Dispersive one-dimensional Majorana modes with emergent supersymmetry in one-dimensional proximitized superconductors via spatially modulated potentials and magnetic fields

Pasquale Marra, Daisuke Inotani, Muneto Nitta

Research output: Contribution to journalArticlepeer-review

Abstract

In condensed matter systems, zero-dimensional or one-dimensional Majorana modes can be realized respectively as the end and edge states of one-dimensional and two-dimensional topological superconductors. In this top-down approach, (d-1)-dimensional Majorana modes are obtained as the boundary states of a topologically nontrivial d-dimensional bulk. In a bottom-up approach instead, d-dimensional Majorana modes in a d-dimensional system can be realized as the continuous limit of a periodic lattice of coupled (d-1)-dimensional Majorana modes. We illustrate this idea by considering one-dimensional proximitized superconductors with spatially modulated potential or magnetic fields. The ensuing inhomogeneous topological state exhibits one-dimensional counterpropagating Majorana modes with finite dispersion, and with a Majorana gap that can be controlled by external fields. In the massless case, the Majorana modes have opposite Majorana polarizations and pseudospins, are conformally invariant, and realize centrally extended quantum mechanical supersymmetry. The supersymmetry exhibits spontaneous partial breaking. Consequently, the massless Majorana fermion can be identified as a Goldstino, i.e., the Nambu-Goldstone fermion associated with the spontaneously broken supersymmetry.

Original languageEnglish
Article number214525
JournalPhysical Review B
Volume105
Issue number21
DOIs
Publication statusPublished - 2022 Jun 1

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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