Gphi which results from the spin dependence of the phase shifts acquired by the electrons upon scattering on the interface. We show that Gphi strongly affects the density of states and supercurrents predicted for superconducting/ferromagnetic hybrid circuits. We show the relevance of this effect by identifying clear signatures of Gphi in the data of T. Kontos et al …
Metal microbridges with a high impurity content and shorter than the energy relaxation length are considered. Their conductance is calculated with allowance made for the Coulomb electron-electron interaction. It is shown that nonequilibrium electrons in the microbridges gives rise to a nonlinear current-voltage characteristic (published in Physics Letters A, 1994).
We report an experimental study of the quantum corrections to the longitudinal conductivity and the Hall coefficient of a low mobility, high density two-dimensional two-dimensional electron gas in a AlGaAs/GaAs/AlGaAs quantum well in a wide temperature range (1.5 K - 110 K). This temperature range covers both the diffusive and the ballistic interaction regimes for our samples. It was therefore possible to study the crossover region for the longitudinal conductivity and the Hall effect.
We present an investigation of the energy dependence of the full charge counting statistics in diffusive normal-insulating-normal-insulating-superconducting junctions. It is found that the current in general is transported via a correlated transfer of pairs of electrons. Only in the case of strongly asymmetric tunnel barriers or energies much larger than the Thouless energy is the pair transfer uncorrelated. The second cumulant, the noise, is found to depend strongly on the applied voltage and temperature. For a junction resistance dominated by the tunnel barrier to the normal reservoir, the d…
Assuming diffusive carrier transport and employing an effective medium theory, we calculate the temperature dependence of bilayer graphene conductivity due to Fermi-surface broadening as a function of carrier density. We find that the temperature dependence of the conductivity depends strongly on the amount of disorder. In the regime relevant to most experiments, the conductivity is a function of T/T*, where T* is the characteristic temperature set by disorder. We demonstrate that experimental data taken from various groups collapse onto a theoretically predicted scaling function.
We consider a planar SIS-type Josephson junction between diffusive superconductors (S) through an insulating tunnel interface (I). We construct fully self-consistent perturbation theory with respect to the interface conductance. As a result, we find correction to the first Josephson harmonic and calculate the second Josephson harmonic. At arbitrary temperatures, we correct previous results for the nonsinusoidal current-phase relation in Josephson tunnel junctions, which were obtained with the help of conjectured form of solution. Our perturbation theory also describes the difference between th…
Motivated by recent experiments on nonlocal transport through multiterminal superconducting hybrid structures, we present self-consistent calculations based on quasiclassical Green's functions for the order parameter, currents and voltages in a system consisting of a diffusive superconductor connected to two normal and one superconducting electrodes. We investigate non-equilibrium effects for different biasing conditions corresponding to measurements of the nonlocal conductance and of the nonlocal resistance. It is shown that while the nonlocal conductance does not change its sign, this change…
We report an experimental study of quantum conductivity corrections in a low mobility, high density two-dimensional electron gas in a AlGaAs/GaAs/AlGaAs quantum well in a wide temperature range (1.5K - 110K). This temperature range covers both the diffusive and the ballistic interaction regimes for our samples. It has been therefore possible to study the crossover between these regimes for both the longitudinal conductivity and the Hall effect. We perform a parameter free comparison of our experimental data for the longitudinal conductivity at zero magnetic field, the Hall coefficient, and the…
