title: Majorana fermions in superconducting 1D systems having periodic, quasiperiodic, and disordered potentials.
abstract: We present a unified study of the effect of periodic, quasiperiodic, and disordered potentials on topological phases that are characterized by Majorana end modes in one-dimensional p-wave superconducting systems. We define a topological invariant derived from the equations of motion for Majorana modes and, as our first application, employ it to characterize the phase diagram for simple periodic structures. Our general result is a relation between the topological invariant and the normal state localization length. This link allows us to leverage the considerable literature on localization physics and obtain the topological phase diagrams and their salient features for quasiperiodic and disordered systems for the entire region of parameter space.
authors.affiliation: Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080, USA.
authors.forename: Wade
authors.initials: W
authors.lastname: DeGottardi
authors.affiliation: Centre for High Energy Physics, Indian Institute of Science, Bangalore 560012, India.
authors.forename: Diptiman
authors.initials: D
authors.lastname: Sen
authors.affiliation: Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080, USA.
authors.forename: Smitha
authors.initials: S
authors.lastname: Vishveshwara