Analytic approach to transport in superconducting junctions with arbitrary carrier density

Abstract

Particle transport across Josephson junctions is commonly described using a simplifying approximation (often called the Andreev approximation), which assumes that excitations are fixed at the Fermi momentum and only Andreev reflections, with no normal reflections, occur at interfaces. While this approximation is appropriate for superconductors with high carrier density (for which the chemical potential vastly exceeds the pairing gap), it breaks down for low-carrier-density superconductors, such as topological superconductors, doped semiconductors, or superfluid quantum gases. Here, we present a general $analytical$ framework for transport in superconducting junctions that does not rely on this limiting Andreev approximation. We apply our framework to describe transport in junctions between $s$-wave superconductors along the BCS-BEC crossover, which interpolates between the conventional high-carrier-density (BCS-)regime and moderate- as well as low-carrier-density regimes (unitary and BEC regimes), for which the Andreev approximation is not valid. As the system is tuned from the BCS to the BEC regime, the magnitude of a subgap current due to multiple Andreev reflections (MAR) decreases. However, nonlinearities in the current-voltage characteristic become more pronounced near the intermediate unitary limit, giving rise to sharp peaks and dips in the differential conductance with even $negative$ differential conductance at specific voltages. Microscopically, the negative differential conductance is related to the van Hove points in the band structures, at which enhanced normal reflection occurs and that become accessible only when the chemical potential is comparable to or smaller than the pairing gap. The subgap current due to MAR vanishes at a critical interaction strength on the BEC side, which we identify as the splitting point where the particle dispersion changes curvature.

26 pages, 12 figures, 1 table. Published version

References in corpus (23)

• Many-Body Physics with Ultracold Gases
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Field-induced superconducting phase of FeSe in the BCS-BEC cross-over
• Observation of Quantized Conductance in Neutral Matter
• High-temperature topological superconductivity in twisted double layer copper oxides
• Two-terminal transport measurements with cold atoms
• Even-odd effect in Andreev Transport through a Carbon Nanotube Quantum Dot
• Transparent Semiconductor-Superconductor Interface and Induced Gap in an Epitaxial Heterostructure Josephson Junction
• Phase diagram of a cold polarized Fermi gas
• Giant superconducting fluctuations in the compensated semimetal FeSe at the BCS-BEC crossover
• Gate-controlled BCS-BEC crossover in a two-dimensional superconductor
• Scattering matrix approach to the description of quantum electron transport
• Moving beyond the transmon: Noise-protected superconducting quantum circuits
• Supercurrent and multiple Andreev reflections in an InSb nanowire Josephson junction
• Connecting dissipation and phase slips in a Josephson junction between fermionic superfluids
• Experimental probe of topological orders and edge excitations in the second Landau level
• Conduction Channels of an InAs-Al nanowire Josephson weak link
• Anomalous conductances in an ultracold quantum wire
• Keldysh study of point-contact tunneling between superconductors
• Conductance spectroscopy of nontopological-topological superconductor junctions
• Anomalous Inner-Gap Structure in Transport Characteristics of Superconducting Junctions with Degraded Interfaces
• Anomalous Conductance of a strongly interacting Fermi Gas through a Quantum Point Contact
• Mesoscopic pairing without superconductivity

Cited by in corpus (13)

• Collective modes in interacting two-dimensional tomographic Fermi liquids
• Superfluid signatures in a dissipative quantum point contact
• DC transport in a dissipative superconducting quantum point contact
• Andreev reflection spectroscopy in strongly paired superconductors
• Junctions and superconducting symmetry in twisted bilayer graphene
• Magnetic field suppression of tomographic electron transport
• Irreversible entropy transport enhanced by fermionic superfluidity
• Fluxoid valve effect in full-shell nanowire Josephson junctions
• Majorana fermions in Kitaev chains side-coupled to normal metals
• Fermi liquid theory of $d$-wave altermagnets: demon modes and Fano-demon states
• SNS Junctions along the BCS-BEC Crossover
• Interplay between evanescent scattering modes and finite dispersion in superconducting junctions
• Majorana edge and end states in planar Josephson junctions