A cross-shaped diffusive system with two superconducting and two normal electrodes is considered. A voltage $eV < Δ$ is applied between the normal leads. Even in the absence of average current through the superconducting electrodes their presence increases the shot noise at the normal electrodes and doubles it in the case of a strong coupling to the superconductors. The nonequilibrium noise at the superconducting electrodes remains finite even in the case of a vanishingly small transport current due to the absence of energy transfer into the superconductors. This noise is suppressed by electro…
There has been much interest in semiconductor superlattices because of showing very low thermal conductivities. This makes them especially suitable for applications in a variety of devices for thermoelectric generation of energy, heat control at the nanometric length scale, etc. Recent experiments have confirmed that the effective thermal conductivity of superlattices at room temperature have a minimum for very short periods (in the order of nanometers) as some kinetic calculations had anticipated previously. This work will show advances on a thermodynamic theory of heat transport in nanometri…
Using a Scanning Tunneling Microscope (STM), we investigate the Local Density of States (LDOS) of artificially fabricated normal metal nano-structures in contact with a superconductor. Very low temperature local spectroscopic measurements (100 mK) reveal the presence of well defined subgap peaks at energy |E|<Delta in the LDOS at various positions of the STM tip. Although no clear correlations between the LDOS and the shape of the samples have emerged, some of the peak features suggest they originate from quasi-particle bound states within the normal metal structures (De Gennes St James states…
We study mesoscopic fluctuations and weak localization correction to the supercurrent in Josephson junctions with coherent diffusive electron dynamics in the normal part. Two kinds of junctions are considered: a chaotic dot coupled to superconductors by tunnel barriers and a diffusive junction with transparent normal--superconducting interfaces. The amplitude of current fluctuations and the weak localization correction to the average current are calculated as functions of the ratio between the superconducting gap and the electron dwell energy, temperature, and superconducting phase difference …
We solve the coherent multiple Andreev reflection (MAR) problem and calculate current-voltage characteristics (IVCs) for Josephson SINIS junctions, where S are local-equilibrium superconducting reservoirs, I denotes tunnel barriers, and N is a short diffusive normal wire, the length of which is much smaller than the coherence length, and the resistance is much smaller than the resistance of the tunnel barriers. The charge transport regime in such junctions qualitatively depends on a characteristic value γ= Δτ_d of relative phase shifts between the electrons and retro-reflected holes accumulate…
We demonstrate that the weak antilocalization effect can serve as a convenient method for detecting decoupled surface transport in topological insulator thin films. In the regime where a bulk Fermi surface coexists with the surface states, the low field magnetoconductivity is described well by the Hikami-Larkin-Nagaoka equation for single component transport of non-interacting electrons. When the electron density is lowered, the magnetotransport behavior deviates from the single component description and strong evidence is found for independent conducting channels at the bottom and top surface…
We calculate the fluctuation correction to the normal state conductivity in the vicinity of a quantum phase transition from a superconducting to normal state, induced by applying a magnetic field parallel to a dirty thin film or a nanowire with thickness smaller than the superconducting coherence length. We find that at zero temperature, where the correction comes purely from quantum fluctuations, the positive Aslamazov-Larkin contribution, the negative density of states contribution, and the Maki-Thompson interference contribution, are all of the same order and the total correction is negativ…
We present a theory for the full distribution of current fluctuations in incoherent diffusive superconducting junctions, subjected to a voltage bias. This theory of full counting statistics of incoherent multiple Andreev reflections is valid for arbitrary applied voltage. We present a detailed discussion of the properties of the first four cumulants as well as the low and high voltage regimes of the full counting statistics. The work is an extension of the results of Pilgram and the author, Phys. Rev. Lett. 94, 086806 (2005).
