Andreev bound states at boundaries of polarized 2D Fermi superfluids with s-wave pairing and spin-orbit coupling

Abstract

A topological superfluid phase characterized by an emergent chiral-p-wave pair potential is expected to form in a two-dimensional Fermi superfluid subject to s-wave pairing, spin-orbit coupling and a large-enough Zeeman splitting. Andreev bound states appear at phase boundaries, including Majorana zero modes whose existence is assured by the bulk-boundary correspondence principle. Here we study the physical properties of these subgap-energy bound states at step-like interfaces using the spin-resolved Bogoliubov-deGennes mean-field formalism and assuming small spin-orbit coupling. Extending a recently developed spin-projection technique based on Feshbach partitioning [SciPost Phys. 5, 016 (2018)] combined with the Andreev approximation allows us to obtain remarkably simple analytical expressions for the bound-state energies as well as the majority and minority spin components of their wave functions. Besides the vacuum boundary, where a majority-spin Majorana excitation is encountered, we also consider the boundary between the topological and a nontopological superfluid phase that can appear in a coexistence scenario due to the first-order topological phase transition predicted for this system. At this superfluid-superfluid interface, we find a localized chiral Majorana mode hosted by the minority-spin sector. Our theory further predicts majority-spin subgap-energy bound states similar to those found at a Josephson junction between same-chirality p-wave superfluids. Their presence affects the Majorana mode due to a coupling of minority and majority spin sectors only in the small energy range where their spectra overlap. Our results may inform experimental efforts aimed at realizing and characterizing unconventional Majorana quasiparticles.

40 pages, 5 figures. Submission to SciPost. v2: minor revisions to improve presentation of the abstract and extend discussion in the conclusions section

References in corpus (22)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics
• Dipolar physics: A review of experiments with magnetic quantum gases
• $p_x+i{p}_y$ superfluid from s-wave interactions of fermionic cold atoms
• Non-Abelian Topological Orders and Majorana Fermions in Spin-Singlet Superconductors
• Stable Topological Superfluid Phase of Ultracold Polar Fermionic Molecules
• Quantum Gases in Optical Boxes
• Tomographic RF Spectroscopy of a Trapped Fermi Gas at Unitarity
• Crossover from 2D to 3D in a weakly interacting Fermi gas
• Surface States, Edge Currents and the Angular Momentum of Chiral p-wave Superfluids
• A road to reality with topological superconductors
• An Index Theorem for the Majorana Zero Modes in Chiral P-Wave Superconductors
• Role of the Majorana Fermion and the Edge Mode in Chiral Superfluidity near a p-Wave Feshbach Resonance
• Single Impurity In Ultracold Fermi Superfluids
• Conductance spectroscopy of nontopological-topological superconductor junctions
• Helical spin texture of surface states in topological superconductors
• Josephson junctions of 2D time-reversal invariant superconductors: signatures of the topological phase
• Probing electron-hole weights of an Andreev bound state by transient currents
• Solutions of the Bogoliubov-de Gennes equation with position dependent Fermi--velocity and gap profiles
• Coexistence of topological and nontopological Fermi-superfluid phases