Phase diagram of the electron-doped La2-xCexCuO4 cuprate superconductor from Andreev bound states at grain boundary junctions

We use quasiparticle tunneling across La2-xCexCuO4 grain boundary junctions to probe the superconducting state and its disappearance with increasing temperature and magnetic field. A zero bias conductance peak due to zero energy surface Andreev bound states is a clear signature of the phase coherence of the superconducting state. Hence, such a peak must disappear at or below the upper critical field Bc2(T). For La2-xCexCuO4 this approach sets a lower bound for Bc2(0) approximately 25 T which is substantially higher than reported previously. The method of probing the superconducting state via Andreev bound states should also be applicable to other cuprate superconductors.     

Spin-symmetric solution of an interacting quantum dot attached to superconducting leads: Andreev states and the 0-<Emphasis Type="Italic">π</Emphasis> transition

Behavior of Andreev gap states in a quantum dot with Coulomb repulsion symmetricallyattached to superconducting leads is studied via the perturbation expansion in theinteraction strength. We find the exact asymptotic form of the spin-symmetric solution forthe Andreev states continuously approaching the Fermi level. We thereby derive a criticalinteraction at which the Andreev states at zero temperature merge at the Fermi energy,being the upper bound for the 0-π transition. We show that the spin-symmetricsolution becomes degenerate beyond this interaction, in the π phase, and the Andreevstates do not split unless the degeneracy is lifted. We further demonstrate that thedegeneracy of the spin-symmetric state extends also into the 0 phase in which the solutions with zero andnon-zero frequencies of the Andreev states may coexist.     

The emergence of bound states in a superconducting gap at the topological insulator edge

We consider the edge of a superconducting topological insulator with the impurity in the presence of the Zeeman field. We analytically prove that in the trivial phase two Andreev bound states (ABSs) arise with energies moving from the superconducting gap edges to zero forming two Majorana-like bound states, as the impurity strength varies from 0 to ±2. When the Zeeman field is locally perturbed, ABSs arise both in the trivial and topological phases, but in the topological phase ABSs with energy near the gap edges cannot transform into Majorana bound states and vice versa.     

Fano effect and Andreev bound states in T-shape double quantum dots

In this Letter, we investigate the transport through a T-shaped double quantum dot coupled to two normal metal leads left and right and a superconducting lead. Analytical expressions of Andreev transmission and local density of states of the system at zero temperature have been obtained. We study the role of the superconducting lead in the quantum interferometric features of the double quantum dot. We report for first time the Fano effect produced by Andreev bound states in a side quantum dot. Our results show that as a consequence of quantum interference and proximity effect, the transmission from normal to normal lead exhibits Fano resonances due to Andreev bound states. We find that this interference effect allows us to study the Andreev bound states in the changes in the conductance between two normal leads.     

Finite-frequency noise in a topological superconducting wire

In this paper we study the finite-frequency current cross-correlations for a topological superconducting nanowire attached to two terminals at one of its ends. Using an analytic 1D model we show that the presence of a Majorana bound state yields vanishing cross-correlations for frequencies larger than twice the applied transport voltage, in contrast to what is found for a zero-energy ordinary Andreev bound state. Zero cross-correlations at high frequency have been confirmed using a more realistic tight-binding model for finite-width topological superconducting nanowires. Finite-temperature effects have also been investigated.     

Andreev reflection in strong magnetic fields

We have studied the interplay of Andreev reflection and cyclotron motion of quasiparticles at a superconductor-normal-metal interface with a strong magnetic field applied parallel to the interface. Bound states are formed due to the confinement introduced by both the external magnetic field and the superconducting gap. These bound states are a coherent superposition of electron and hole edge excitations similar to those realized in finite quantum-Hall samples. We find the energy spectrum for these Andreev edge states and calculate transport properties.     

Controllable π junction in a Josephson quantum-dot device with molecular spin

We consider a model for a single molecule with a large frozen spin sandwiched in between two BCS superconductors at equilibrium, and show that this system has a π junction behavior at low temperature. The π shift can be reversed by varying the other parameters of the system, e.g., temperature or the position of the quantum dot level, implying a controllable π junction with novel application as a Josephson current switch. We show that the mechanism leading to the π shift can be explained simply in terms of the contributions of the Andreev bound states and of the continuum of states above the superconducting gap. The free energy for certain configuration of parameters shows a bistable nature, which is a necessary pre-condition for achievement of a qubit.     

