E. N. Bratus

Multiple Andreev reflection in single-atom niobium junctions

Single atom junctions between superconducting niobium leads are produced using the Mechanically Controllable Break Junction technique. The current-voltage characteristics of these junctions are analysed using an exact formulation for a superconducting quantum point contact. For tunnelling between two single atoms with a sufficiently large vacuum barrier, it is found that a single channel dominates the current, and that the current-voltage characteristic is described by the theory, without adjustable parameters. For a contact of a single Nb atom it is shown that five conductance channels contribute to the conductance, in agreement with the number expected based on the number of valence orbitals for this d-metal. For each of the channels the transmission probability is obtained from the fits and the limits of accuracy for these numbers are discussed.

Andreev level qubit.

We investigate the dynamics of a two-level Andreev bound state system in a transmissive quantum point contact embedded in an rf SQUID. Coherent coupling of the Andreev levels to the circulating supercurrent allows manipulation and readout of the level states. The two-level Hamiltonian for the Andreev levels is derived, and the effect of interaction with the quantum fluctuations of the induced flux is studied. We also consider an inductive coupling of qubits and discuss the relevant SQUID parameters for qubit operation and readout.

Dynamics and phonon-induced decoherence of Andreev level qubit

We present a detailed theory for the Andreev level qubit, a system consisting of a highly transmissive quantum point contact embedded in a superconducting loop. The two-level Hamiltonian for Andreev levels interacting with quantum phase fluctuations is derived by using a path integral method. We also derive a kinetic equation describing qubit decoherence due to interaction of the Andreev levels with acoustic phonons. The collision terms are nonlinear due to the fermionic nature of the Andreev states, leading to slow nonexponential relaxation and dephasing of the qubit at temperatures smaller than the qubit level spacing.

Current noise in long diffusive SNS junctions in the incoherent multiple Andreev reflections regime

Spectral density of current fluctuations at zero frequency is calculated for a long diffusive SNS junction with low-resistive interfaces. At low temperature, T << Delta, the subgap shot noise approaches linear voltage dependence, S=(2/ 3R)(eV + 2Delta), which is the sum of the shot noise of the normal conductor and voltage independent excess noise. This result can also be interpreted as the 1/3-suppressed Poisson noise for the effective charge q = e(1+2Delta/eV) transferred by incoherent multiple Andreev reflections (MAR). At higher temperatures, anomalies of the current noise develop at the gap subharmonics, eV = 2Delta/n. The crossover to the hot electron regime from the MAR regime is analyzed in the limit of small applied voltages.

Phase-dependent multiple Andreev reflections in SNS interferometers

A theory of coherent multiple Andreev reflections (MAR) is developed for superconductor-normal-metal-superconductor interferometers. We consider a Y-shaped normal-electron-beam splitter connecting two superconducting reservoirs, where the two connection points to the same superconductor can have different phases. The current is calculated in the quantum transport regime as a function of applied voltage and phase difference, I(V,o). MAR in interferometers incorporate two features: interference in the arms of the splitter, and interplay with Andreev resonances. The latter feature yields enhancement of the subgap current and current peaks with phase-dependent positions and magnitudes. The interference effect leads to suppression of the subgap current and complete disappearance of the current peaks at o=π. The excess current at large voltage decreases and changes sign with increasing phase difference.

Flux qubit with a quantum point contact

Andreev bound states in superconducting quantum point contacts (QPC) can be accessed for manipulation and measurement by embedding the QPC in a superconducting loop. We discuss the characteristics of such a device suitable for qubit operation, methods of manipulations with the Andreev levels, and qubit coupling.

Subgap current in superconducting tunnel junctions with diffusive electrodes

We calculate subgap current in planar superconducting tunnel junctions with thin-film diffusive leads. It is found that the subharmonic gap structure of the tunnel current scales with an effective tunneling transparency which may exceed the junction transparency by up to two orders of magnitude depending on the junction geometry, and the ratio between the coherence length and the elastic scattering length. These results provide an alternative explanation of anomalously high values of the subgap current in tunnelling experiments often ascribed to imperfectness of the insulating layer. We also discuss the effect of finite lifetime of quasiparticles as the possible origin of additional enhancement of multiparticle tunnel currents.

On the theory of Josephson effect in a diffusive tunnel junction

Specific features of the equilibrium current-carrying state of a Josephson tunnel junction between diffusive superconductors (with the electron mean free path l smaller than the coherence length ξ0) are studied theoretically in the 1D geometry when the current does not spread in the junction banks. It is shown that the concept of “weak link” with the phase jump Φ∼1 of the order parameter exists only for a low transmissivity of the barrier Γ≪l/ξ0≪1. Otherwise, the presence of the tunnel junction virtually does not affect the distributions of the order parameter modulus and phase. It is found that the Josephson current flowing in the vicinity of the tunnel barrier induces localized states of electron excitations, which are a continuous analog of Andreev’s levels in a ballistic junction. The depth of the corresponding “potential well” is much larger than the separation between an Andreev’s level and the continuous energy spectrum boundary for the same transmissivity of the barrier. In contrast to a ballistic...

Dissipative charge transport in diffusive superconducting double-barrier junctions

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 gamma = tau(d)Delta of relative phase shifts between the electrons and retroreflected holes accumulated during the dwell time tau(d). In the limit of small electron-hole dephasing gamma << 1, our solution recovers a known formula for a short mesoscopic connector extended to the MAR regime. At large dephasing, the subharmonic gap structure in the IVC scales with gamma(-1), which thus plays the role of an effective tunneling parameter. In this limit, the even gap subharmonics are resonantly enhanced, and the IVC exhibits portions with negative differential resistance.

Resonant subgap current transport in Josephson field effect transistor

We study theoretically the current-voltage characteristics (IVCs) of the Josephson field effect transistor - a ballistic SNINS junction with superconducting (S) electrodes confining a planar normal-metal region (N), which is controlled by the gate-induced potential barrier (I). Using the computation technique developed earlier for long single-channel junctions in the coherent multiple Andreev reflection (MAR) regime, we find a significant difference of the subgap current structure compared to the subharmonic gap structure in tunnel junctions and atomic-size point contacts. For long junctions, whose lengths significantly exceed the coherence length, the IVC exhibits current peaks at multiples (harmonics) of the distance ?m between the static Andreev levels eVn=n?m. Moreover, the averaged IVC follows the powerlike behavior rather than the exponential one and has a universal scaling with the junction transparency. This result is qualitatively understood using an analytical approach based on the concept of resonant MAR trajectories. In shorter junctions having lengths comparable to the coherence length, the IVC has an exponential form common for point contacts, however the current structures appear at the subharmonics of the interlevel distance eVn=?m/n rather than the gap subharmonics 2?/n.