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

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

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

Electronic Structure of Vortices Pinned by Columnar Defects

The electronic structure of a vortex line trapped by an insulating columnar defect in a type-II superconductor is analysed within the Bogolubov-de Gennes theory. For quasiparticle trajectories with small impact parameters defined with respect to the vortex axis the normal reflection of electrons and holes at the defect surface results in the formation of an additional subgap spectral branch. The increase in the impact parameter at this branch is accompanied by the decrease of the excitation energy. When the impact parameter exceeds the radius of the defect this branch transforms into the Caroli--de Gennes--Matricon one. As a result, the minigap in the quasiparticle spectrum increases with the increase in the defect radius. The scenario of the spectrum transformation is generalized for the case of arbitrary vorticity.Comment: 7 pages, 4 figure

Physical properties of insulation materials based on straw and flax boon

Performance evaluation of environmentally friendly thermal insulation materials based on crushed straw and flax boon was determined by studying the physical parameters of thermal insulation in a climatic chamber and full-scale tests in buildings. In the climatic chamber at an air temperature of –20 °С, depending on the insulation moisture content, the thermal conductivity of the flax boon and straw slabs is 0.058 - 0.072 W/(m·°С), which is 27 - 31% lower than that of straw slabs equal to 0.08 - 0.105 W/(m·°C). With a relative air humidity of 50 - 95%, the moisture content of the flax boon and straw slabs varies within the range of 14 - 18.1% or less by 24% of the values of the crushed straw insulation. Under operating conditions, the thermal conductivity of the attic floor structure with flax boon and straw slabs corresponds to 0.07 W/(m·°C) at an air temperature of –20°C and is 22% less than the similar indicator of flooring with straw slabs equal to 0.09 W/(m·°C). A lower thermal conductivity of the floor structure with the use of flax boon and straw slabs provides an increase in temperature amplitude by 5 - 5.8 °C compared with the use of straw slabs. The results of studies in the climatic chamber and full-scale tests have confirmed the most effective operation of the flax boon and straw slabs as a thermal insulation material, which reduces energy consumption and, consequently, reduces financial costs for heating buildings

Constraints on the disk geometry of the T Tauri star AA Tau from linear polarimetry

We have simultaneously monitored the photometric and polarimetric variations of the Classical T Tauri star AA Tau during the fall of 2002. We combine these data with previously published polarimetric data covering two earlier epochs. The phase coverage is complete, although not contiguous. AA Tau clearly shows cyclic variations coupled with the rotation of the system. The star-disk system produces a repeatable polarisation curve where the polarisation increases with decreasing brightness. The data fit well with the model put forward by Bouvier et al. (1999) where AA Tau is viewed almost edge-on and its disk is actively dumping material onto the central star via magnetospheric accretion. The inner edge of the disk is deformed by its interaction with the tilted magnetosphere, producing eclipses as it rotates and occults the photosphere periodically. From the shape of the polarisation curve in the QU-Plane we confirm that the accretion disk is seen at a large inclination, almost edge-on, and predict that its position angle is PA~90 deg., i.e., that the disk's major axis is oriented in the East-West direction.Comment: Astron. Astrophys., in pres

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

Localization length in Dorokhov's microscopic model of multichannel wires

We derive exact quantum expressions for the localization length $L_c$ for weak disorder in two- and three chain tight-binding systems coupled by random nearest-neighbour interchain hopping terms and including random energies of the atomic sites. These quasi-1D systems are the two- and three channel versions of Dorokhov's model of localization in a wire of $N$ periodically arranged atomic chains. We find that $L^{-1}_c=N.\xi^{-1}$ for the considered systems with $N=(1,2,3)$, where $\xi$ is Thouless' quantum expression for the inverse localization length in a single 1D Anderson chain, for weak disorder. The inverse localization length is defined from the exponential decay of the two-probe Landauer conductance, which is determined from an earlier transfer matrix solution of the Schr\"{o}dinger equation in a Bloch basis. Our exact expressions above differ qualitatively from Dorokhov's localization length identified as the length scaling parameter in his scaling description of the distribution of the participation ratio. For N=3 we also discuss the case where the coupled chains are arranged on a strip rather than periodically on a tube. From the transfer matrix treatment we also obtain reflection coefficients matrices which allow us to find mean free paths and to discuss their relation to localization lengths in the two- and three channel systems