We revisit the problem of diffusive proximity systems involving superconductors and normal metals (or ferromagnets) with magnetic disorder. On the length scales much larger than its correlation length, the effect of sufficiently weak magnetic disorder may be incorporated as a local spin-flip term in the Usadel equations. We derive this spin-flip term in the general case of a three-dimensional disordered Zeeman-type field with an arbitrary correlation length. Three different regimes may be distinguished: pointlike impurities (the correlation length is shorter than the Fermi wavelength), medium-…
We study the non linear response of current-transport in a superconducting diffusive nanowire between normal reservoirs. We demonstrate theoretically and experimentally the existence of two different superconducting states appearing when the wire is driven out of equilibrium by an applied bias, called global and bimodal superconducting state. The different states are identified by using two probe measurements of the wire, and measurements of the local density of states with tunneling probes. The analysis is performed within the framework of the quasiclassical kinetic equations for diffusive su…
We present a theoretical study of diffusive superconducting systems with extrinsic spin-orbit coupling and arbitrarily strong impurity potential. We derive from a microscopic Hamiltonian a diffusion equation for the quasi-classical Green function, and demonstrate that all mechanisms related to the spin-orbit coupling are expressed in terms of three kinetic coefficients: the spin Hall angle, the spin current swapping coefficient, and the spin relaxation rate due to Elliott-Yafet mechanism. The derived diffusion equation contains a hitherto unknown term describing a spin-orbit torque that appear…
By using the momentum-space Lanczos recursive method which considers rigorously all multiple-scattering events, we unveil that the non-perturbative disorder effect has dramatic impact on the charge transport of a two-dimensional electron system with Rashba spin-orbit coupling in the low-density region. Our simulations find a power-law dependence of the dc longitudinal conductivity on the carrier density, with the exponent linearly dependent on the Rashba spin-orbit strength but independent of the disorder strength. Therefore, the classical charge transport influenced by complicated multiple-sc…
Using the phonon Boltzmann transport formalism and density functional theory based calculations, we show that stanene has a low thermal conductivity. For a sample size of 1$\times$1 $μ$m$^{2}$ ($L\times W$), the lattice thermal conductivities along the zigzag and armchair directions are 10.83 W/m-K and 9.2 W/m-K respectively, at room temperature, indicating anisotropy in the thermal transport. The low values of thermal conductivity are due to large anharmonicity in the crystal resulting in high Grüneisen parameters, and low group velocities. The room temperature effective phonon mean free path…
We have measured the number of quasiparticles and their lifetime in aluminium superconducting microwave resonators. The number of excess quasiparticles below 160 mK decreases from 72 to 17 $μ$m$^{-3}$ with a 6 dB decrease of the microwave power. The quasiparticle lifetime increases accordingly from 1.4 to 3.5 ms. These properties of the superconductor were measured through the spectrum of correlated fluctuations in the quasiparticle system and condensate of the superconductor, which show up in the resonator amplitude and phase respectively. Because uncorrelated noise sources vanish, fluctuatio…
Interference of electronic waves undergoing Andreev reflection in diffusive conductors determines the energy profile of the conductance on the scale of the Thouless energy. A similar dependence exists in the current noise, but its behavior is known only in few limiting cases. We consider a metallic diffusive wire connected to a superconducting reservoir through an interface characterized by an arbitrary distribution of channel transparencies. Within the quasiclassical theory for current fluctuations we provide a general expression for the energy dependence of the current noise. We derive close…
The superconducting proximity effect leads to strong modifications of the local density of states in diffusive or chaotic cavity Josephson junctions, which displays a phase-dependent energy gap around the Fermi energy. The so-called minigap of the order of the Thouless energy $E_{\mathrm{Th}}$ is related to the inverse dwell time in the diffusive region in the limit $E_{\mathrm{Th}}\llΔ$, where $Δ$ is the superconducting energy gap. In the opposite limit of a large Thouless energy $E_{\mathrm{Th}}\ggΔ$, a small new feature has recently attracted attention, namely, the appearance of a further s…
The critical fluctuations in a mesoscopic superconducting ring are studied within the Ginzburg-Landau approach. The nonlocal conductivity as well as the specific heat are calculated as functions of the magnetic flux $Φ$ through the ring. At $Φ=Φ_0/2$ two low-energy eigenstates become degenerate and near this point the behavior of fluctuations-dependent quantities change dramatically: both the zero Fourier component $σ_0$ of the fluctuation conductivity and the specific heat become non-monotonic functions of $|Φ-Φ_0/2|$ with rather special resonant structure.
