Majorana fermions in superconducting wires: Effects of long-range hopping, broken time-reversal symmetry, and potential landscapes

DeGottardi, Wade and Thakurathi, Manisha and Vishveshwara, Smitha and Sen, Diptiman (2013) Majorana fermions in superconducting wires: Effects of long-range hopping, broken time-reversal symmetry, and potential landscapes. In: PHYSICAL REVIEW B, 88 (16).

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Abstract

We present a comprehensive study of two of the most experimentally relevant extensions of Kitaev's spinless model of a one-dimensional p-wave superconductor: those involving (i) longer-range hopping and superconductivity and (ii) inhomogeneous potentials. We commence with a pedagogical review of the spinless model and, as a means of characterizing topological phases exhibited by the systems studied here, we introduce bulk topological invariants as well as those derived from an explicit consideration of boundary modes. In time-reversal symmetric systems, we find that the longer range hopping leads to topological phases characterized by multiple Majorana modes. In particular, we investigate a spin model that respects a duality and maps to a fermionic model with multiple Majorana modes; we highlight the connection between these topological phases and the broken symmetry phases in the original spin model. In the presence of time-reversal symmetry breaking terms, we show that the topological phase diagram is characterized by an extended gapless regime. For the case of inhomogeneous potentials, we explore phase diagrams of periodic, quasiperiodic, and disordered systems. We present a detailed mapping between normal state localization properties of such systems and the topological phases of the corresponding superconducting systems. This powerful tool allows us to leverage the analyses of Hofstadter's butterfly and the vast literature on Anderson localization to the question of Majorana modes in superconducting quasiperiodic and disordered systems, respectively. We briefly touch upon the synergistic effects that can be expected in cases where long-range hopping and disorder are both present.

Item Type:	Journal Article
Publication:	PHYSICAL REVIEW B
Publisher:	AMER PHYSICAL SOC
Additional Information:	copyright for this article belongs to AMER PHYSICAL SOC
Department/Centre:	Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited:	04 Nov 2013 06:26
Last Modified:	04 Nov 2013 06:30
URI:	http://eprints.iisc.ac.in/id/eprint/47669

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