Observation of broken time-reversal symmetry with Andreev bound state tunneling spectroscopy

Quasiparticle (QP) planar tunneling spectroscopy is used to investigate the density of states (DoS) of YBa₂Cu₃O₇ (YBCO). Temperature, crystallographic orientation, doping, damage and magnetic field dependencies confirm that the observed zero-bias conductance peak (ZBCP) is an Andreev bound state (ABS), an intrinsic property of a d-wave superconducting order parameter (OP) at an interface. In zero applied field, the splitting of the ZBCP below 8 K confirms a near-surface phase transition into a superconducting state with spontaneously broken time-reversal symmetry (BTRS). Tunneling into the ABS provides a phase-sensitive spectroscopy that can be used to measure a variety of DoS properties in an unconventional superconductor.     

Origin of excess low-energy states in a disordered superconductor in a Zeeman field

Tunneling density of states measurements of disordered superconducting Al films in high Zeeman fields reveal a significant population of subgap states which cannot be explained by standard BCS theory. We provide a natural explanation of these excess states in terms of a novel disordered Larkin-Ovchinnikov phase that occurs near the spin-paramagnetic transition at the Chandrasekhar-Clogston critical field. The disordered Larkin-Ovchinnikov superconductor is characterized by a pairing amplitude that changes sign at domain walls. These domain walls carry magnetization and support Andreev bound states that lead to distinct spectral signatures at low energy.     

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.     

Phase modulated thermal conductance of Josephson weak links

We present a theory for quasiparticle heat transport through superconducting weak links. The thermal conductance depends on the phase difference (phi) of the superconducting leads. Branch-conversion processes, low-energy Andreev bound states near the contact, and the suppression of the local density of states near the gap edge are related to phase-sensitive transport processes. Theoretical results for the influence of junction transparency, temperature, and disorder, on the conductance, are reported. For high-transmission weak links, D-->1, the formation of an Andreev bound state leads to suppression of the density of states for the continuum excitations, and thus, to a reduction in the conductance for phi approximately pi. For low-transmission (D<1) barriers resonant scattering leads to an increase in the thermal conductance as T drops below T(c) (for phase differences near phi=pi).     

Dominant Majorana bound energy and critical current enhancement in ferromagnetic-superconducting topological insulator

Among the potential applications of topological insulators, we theoretically study the coexistence of proximity-induced ferromagnetic and superconducting orders in the surface states of a 3-dimensional topological insulator. The superconducting electron-hole excitations can be significantly affected by the magnetic order induced by a ferromagnet. In one hand, the surface state of the topological insulator, protected by the time-reversal symmetry, creates a spin-triplet and, on the other hand, magnetic order causes to renormalize the effective superconducting gap. We find Majorana mode energy along the ferromagnet/superconductor interface to sensitively depend on the magnitude of magnetization m _zfs from superconductor region, and its slope around perpendicular incidence is steep with very low dependency on m _zfs . The superconducting effective gap is renormalized by a factor η(m _zfs ), and Andreev bound state in ferromagnet-superconductor/ferromagnet/ferromagnet-superconductor (FS/F/FS) Josephson junction is more sensitive to the magnitude of magnetizations of FS and F regions. In particular, we show that the presence of m _zfs has a noticeable impact on the gap opening in Andreev bound state, which occurs in finite angle of incidence. This directly results in zero-energy Andreev state being dominant. By introducing the proper form of corresponding Dirac spinors for FS electron-hole states, we find that via the inclusion of m _zfs , the Josephson supercurrent is enhanced and exhibits almost abrupt crossover curve, featuring the dominant zero-energy Majorana bound states.     

Andreev bound states in high temperature superconductors

Andreev bound states at the surface of superconductors are expected for any pair potential showing a sign change in different k-directions with their spectral weight depending on the relative orientation of the surface and the pair potential. We report on the observation of Andreev bound states in high temperature superconductors (HTS) employing tunneling spectroscopy on bicrystal grain boundary Josephson junctions (GBJs). The tunneling spectra were studied as a function of temperature and applied magnetic field. The tunneling spectra of GBJ formed by YBa₂Cu₃O (YBCO), Bi₂Sr₂CaCu₂O(BSCCO), and La_1.85Sr_0.15CuO₄ (LSCO) show a pronounced zero bias conductance peak that can be interpreted in terms of Andreev bound states at zero energy that are expected at the surface of HTS having a d-wave symmetry of the order parameter. In contrast, for the most likely s-wave HTS Nd_1.85Ce_0.15CuO_4-y (NCCO) no zero bias conductance peak was observed. Applying a magnetic field results in a shift of spectral weight from zero to finite energy. This shift is found to depend nonlinearly on the applied magnetic field. Further consequences of the Andreev bound states are discussed and experimental evidence for anomalous Meissner currents is presented. Received: 17 February 1998 / Revised: 27 April 1998 / Accepted: 23 June 1998     

