Majorana edge modes in the Kitaev model

Manisha Thakurathi, K. Sengupta, and Diptiman Sen
Phys. Rev. B 89, 235434 – Published 27 June 2014

Abstract

We study the Majorana modes, both equilibrium and Floquet, which can appear at the edges of the Kitaev model on the honeycomb lattice. We first present the analytical solutions known for the equilibrium Majorana edge modes for both zigzag and armchair edges of a semi-infinite Kitaev model and chart the parameter regimes in which they appear. We then examine how edge modes can be generated if the Kitaev coupling on the bonds perpendicular to the edge is varied periodically in time as periodic δ-function kicks. We derive a general condition for the appearance and disappearance of the Floquet edge modes as a function of the drive frequency for a generic d-dimensional integrable system. We confirm this general condition for the Kitaev model with a finite width by mapping it to a one-dimensional model. Our numerical and analytical study of this problem shows that Floquet Majorana modes can appear on some edges in the kicked system even when the corresponding equilibrium Hamiltonian has no Majorana mode solutions on those edges. We support our analytical studies by numerics for a finite sized system which show that periodic kicks can generate modes at the edges and the corners of the lattice.

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  • Received 25 October 2013
  • Revised 2 June 2014

DOI:https://doi.org/10.1103/PhysRevB.89.235434

©2014 American Physical Society

Authors & Affiliations

Manisha Thakurathi1, K. Sengupta2, and Diptiman Sen1

  • 1Centre for High Energy Physics, Indian Institute of Science, Bangalore 560 012, India
  • 2Theoretical Physics Department, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India

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Issue

Vol. 89, Iss. 23 — 15 June 2014

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