Exceptional points for chiral Majorana fermions in arbitrary dimensions

Perimeter Institute for Theoretical Physics - 31 Caroline St. N., Waterloo ON N2L 2Y5, Canada

Received: 29 April 2015
Accepted: 18 June 2015

Abstract

Certain real parameters of a Hamiltonian, when continued to complex values, can give rise to singular points called exceptional points (EP's), where two or more eigenvalues coincide and the complexified Hamiltonian becomes non-diagonalizable. We show that for a generic d-dimensional topological superconductor/superfluid with a chiral symmetry, one can find EP's associated with the chiral zero-energy Majorana fermions bound to a topological defect/edge. Exploiting the chiral symmetry, we propose a formula for counting the number (n) of such chiral zero modes. We also establish the connection of these solutions to the Majorana fermion wave functions in the position space. Finally, we conclude that EP's cannot be associated with the Majorana fermion wave functions for systems with no chiral symmetry, though one can use our formula for counting n, using complex k solutions where the determinant of the corresponding BdG Hamiltonian vanishes.