We present a calculation of the lattice thermal conductivity of Si-Ge nanowires (NWs), based on solving the Boltzmann transport equation by the Monte Carlo method of sampling the phonon mean free paths. We augment the previous work with the full phonon dispersion and a partially diffuse momentum-dependent specularity model for boundary roughness scattering. We find that phonon flights are comprised of a mix of long free-flights over several μm interrupted by bursts of short flights, resulting in a heavy tailed distribution of flight lengths, typically encountered in Lévy walk dynamics. Consequ…
The phase space for graphene's minimum conductivity $σ_\mathrm{min}$ is mapped out using Landauer theory modified for scattering using Fermi's Golden Rule, as well as the Non-Equilibrium Green's Function (NEGF) simulation with a Monte Carlo sampling over impurity distributions. The resulting `fan diagram' spans the range from ballistic to diffusive over varying aspect ratios ($W/L$), and bears several surprises. {The device aspect ratio determines how much tunneling (between contacts) is allowed and becomes the dominant factor for the evolution of $σ_{min}$ from ballistic to diffusive regime. …
We study the heat conductance of hybrid superconducting junctions. Our analysis involves single-channel junctions with arbitrary transmission as well as diffusive connectors and shows the influence of the superconducting gaps and phases of the contacts on the heat conductance. If the junction is diffusive, these effects are completely quenched on average, however, we find that their influence persists in weak-localization corrections and conductance fluctuations. While these statistical properties strongly deviate from the well-known analogues for the charge conductance, we demonstrate that th…
We study the electronic transport in the lowest Landau level of disordered two-dimensional semimetals placed in a homogeneous perpendicular magnetic field. The material system is modeled by the Bernevig-Hughes-Zhang Hamiltonian, which has zero energy Landau modes due to the material's intrinsic Berry curvature. These turn out to be crucially important for the density of states and the static conductivity of the disordered system. We develop an analytical approach to the diffusion and conductivity based on a self-consistent equation of motion for the mean squared displacement. The obtained valu…
We study the effects of the long-range disorder potential and warping on the conductivity and mobility of graphene ribbons using the Landauer formalism and the tight-binding p-orbital Hamiltonian. We demonstrate that as the length of the structure increases the system undergoes a transition from the ballistic to the diffusive regime. This is reflected in the calculated electron density dependencies of the conductivity and the mobility. In particular, we show that the mobility of graphene ribbons varies as mu(n) n^(-lambda), with 0<lambda<0.5. The exponent lambda depends on the length of the sy…
Interference of electronic waves undergoing Andreev reflection in diffusive conductors determines the energy profile of the conductance on the scale of the Thouless energy. A similar dependence exists in the current noise, but its behavior is known only in few limiting cases. We consider a metallic diffusive wire connected to a superconducting reservoir through an interface characterized by an arbitrary distribution of channel transparencies. Within the quasiclassical theory for current fluctuations we provide a general expression for the energy dependence of the current noise.
A nonequilibrium Green's function approach is employed to investigate the spin-Hall effect in diffusive two-dimensional electron systems with Rashba spin-orbit interaction. Considering a long-range electron-impurity scattering potential in the self-consistent Born approximation, we find that the spin-Hall effect arises from two distinct interband polarizations in helicity basis: a disorder-unrelated polarization directly induced by the electric field and a polarization mediated by electron-impurity scattering. The disorder-unrelated polarization is associated with all electron states below the…
We study the thermal conductivity in disordered $s$-wave superconductors. Expanding on previous works for normal metals, we develop a formalism that tackles particle diffusion as well as the weak localization (WL) and weak anti-localization (WAL) effects. Using a Green's functions diagrammatic technique, which takes into account the superconducting nature of the system by working in Nambu space, we identify the system's low-energy modes, the diffuson and the Cooperon. The time scales that characterize the diffusive regime are energy dependent; this is in contrast with the the normal state, whe…
We report the first comparative study of the properties of two-dimensional arrays and single superconducting film - normal wire - superconducting film (SNS) junctions. The NS interfaces of our SNS junctions are really high transparent, for superconducting and normal metal parts are made from the same material (superconducting polycrystalline PtSi film). We have found that the two-dimensional arrays reveal some novel features: (i) the significant narrowing of the zero bias anomaly (ZBA) in comparison with single SNS junctions, (ii) the appearance of subharmonic energy gap structure (SGS), with …
A mesoscopic hybrid Normal/ Superconducting (NS) ring is characterized by a dense Andreev spectrum with a flux dependent minigap. We measure the linear response to a high frequency flux, in a wide frequency range, with a multimode superconducting resonator. We find that the current response contains, beside the well known dissipation-less Josephson contribution, a large dissipative component. At high frequency compared to the minigap and low temperature we find that the dissipation is due to transitions above the minigap. In contrast, at lower frequency there is range of temperature for which …
Coexisting Ballistic and Diffusive Heat Transport in Micrometer-Long Molecular Junctions
Instituto de Ciencia de Materiales de Madrid (ICMM), CSIC（马德里材料科学研究所）；Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid（马德里自治大学凝聚态物理理论系）；Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid（马德里自治大学凝聚态物理中心）
We study the fluctuation conductivity of superconducting granular metals at low temperatures and strong magnetic field destroying the Cooper pairs. Explicit calculations are performed for larger values of the coupling between the grains than those considered in previous works. We show that in a broad region of the coupling constants the superconducting fluctuations still significantly reduce the conductivity leading to a negative magnetoresistance.
