Conductance and Thermopower of Ballistic Andreev Cavities

Abstract

When coupling a superconductor to a normal conducting region the physical properties of the system are highly affected by the superconductor. We will investigate the effect of one or two superconductors on the conductance of a ballistic chaotic quantum dot to leading order in the total channel number using trajectory based semiclassics. The results show that the effect of one superconductor on the conductance is of the order of the number of channels and that the sign of the correction from the Drude conductance depends on the particular ratios of the numbers of channels of the superconducting and normal conducting leads. In the case of two superconductors with the same chemical potential we will also see how the conductance and the sign of quantum corrections are affected by their phase difference. As far as random matrix theory results exist these are reproduced by our calculations. Furthermore in the case that the chemical potential of the superconductors is the same as that of one of the two normal leads the conductance shows, under certain conditions, similar effects as a normal metal-superconductor junction. The semiclassical framework is also able to treat the thermopower of chaotic Andreev billiards consisting of one chaotic dot, two normal leads and two superconducting islands and shows it to be antisymmetric in the phase difference of the superconductors.

23 pages

References in corpus (9)

• Semiclassical Approach to Chaotic Quantum Transport
• Full counting statistics of chaotic cavities from classical action correlations
• Quantitative measurements of the thermal resistance of Andreev interferometers
• Ehrenfest-time dependence of counting statistics for chaotic ballistic systems
• Thermopower oscillations in mesoscopic Andreev interferometers
• Anderson localization from classical trajectories
• Magnetic-field dependence of transport in normal and Andreev billiards: a classical interpretation to the averaged quantum behavior
• Effects of Andreev reflection on the conductance of quantum-chaotic dots
• Macroscopic Resonant Tunneling through Andreev Interferometers

Cited by in corpus (10)

• Zero-voltage conductance peak from weak antilocalization in a Majorana nanowire
• Onsager Relations in Coupled Electric, Thermoelectric and Spin Transport: The Ten-Fold Way
• Separation of heat and charge currents for boosted thermoelectric conversion
• Semiclassical roots of universality in many-body quantum chaos
• Transport moments beyond the leading order
• Nonlocal thermoelectricity in a topological Andreev interferometer
• Transport moments and Andreev billiards with tunnel barriers
• Combinatorial theory of the semiclassical evaluation of transport moments II: Algorithmic approach for moment generating functions
• Thermoelectric processes of quantum normal-superconductor interfaces
• Macroscopic Coherent Rectification in Andreev Interferometers