Odd-frequency pairing in a nonunitary p-wave superconductor with multiple Majorana fermions

Abstract

Odd-frequency Cooper pairs are gathering attention for the convenience of investigating the edge state of topological superconductors including Majorana fermions. Although a spinless p-wave superconductor has only one Majorana fermion in a topological phase, the system with magnetic fields can reach the topological phases with multiple Majorana fermions. To distinguish these multiple Majorana fermion phases, we correlate the energy spectrum with the odd-frequency pair amplitude as increasing the system size. The system size dependence tells us three pieces of information: the parity of the number of the Majorana fermions at the edge, the number of low-energy modes corresponding to the Majorana fermions with different localization lengths, and the fingerprints of the Majorana fermions. Also, we present the spatial dependence of the odd-frequency f vector that is created from odd-frequency pair amplitude and the spin structure of odd-frequency Cooper pairs. We find that the odd-frequency f vector is fixed in the same direction in any topological phase. Also, we show that the spin state of odd-frequency Cooper pairs tends to be oriented toward the direction of the magnetic fields. Our results highlight the odd-frequency Cooper pairs can be a good indicator for the detection of the multiple Majorana fermions and the distinction among the topological phases.

14 pages, 13 figures

References in corpus (12)

• Non-Abelian Anyons and Topological Quantum Computation
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Theory of the proximity effect in junctions with unconventional superconductors
• Symmetries of Pairing Correlations in Superconductor-Ferromagnet Nanostructures
• Odd-frequency pairing in normal metal/superconductor junctions
• Majorana Fermions and Odd-frequency Cooper Pairs in a Nano Wire
• Anomalous Josephson effect in p-wave dirty junctions
• Odd-frequency superconducting pairing and subgap density of states at the edge of a two-dimensional topological insulator without magnetism
• Odd-frequency superconducting states with different types of Meissner response: Problem of coexistence
• On stability of odd-frequency superconducting state
• Magnetic-Field-Induced Topological Reorganization of a P-wave Superconductor
• Generation of odd-frequency surface superconductivity with spontaneous spin current due to the zero-energy Andreev bound state

Cited by in corpus (5)

• Superconducting phenomena in systems with unconventional magnets
• Controllable odd-frequency Cooper pairs in multi-superconductor Josephson junctions
• Odd-frequency pairing due to Majorana and trivial Andreev bound states
• Odd-frequency pairs and anomalous proximity effect in nematic and chiral states of superconducting topological insulators
• Topological phase transitions in superconductors with chiral symmetry