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 Z 2 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 a p x -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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Dec 01, 2019
- Source ID
- 10.1088/1367-2630/ab5cad
Entities
People
- Erhai Zhao
- Haiping Hu
- Indubala I. Satija
Organizations
- Air Force Office of Scientific Research
- National Science Foundation