Nonlocal Andreev reflection in a three-terminal Aharonov-Bohm interferometer

We theoretically report a nonlocal Andreev reflection in an Aharonov-Bohm interferometer, which is a three-terminal normal metal/superconductor (NS) mesoscopic hybrid system. It is found that this nonlocal Andreev reflection is sensitive to the systematic parameters, such as the bias voltages, the quantum dot levels, and the external magnetic flux. If we set the chemical potential of one normal metal lead equal to zero, the electronic current in the lead results from two competing processes: the quasiparticle transmission and nonlocal Andreev reflection. The appearance of zero electronic current signals unambiguously the existence of this nonlocal Andreev reflection.     

Circuit theory for crossed Andreev reflection and nonlocal conductance

Nonlocal currents, in devices where two normal-metal terminals are contacted to a superconductor, are determined using the circuit theory of mesoscopic superconductivity. We calculate the conductance associated with crossed Andreev reflection and electron transfer between the two normal-metal terminals, in addition to the conductance from direct Andreev reflection and quasiparticle tunneling. Dephasing and proximity effect are taken into account. PACS 74.45.+c, 74.25.Fy, 73.23.-b     

Entanglement distribution statistic in Andreev billiards

We investigate statistical aspects of the entanglement production for open chaotic mesoscopic billiards in contact with superconducting parts, known as Andreev billiards. The complete distributions of concurrence and entanglement of formation are obtained by using the Altland–Zirnbauer symmetry classes of circular ensembles of scattering matrices, which complements previous studies in chaotic universal billiards belonging to other classes of random matrix theory. Our results show a unique and very peculiar behavior: the realization of entanglement in a Andreev billiard always results in non-separable state, regardless of the time reversal symmetry. The analytical calculations are supported by a numerical Monte Carlo simulation.     

Long-range coherence and mesoscopic transport in N–S metallic structures

We review the mesoscopic transport in a diffusive proximity superconductor made of a normal metal (N) in metallic contact with a superconductor (S). The Andreev reflection of electrons on the N–S interface is responsible for the diffusion of electron pairs in N. Superconducting-like properties are induced in the normal metal. In particular, the conductivity of the N metal is locally enhanced by the proximity effect. A re-entrance of the metallic conductance occurs when all the energies involved (e.g. temperature and voltage) are small. The relevant characteristic energy is the Thouless energy which is divided by the diffusion time for an electron travelling throughout the sample. In loop-shaped devices, a 1 / T temperature-dependent oscillation of the magnetoresistance arises with a large amplitude from the long-range coherence of low-energy pairs.     

Circuit theory of unconventional superconductor junctions

We extend the circuit theory of superconductivity to cover transport and proximity effect in mesoscopic systems that contain unconventional superconductor junctions. The approach fully accounts for zero-energy Andreev bound states forming at the surface of unconventional superconductors. As a simple application, we investigate the transport properties of a diffusive normal metal in series with a d-wave superconductor junction. We reveal the competition between the formation of Andreev bound states and proximity effect that depends on the crystal orientation of the junction interface.     

Nanotransformation and current fluctuations in exciton condensate junctions

We analyze the nonlinear transport properties of a bilayer exciton condensate that is contacted by four metallic leads by calculating the full counting statistics of electron transport for arbitrary system parameters. Despite its formal similarity to a superconductor the transport properties of the exciton condensate turn out to be completely different. We recover the generic features of exciton condensates such as counterpropagating currents driven by excitonic Andreev reflections and make predictions for nonlinear transconductance between the layers as well as for the current (cross)correlations and generalized Johnson-Nyquist relationships. Finally, we explore the possibility of connecting another mesoscopic system (in our case a quantum point contact) to the bottom layer of the exciton condensate and show how the excitonic Andreev reflections can be used for transforming voltage at the nanoscale.     

