Theory of time reversal topological superconductivity in double Rashba wires -- symmetries of Cooper pair and Andreev bound states

Abstract

We study the system of double Rashba wires brought into the proximity to an $s$-wave superconductor. The time reversal invariant topological superconductivity is realized if the interwire pairing corresponding to crossed Andreev reflection dominates over the standard intrawire pairing. We derive the topological criterion and show that the system hosts zero energy Andreev bound states such as a Kramers pair of Majorana fermions. We classify symmetry of the Cooper pairs focusing on the four degrees of freedom, $i.e.$, frequency, spin, spatial parity inside wires, and spatial parity between wires. The magnitude of the odd-frequency pairing is strongly enhanced in the topological state. We also explore properties of junctions occurring in such double wire systems. If one section of the junction is in the topological state and the other is in the trivial state, the energy dispersion of Andreev bound states is proportional to $\sim \pm \sin \phi$, where $\phi$ denotes the macroscopic phase difference between two sections. This behavior can be intuitively explained by the couplings of a Kramers pair of Majorana fermions and spin-singlet $s$-wave Cooper pair and can also be understood by analyzing an effective continuum model of the $s+p$/$s$-wave superconductor hybrid system.

16 pages, 7 figures

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• Odd-frequency superconducting pairing in one-dimensional systems
• Odd-frequency superconducting pairing and subgap density of states at the edge of a two-dimensional topological insulator without magnetism
• Theory of Majorana zero modes in unconventional superconductors
• The Role of Odd-Frequency Pairing in Multiband Superconductors
• Majorana bound states in semiconducting nanostructures
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• Highly tunable time-reversal-invariant topological superconductivity in topological insulator thin films
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• Van der Waals heterostructures with spin-orbit coupling
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• Signatures of time-reversal-invariant topological superconductivity in the Josephson effect
• Theory of proximity effect in two-dimensional unconventional superconductor with Rashba spin-orbit interaction
• Josephson junctions in double nanowires bridged by in-situ deposited superconductors
• Supercurrent as a Probe for Topological Superconductivity in Magnetic Adatom Chains
• Charge transport of a spin-orbit-coupled Luttinger liquid
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• Time-reversal-invariant topological superconductivity
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• Realizing Majorana Kramers pairs in two-channel InAs-Al nanowires with highly misaligned electric fields
• Electronic transport in double-nanowire superconducting islands with multiple terminals