We report an unconventional behavior of electron transport in the limit of zero magnetic flux in a one-dimensional disordered ring, be it completely random or any correlated one, subjected to Rashba spin-orbit (SO) coupling. It exhibits much higher circulating current compared to a fully perfect ring for a wide range of SO coupling yielding larger electrical conductivity which is clearly verified from our Drude weight analysis.
We present a two-band kinetic equation method to investigate the anomalous Hall effect in a Rashba two-dimensional electron system subjected to a homogeneous magnetization. The electron-impurity scattering is taken into account in the self-consistent Born approximation. It is demonstrated that the impurity-density-free anomalous Hall conductivity arises from an intrinsic and a disorder-mediated mechanisms, associated respectively with the electron states under and near the Fermi surface. The intrinsic mechanism relates to a dc-field-induced transition process, or in other words, a linear stati…
We consider the spin-orbit-induced spin Hall effect and spin swapping in diffusive superconductors. By employing the non-equilibrium Keldysh Green's function technique in the quasiclassical approximation, we derive coupled transport equations for the spectral spin and particle distributions and for the energy density in the elastic scattering regime. We compute four contributions to the spin Hall conductivity, namely, skew scattering, side-jump, anomalous velocity, and the Yafet contribution. The reduced density of states in the superconductor causes a renormalization of the spin Hall angle. W…
We study interaction-induced quantum correction to the conductivity tensor of electrons in two dimensions for arbitrary T tau, where T is the temperature and tau the transport mean free time. A general formula is derived, expressing the correction in terms of classical propagators ("ballistic diffusons"). The formalism is used to calculate the interaction contribution to the magnetoresistance in a classically strong transverse field and smooth disorder in the whole range of temperatures from the diffusive (T tau<<1) to the ballistic (T tau>1) regime.
Layered materials have uncommonly anisotropic thermal properties due to their strong in-plane covalent bonds and weak out-of-plane van der Waals interactions. Here we examine heat flow in graphene (graphite), h-BN, MoS2, and WS2 monolayers and bulk films, from diffusive to ballistic limits. We determine the ballistic thermal conductance limit (Gball) both in-plane and out-of-plane, based on full phonon dispersions from first-principles calculations. An overall phonon mean free path (λ) is expressed in terms of Gball and the diffusive thermal conductivity, consistent with kinetic theory if prop…
On a high-mobility 2D electron gas we have observed, in strong magnetic fields (omega_{c} tau > 1), a parabolic negative magnetoresistance caused by electron-electron interactions in the regime of k_{B} T tau / hbar ~ 1, which is the transition from the diffusive to the ballistic regime. From the temperature dependence of this magnetoresistance the interaction correction to the conductivity delta sigma_{xx}^{ee}(T) is obtained in the situation of a long-range fluctuation potential and strong magnetic field. The results are compared with predictions of the new theory of interaction-induced magn…