Field theory of mesoscopic fluctuations in superconductor/normal-metal systems

The thermodynamic and transport properties of normal disordered conductors are strongly influenced by the proximity of a superconductor. A cooperation between mesoscopic coherence and Andreev scattering of particles from the superconductor generates new types of interference phenomena. A field theoretic approach is introduced which is capable of exploring both the averaged properties and mesoscopic fluctuations of superconductor/normal-metal systems. As an example the method is applied to the study of the level statistics of a SNS junction. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 1, 21–26 (10 January 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Josephson transport in complex mesoscopic structures

A universal spectral equation is derived for Andreev bound states in superconducting quantum junctions, relating bound state energies with the normal electron scattering amplitudes. The equation is applied to calculation of d.c. Josephson effect in mesoscopic S-2DEG-S junctions.     

Positive and negative Hanbury-Brown and Twiss correlations in normal metal-superconducting devices

In the light of the recent analogs of the Hanbury-Brown and Twiss experiments [1] in mesoscopic beam splitters, negative current noise correlations are recalled to be the consequence of an exclusion principle. Here, positive (bosonic) correlations are shown to exist in a fermionic system, composed of a superconductor connected to two normal reservoirs. In the Andreev regime, the correlations can either be positive or negative depending on the reflection coefficient of the beam splitter. For biases beyond the gap, the transmission of quasiparticles favors fermionic correlations. The presence of disorder enhances positive noise correlations. Potential experimental applications are discussed. Received 1 June 1999     

Andreev reflection eigenvalue density in mesoscopic conductors

The energy-dependent Andreev reflection eigenvalues determine the transport properties of normal-superconducting systems. We evaluate the eigenvalue density to get insight into the formation of resonant electron-hole transport channels. The circuit-theory-like method developed can be applied to any generic mesoscopic conductor or combinations thereof. We present the results for experimentally relevant cases of a diffusive wire and a double tunnel junction.     

Non-rigid hole band in the extended t-J model

Based on a simple matrix method, we investigate the effects of Fermi vector mismatch and elastic barrier on the dc Josephoson current through a ballistic, normal, one-dimensional quantum channel in contact with two superconducting electrodes. The coexistence of Andreev reflection and normal reflection forms quasibound states with open gaps in the normal conductor. The quantum transmission of individual electrons (or holes) gives new features to this mesoscopic system. The critical current character of a 2DEG coupled superconducting heterostructure with a length of sevral m0 is extensively studied. More importantly, our theoritical results are able to account for the recent anomalous experimental results.     

Negative length orbits in normal-superconductor billiard systems

The path-length spectra of mesoscopic systems including diffractive scatterers and connected to a superconductor are studied theoretically. We show that the spectra differ fundamentally from that of normal systems due to the presence of Andreev reflection. It is shown that negative path lengths should arise in the spectra as opposed to the normal system. To highlight this effect we carried out both quantum mechanical and semiclassical calculations for the simplest possible diffractive scatterer. The most pronounced peaks in the path-length spectra of the reflection amplitude are identified by the routes that the electron and/or hole travels.     

正常金属-分子量子点-超导耦合系统的介观输运研究

运用非平衡格林函数理论、正则变换以及BCS平均场理论研究了正常金属-分子量子点-超导耦合系统（N-MQD-S）的介观输运,得到了系统的电流公式并选择适当的参数进行了数值计算。数值计算结果表明：电声子耦合强度 与线宽函数 对系统的输运行为有较大影响。当 增大时,由声子辅助隧穿所产生的共振峰将高于分子量子点自身能级产生的共振峰;当线宽函数 增大时,在Andreev反射共振峰的两侧将出现新的边峰。     

正常金属-分子量子点-超导耦合系统的介观输运研究

运用非平衡格林函数理论、正则变换以及BCS平均场理论研究了正常金属-分子量子点-超导耦合系统（N-MQD-S）的介观输运,得到了系统的电流公式并选择适当的参数进行了数值计算。数值计算结果表明：电声子耦合强度 与线宽函数 对系统的输运行为有较大影响。当 增大时,由声子辅助隧穿所产生的共振峰将高于分子量子点自身能级产生的共振峰;当线宽函数 增大时,在Andreev反射共振峰的两侧将出现新的边峰。     

