Evolution of edge states in topological superfluids during the quantum phase transition
M. A. Silaev*, G. E. Volovik
* Institute for Physics of Microstructures RAS, 603950 Nizhny Novgorod, Russia
Low Temperature Laboratory, Aalto University, School of Science and Technology, FI-00076 Aalto, Finland
Landau Institute for Theoretical Physics RAS, 119334 Moscow, Russia
Abstract
The quantum phase transition between topological and
non-topological insulators or between fully gapped
superfluids/superconductors can occur without closing the gap. We
consider the evolution of the Majorana edge states on the surface
of topological superconductor during transition to the
topologically trivial superconductor on example of non-interacting
Hamiltonian describing the spin-triplet superfluid 3He-B. In
conventional situation when the gap is nullified at the
transition, the spectrum of Majorana fermions shrinks and vanishes
after the transition to the trivial state. If the topological
transition occurs without the gap closing, the Majorana fermion
spectrum disappears by escaping to ultraviolet, where Green's
function approaches zero. This demonstrates the close connection
between the topological transition without closing the gap and
zeroes in the Green's function. Similar connection takes place in
interacting systems where zeroes may occur due to interaction.