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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 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.
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.
Employing quasiclassical theory of superconductivity combined with Keldysh technique we investigate large thermoelectric effect in multiterminal ballistic normal-superconducting (NS) hybrid structures. We argue that this effect is caused by electron-hole asymmetry generated by coherent Andreev reflection of quasiparticles at interfaces of two different superconductors with non-zero phase difference. Within our model we derive a general expression for thermoelectric voltages $V_{T1,2}$ induced in two different normal terminals exposed to a thermal gradient. Our results apply at any temperature difference in the subgap regime and allow to explicitly analyze both temperature and phase dependencies of $V_{T1,2}$ demonstrating that in general there exists no fundamental relation between these voltages and the equilibrium Josephson current in SNS junctions.
We use point contact spectroscopy (PCS) to probe the superconducting properties of electron doped $rm{Ba(Fe_{1-x}Co_x)_2As_2}$ ($rm{x = 0.05, 0.055, 0.07, 0.08}$) and hole doped $rm{Ba_{0.8}K_{0.2}Fe_2As_2}$. PCS directly probes the low energy density of states via Andreev reflection, revealing two distinct superconducting gaps in both compound families. Apart from the electron underdoped $rm{Ba(Fe_{1-x}Co_{x})_2As_2}$, the excess current due to Andreev reflection for the compounds follows the typical BCS temperature dependence. For underdoped $rm{Ba(Fe_{1-x}Co_{x})_2As_2}$, the temperature dependence of the excess current deviates from that of BCS, developing a tail at higher temperatures and surviving above bulk $T_c$. Possible explanations for this anomalous behavior are explored.
We consider theoretically an electronic Mach-Zehnder interferometer constructed from quantum Hall edge channels and quantum point contacts, fed with single electrons from a dynamic quantum dot source. By considering the energy dependence of the edge-channel guide centres, we give an account of the phase averaging in this set up that is particularly relevant for the short, high-energy wavepackets injected by this type of electron source. We present both analytic and numerical results for the energy-dependent arrival time distributions of the electrons and also give an analysis of the delay times associated with the quantum point contacts and their effects on the interference patterns. A key finding is that, contrary to expectation, maximum visibility requires the interferometer arms to be different in length, with an offset of up to a micron for typical parameters. By designing interferometers that incorporate this asymmetry in their geometry, phase-averaging effects can be overcome such that visibility is only limited by other incoherent mechanisms.