Proximity-induced transport in hybrid mesoscopic normal–superconducting metal structures

Using an approach based on quasiclassical Green’s functions we present a theoretical study of transport in mesoscopic SN structures in the diffusive limit. The subgap conductance in SN structures with barriers (zero bias and finite bias anomalies) are discussed. We also analyse the temperature dependence of the conductance variationδS (T) for a Andreev interferometer. We show that besides the well know low temperature maximum a second maximum near T_cmay appear. We present the results of studies on the Josephson effect in 4-terminal SNS contacts and on the possible sign reversal of the Josephson critical current.     

Coupling of superconductivity with low-dimensional electron systems in mesoscopic geometries

We describe effects seen in coupled superconductor–semiconductor hybrid systems in various mesoscopic geometries. The hybrid structures consist of niobium films on high mobility InAs:GaSb quantum wells which form high transparency, low-resistance interfaces exhibiting a variety of effects in their resistive transitions and differential resistance scans. Grating structures show effects arising out of the confinement of quasiparticles while dot arrays show evidence of proximity induced superconductivity scaling as the density of dots. Superconducting dots deposited on narrow semiconductor channels show suppression of Andreev reflection which we attribute to interdot diffuse scattering from the walls of the channel.     

The Aharonov–Bohm effect in graphene rings

This is a review of electronic quantum interference in mesoscopic ring structures based on graphene, with a focus on the interplay between the Aharonov–Bohm effect and the peculiar electronic and transport properties of this material. We first present an overview on recent developments of this topic, both from the experimental as well as the theoretical side. We then review our recent work on signatures of two prominent graphene-specific features in the Aharonov–Bohm conductance oscillations, namely Klein tunneling and specular Andreev reflection. We close with an assessment of experimental and theoretical development in the field and highlight open questions as well as potential directions of the developments in future work.     

Spin transport properties in ferromagnet/superconductor junctions on topological insulator

The spin-dependent Andreev reflection is investigated theoretically by analyzing the electronic transport in a thin-film topological insulator (TI) ferromagnet/superconductor (FM/SC) junction. The tunneling conductance and shot noise are calculated based on the Dirac-Bogoliubov-de Gennes equation and Blonder-Tinkham-Klapwijk theory. It is found that the magnetic gap in ferromagnet can enhance the Andreev retro-reflection but suppress the specular Andreev reflection. The gate potential applied to the electrode on top of superconductor can enhance the two types of reflections. There is a transition between the two types of reflections at which both the tunneling conductance and differential shot noise become zero. These results provide a method to realize and detect experimentally the intra-band specular Andreev reflection in thin film TI-based FM/SC structures.     

Effect of spin-dependent phases of tunneling electrons on the conductance of a point ferromagnet/isolator/superconductor contact

The Andreev reflection probability for a ferromagnet/isolator/superconductor (FIS) contact at the arbitrary spin-dependent amplitudes of the electron waves transmitted through and reflected from the potential barrier is found. It is shown that the Andreev reflection probabilities of electron and hole excitations in the FIS contact are different. The energy levels of the Andreev bound states are found. The ballistic conductance of the point FIS contact is calculated. The text was submitted by the author in English.     

Thermoelectric effects in normal metal/superconductor interface structures

The thermopower of Andreev interferometers, which are doubly connected loops in which one arm is a superconductor and one arm is a normal metal, oscillates as a function of magnetic field with a fundamental period corresponding to a flux quantum h / 2 e through the area of the loop. While the magnetoresistance of an Andreev interferometer is symmetric with respect to the magnetic field, the thermopower can be either symmetric or antisymmetric, depending on the topology of the sample. The temperature dependence of the thermopower oscillations is nonmonotonic. This nonmonotonic behavior does not appear to be related to the reentrance observed by many groups in the conductance of normal-metal/superconductor (NS) structures.