Andreev-reflected wave packets in voltage-biased superconducting quantum wells

Quasiparticle wave packets of alternating charges, bound by Andreev reflection in the pair potential wells of voltage-biased SNS-junctions, are calculated from the non-equilibrium solutions of the time-dependent Bogoliubov-de Gennes Equations. Depending upon the direction of their momentum relative to the stationary, homogeneous electric field in theN-region they either gain energy 2 eV in each electron-hole cycle until they leave the quantum well, or they lose energy to the field and merge into the ground state. The microscopic picture supports the recently proposed explanation of subharmonic energy gap structure in superconducting weak links by multiple Andreev reflections.     

Surface Andreev bound states of superfluid (3)He and Majorana fermions

Superfluid (3)He is an intensively investigated and well characterized p-wave superfluid. In the bulk Balian-Werthamer state, which is commonly called the (3)He B phase, the superfluid gap is opened isotropically but near a flat boundary such as a wall of a container it can harbor interesting quasi-particle states inside the gap. These states are called surface Andreev bound states, and have not been experimentally explored in detail. Transverse acoustic impedance measurement has revealed their existence and provided spectroscopic details of the dispersion of the bound states. Recent theoretical arguments claim that the surface Andreev bound states of the superfluid (3)He B phase can be recognized as the edge states of the topological superfluid and be regarded as a Majorana fermion, a fancy particle which has not been confirmed in elementary particle physics. In this review, we present up-to-date knowledge on the surface Andreev bound states of the (3)He B phase revealed by acoustic spectroscopy and the possible realization of a Majorana fermion, along with related studies on this topic.     

Splitting of a Cooper pair by a pair of Majorana bound states

We propose a method to probe the nonlocality of a pair of Majorana bound states by crossed Andreev reflection, which is the injection of an electron into one bound state followed by the emission of a hole by the other (equivalent to the splitting of a Cooper pair). We find that, at sufficiently low excitation energies, this nonlocal scattering process dominates over local Andreev reflection involving a single bound state. As a consequence, the low-temperature and low-frequency fluctuations deltaI(i) of currents into the two bound states i=1, 2 are maximally correlated: deltaI_1deltaI_2[over ]=deltaI_i(2).[over ].     

Mesoscopic superconductors under irradiation: microwave spectroscopy of Andreev states

We show that irradiation of a voltage-biased superconducting quantum point contact at frequencies of the order of the gap energy can remove the suppression of subgap dc transport through Andreev levels. Quantum interference among resonant scattering events involving photon absorption is furthermore shown to make microwave spectroscopy of the Andreev levels feasible. We also discuss how the same interference effect can be applied for detecting weak electromagnetic signals up to the gap frequency, and how it is affected by dephasing and relaxation.     

Nonequilibrium Josephson effect through helical edge states

We study Josephson junctions between superconductors connected through the helical edge states of a two-dimensional topological insulator in the presence of a magnetic barrier. As the equilibrium Andreev bound states of the junction are 4π periodic in the superconducting phase difference, it was speculated that, at finite dc bias voltage, the junction exhibits a fractional Josephson effect with half the Josephson frequency. Using the scattering matrix formalism, we show that his effect is absent in the average current. However, clear signatures can be seen in the finite-frequency current noise. Furthermore, we discuss other manifestations of the Majorana bound states forming at the edges of the superconductors.     

Nonequilibrium transport through a spinful quantum dot with superconducting leads

We study the nonlinear cotunneling current through a spinful quantum dot contacted by two superconducting leads. Applying a general nonequilibrium Green function formalism to an effective Kondo model, we study the rich variation in the IV characteristics with varying asymmetry in the tunnel coupling to source and drain electrodes. The current is found to be carried, respectively, by multiple Andreev reflections in the symmetric limit, and by spin-induced Yu-Shiba-Rusinov bound states in the strongly asymmetric limit. The interplay between these two mechanisms leads to qualitatively different IV characteristics in the crossover regime of intermediate symmetry, consistent with recent experimental observations of negative differential conductance and repositioned conductance peaks in subgap cotunneling spectroscopy.