Chiral and counter-propagating Majorana fermions in a p-wave superconductor
Abstract

Chiral and helical Majorana fermions are two archetypal edge excitations in two-dimensional topological superconductors. They emerge from systems of different Altland–Zirnbauer symmetries and characterized by$Z$and$Z2$topological invariants respectively. It seems improbable to tune a pair of co-propagating chiral edge modes to counter-propagate in a single system without symmetry breaking. Here, we explore the peculiar behaviors of Majorana edge modes in topological superconductors with an additional ‘mirror’ symmetry which changes the bulk topological invariant to$Z⊕Z$type. A theoretical toy model describing the proximity structure of a Chern insulator and apx-wave superconductor is proposed and solved analytically to illustrate a direct transition between two topologically nontrivial phases. The weak pairing phase has two chiral Majorana edge modes, while the strong pairing phase is characterized by mirror-graded Chern number and hosts a pair of counter-propagating Majorana fermions protected by the mirror symmetry. The edge theory is worked out in detail, and implications to braiding of Majorana fermions are discussed.

Authors:
; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10303260
Journal Name:
New Journal of Physics
Volume:
21
Issue:
12
Page Range or eLocation-ID:
Article No. 123014
ISSN:
1367-2630
Publisher:
IOP Publishing
National Science Foundation
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