Conductance of 1D quantum wires with anomalous electron-wavefunction localization

We study the statistics of the conductance $g$ through one-dimensional disordered systems where electron wavefunctions decay spatially as $|\psi| \sim \exp (-\lambda r^{\alpha})$ for $0 <\alpha <1$, $\lambda$ being a constant. In contrast to the conventional Anderson localization where $|\psi| \sim \exp (-\lambda r)$ and the conductance statistics is determined by a single parameter: the mean free path, here we show that when the wave function is anomalously localized ($\alpha <1$) the full statistics of the conductance is determined by the average $$ and the power $\alpha$. Our theoretical predictions are verified numerically by using a random hopping tight-binding model at zero energy, where due to the presence of chiral symmetry in the lattice there exists anomalous localization; this case corresponds to the particular value $\alpha =1/2$. To test our theory for other values of $\alpha$, we introduce a statistical model for the random hopping in the tight binding Hamiltonian.Comment: 6 pages, 8 figures. Few changes in the presentation and references updated. Published in PRB, Phys. Rev. B 85, 235450 (2012

Anderson localization of one-dimensional hybrid particles

We solve the Anderson localization problem on a two-leg ladder by the Fokker-Planck equation approach. The solution is exact in the weak disorder limit at a fixed inter-chain coupling. The study is motivated by progress in investigating the hybrid particles such as cavity polaritons. This application corresponds to parametrically different intra-chain hopping integrals (a "fast" chain coupled to a "slow" chain). We show that the canonical Dorokhov-Mello-Pereyra-Kumar (DMPK) equation is insufficient for this problem. Indeed, the angular variables describing the eigenvectors of the transmission matrix enter into an extended DMPK equation in a non-trivial way, being entangled with the two transmission eigenvalues. This extended DMPK equation is solved analytically and the two Lyapunov exponents are obtained as functions of the parameters of the disordered ladder. The main result of the paper is that near the resonance energy, where the dispersion curves of the two decoupled and disorder-free chains intersect, the localization properties of the ladder are dominated by those of the slow chain. Away from the resonance they are dominated by the fast chain: a local excitation on the slow chain may travel a distance of the order of the localization length of the fast chain.Comment: 31 pages, 13 figure

Giant oscillations of energy levels in mesoscopic superconductors

The interplay of geometrical and Andreev quantization in mesoscopic superconductors leads to giant mesoscopic oscillations of energy levels as functions of the Fermi momentum and/or sample size. Quantization rules are formulated for closed quasiparticle trajectories in the presence of normal scattering at the sample boundaries. Two generic examples of mesoscopic systems are studied: (i) one dimensional Andreev states in a quantum box, (ii) a single vortex in a mesoscopic cylinder.Comment: 4 pages, 3 figure

Andreev transport in two-dimensional normal-superconducting systems in strong magnetic fields

The conductance in two-dimensional (2D) normal-superconducting (NS) systems is analyzed in the limit of strong magnetic fields when the transport is mediated by the electron-hole states bound to the sample edges and NS interface, i.e., in the Integer Quantum Hall Effect regime.The Andreev-type process of the conversion of the quasiparticle current into the superflow is shown to be strongly affected by the mixing of the edge states localized at the NS and insulating boundaries. The magnetoconductance in 2D NS structures is calculated for both quadratic and Dirac-like normal state spectra. Assuming a random scattering of the edge modes we analyze both the average value and fluctuations of conductance for an arbitrary number of conducting channels.Comment: 5 pages, 1 figur

Anisotropy and effective dimensionality crossover of the fluctuation conductivity of hybrid superconductor/ferromagnet structures

We study the fluctuation conductivity of a superconducting film, which is placed to perpendicular non-uniform magnetic field with the amplitude $H_0$ induced by the ferromagnet with domain structure. The conductivity tensor is shown to be essentially anisotropic. The magnitude of this anisotropy is governed by the temperature and the typical width of magnetic domains $d$. For $d\ll L_{H_0}=\sqrt{\Phi_0/H_0}$ the difference between diagonal fluctuation conductivity components $\Delta\sigma_\parallel$ along the domain walls and $\Delta\sigma_\perp$ across them has the order of $(d/L_{H_0})^4$. In the opposite case for $d\gg L_{H_0}$ the fluctuation conductivity tensor reveals effective dimensionality crossover from standard two-dimensional $(T-T_c)^{-1}$ behavior well above the critical temperature $T_c$ to the one-dimensional $(T-T_c)^{-3/2}$ one close to $T_c$ for $\Delta\sigma_\parallel$ or to the $(T-T_c)^{-1/2}$ dependence for $\Delta\sigma_\perp$. In the intermediate case $d\approx L_{H_0}$ for a fixed temperature shift from $T_c$ the dependence $\Delta\sigma_\parallel(H_0)$ is shown to have a minimum at $H_0\sim\Phi_0/d^2$ while $\Delta\sigma_\perp(H_0)$ is a monotonically increasing function.Comment: 11 pages, 8 figure

Enhanced Transmission Through Disordered Potential Barrier

Effect of weak disorder on tunneling through a potential barrier is studied analytically. A diagrammatic approach based on the specific behavior of subbarrier wave functions is developed. The problem is shown to be equivalent to that of tunneling through rectangular barriers with Gaussian distributed heights. The distribution function for the transmission coefficient $T$ is derived, and statistical moments \left are calculated. The surprising result is that in average disorder increases both tunneling conductance and resistance.Comment: 10 pages, REVTeX 3.0, 2 figures available upon reques

Passive scalar convection in 2D long-range delta-correlated velocity field: Exact results

The letter presents new field-theoretical approach to 2D passive scalar problem. The Gaussian form of the distribution for the Lyapunov exponent is derived and its parameters are found explicitly.Comment: 11 pages, RevTex 3.0, IFUM-94/455/January-F

Electron-phonon heat transfer in giant vortex states

We examine energy relaxation of nonequilibrium quasiparticles (QPs) in different vortex configurations in "dirty" s-wave superconductors (SCs). The heat flow from the electronic subsystem to phonons in a mesoscopic SC disk with a radius of the order of several coherence lengths is calculated both in the Meissner and in the giant vortex states using the Usadel approach. The recombination process is shown to be strongly affected by interplay of the subgap states, located in the vortex core and in the region at the sample edge where the spectral gap Eg is reduced by the Meissner currents. In order to uncover the physical origin of the results, we develop a semiquantitative analytical approximation based on the combination of homogeneous solutions of Usadel equations in Meissner and vortex states of a mesoscopic SC disk and analytically calculate the corresponding spatially resolved electron-phonon heat rates. Our approach provides important information about nonequilibrium QPs cooling by the magnetic field-induced traps in various mesoscopic SC devices

Hybridization and interference effects for localized superconducting states in strong magnetic field

Within the Ginzburg-Landau model we study the critical field and temperature enhancement for crossing superconducting channels formed either along the sample edges or domain walls in thin-film magnetically coupled superconducting - ferromagnetic bilayers. The corresponding Cooper pair wave function can be viewed as a hybridization of two order parameter (OP) modes propagating along the boundaries and/or domain walls. Different momenta of hybridized OP modes result in the formation of vortex chains outgoing from the crossing point of these channels. Near this crossing point the wave functions of the modes merge giving rise to the increase in the critical temperature for a localized superconducting state. The origin of this critical temperature enhancement caused by the wave function squeezing is illustrated for a limiting case of approaching parallel boundaries and/or domain walls. Using both the variational method and numerical simulations we have studied the critical temperature dependence and OP structure vs the applied magnetic field and the angle between the crossing channels.Comment: 12 pages, 13 figure