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Register a new userPhase-coherent thermoelectricity and non-equilibrium Josephson current in Andreev interferometers
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We develop a detailed theory describing a non-trivial interplay between non-equilibrium effects and long-range quantum coherence in superconducting hybrid nanostructures exposed to a temperature gradient. We establish a direct relation between thermoelectric and Josephson effects in such structures and demonstrate that at temperatures exceeding the Thouless energy of our device both phase-coherent thermoelectric signal and the supercurrent may be strongly enhanced due to non-equilibrium low energy quasiparticles propagating across the system without any significant phase relaxation. By applying a temperature gradient one can drive the system into a well pronounced $pi$-junction state, thereby creating novel opportunities for applications of Andreev interferometers.
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We predict a novel $(I_0,phi_0)$-junction state of multi-terminal Andreev interferometers that emerges from an interplay between long-range quantum coherence and non-equilibrium effects. Under non-zero bias $V$ the current-phase relation $I_S(phi)$ resembles that of a $phi_0$-junction differing from the latter due to a non-zero average $I_0(V) = left< I_S(phi)right>_{phi}$. The flux-dependent thermopower ${mathcal S}(Phi)$ of the system exhibits features similar to those of a $(I_0,phi_0)$-junction and in certain limits it can reduce to either odd or even function of $Phi$ in the agreement with a number of experimental observations.
We present a detailed theoretical description of quantum coherent electron transport in voltage-biased cross-like Andreev interferometers. Making use of the charge conjugation symmetry encoded in the quasiclassical formalism, we elucidate a crucial role played by geometric and electron-hole asymmetries in these structures. We argue that a non-vanishing Aharonov-Bohm-like contribution to the current $I_S$ flowing in the superconducting contour may develop only in geometrically asymmetric interferometers making their behavior qualitatively different from that of symmetric devices. The current $I_N$ in the normal contour -- along with $I_S$ -- is found to be sensitive to phase-coherent effects thereby also acquiring a $2pi$-periodic dependence on the Josephson phase. In asymmetric structures this current develops an odd-in-phase contribution originating from electron-hole asymmetry. We demonstrate that both phase dependent currents $I_S$ and $I_N$ can be controlled and manipulated by tuning the applied voltage, temperature and system topology, thus rendering Andreev interferometers particularly important for future applications in modern electronics.
We consider a diffusive S-N-S junction with electrons in the normal layer driven out of equilibrium by external bias. We show that, the non-equilibrium fluctuations of the electron density in the normal layer cause the fluctuations of the phase of the order parameter in the S-layers. As a result, the magnitude of the Josephson current in the non-equilibrium junction is significantly supressed relative to its mean field value.
Andreev scattering and the Josephson current through a one-dimensional interacting electron liquid sandwiched between two superconductors are re-examined. We first present some apparently new results on the non-interacting case by studying an exactly solvable tight-binding model rather than the usual continuum model. We show that perfect Andreev scattering (i.e. zero normal scattering) at the Fermi energy can only be achieved by fine-tuning junction parameters. We also obtain exact results for the Josephson current, which is generally a smooth function of the superconducting phase difference except when the junction parameters are adjusted to give perfect Andreev scattering, in which case it becomes a sawtooth function. We then observe that, even when interactions are included, all low energy properties of a junction (E<<Delta, the superconducting gap) can be obtained by integrating out the superconducting electrons to obtain an effective Hamiltonian describing the metallic electrons only with a boundary pairing interaction. This boundary model provides a suitable starting point for bosonization/renormalization group/boundary conformal field theory analysis. We argue that total normal reflection and total Andreev reflection correspond to two fixed points of the boundary renormalization group. For repulsive bulk interactions the Andreev fixed point is unstable and the normal one stable. However, the reverse is true for attractive interactions. This implies that a generic junction Hamiltonian (without fine-tuned junction parameters) will renormalize to the normal fixed point for repulsive interactions but to the Andreev one for attractive interactions. An exact mapping of our tight-binding model to the Hubbard model with a transverse magnetic field is used to help understand this behavior.
Josephson junctions with an intrinsic phase shift of pi, so-called pi Josephson junctions, can be realized by a weak link of a d-wave superconductor with an appropriate boundary geometry. A model for the pairing potential of an according weak link is introduced which allows for the calculation of the influence of geometric parameters and temperature. From this model, current-phase relations and the critical current of the device are derived. The range of validity of the model is determined by comparison with selfconsistent solutions.
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