Quasiclassical theory for the superconducting proximity effect in Dirac materials

Abstract

We derive the quasiclassical non-equilibrium Eilenberger and Usadel equations to first order in quantities small compared to the Fermi energy, valid for Dirac edge and surface electrons with spin-momentum locking, as relevant for topological insulators. We discuss in detail several of the key technical points and assumptions of the derivation, and provide a Riccati-parametrization of the equations. Solving first the equilibrium equations for S/N and S/F bilayers and Josephson junctions, we study the superconducting proximity effect in Dirac materials. Similarly to related works, we find that the effect of an exchange field depends strongly on the direction of the field. Only components normal to the transport direction lead to attenuation of the Cooper pair wavefunction inside the F. Fields parallel to the transport direction lead to phase-shifts in the dependence on the superconducting phase difference for both the charge current and density of states in an S/F/S-junction. Moreover, we compute the differential conductance in S/N and S/F bilayers with an applied voltage bias, and determine the dependence on the length of the N and F regions and the exchange field.

13 pages, 5 figures. Accepted for publication in Phys. Rev. B

References in corpus (9)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Dirac materials
• Direct coupling between magnetism and superconducting current in Josephson Phi junction
• Proximity effect at the superconductor - topological insulator interface
• Spin-dependent Cooper Pair Phase and Pure Spin Supercurrents in Strongly Polarized Ferromagnets
• Non-sinusoidal current-phase relationship in Josephson junctions from the 3D topological insulator HgTe
• Magnetoelectrics in Disordered Topological Insulator Josephson Junctions
• Spin Supercurrent, Magnetization Dynamics, and Phi-State in Spin-Textured Josephson Junctions
• Majorana state on the surface of a disordered 3D topological insulator

Cited by in corpus (21)

• Odd-frequency superconductivity
• Transport in two-dimensional topological materials: recent developments in experiment and theory
• Magnetoelectric effects in Josephson junctions
• Electrical control of magnetization in S/F/S junctions on a 3D topological insulator
• Impurity scattering in superconductors revisited
• Electrically controllable spin filtering based on superconducting helical states
• Quasiclassical theory for antiferromagnetic metals
• Electrical response of S-F-TI-S junctions on magnetic texture dynamics
• Optical response of Higgs mode in superconductors at clean limit
• Long-range effect of a Zeeman field on the electric current through the helical metal-superconductor interface in Andreev interferometer
• Diamagnetic property and optical absorption in conventional superconductors with magnetic impurities
• Reentrant superconductivity in proximity to a topological insulator
• Spontaneous generation of vortices by a nonuniform Zeeman field in a two-dimensional Rashba coupled superconductor
• Bound fermion states in pinned vortices in the surface states of a superconducting topological insulator: The Majorana bound state
• Proximity Effect in Superconducting Heterostructures with Strong Spin-Orbit Coupling and Spin Splitting
• Non-exponential long-range interaction of magnetic impurities in spin-orbit coupled superconductors
• Optical response of Higgs mode in superconductors at clean limit: formulation through Eilenberger equation and Ginzburg-Landau Lagrangian
• Vortex spin-valve on a topological insulator
• Probing the magnetoelectric effect in noncentrosymmetric superconductors by equal-spin Andreev tunneling
• Fraunhofer oscillations of the critical current at a varying Zeeman field in a spin-orbit coupled Josephson junction
• Spin-orbit pumping