Topological superconductors in one-dimensional mosaic lattices

¹ Department of Physics, Capital Normal University - Beijing 100048, China
² State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University Beijing 100084, China
³ Frontier Science Center for Quantum Information - Beijing, China

^(a) zengqibo@cnu.edu.cn (corresponding author)

Received: 20 May 2021
Accepted: 28 July 2021

Abstract

We study topological superconductors in a one-dimensional (1D) mosaic lattice whose on-site potentials are modulated for equally spaced sites. When the system is topologically nontrivial, Majorana zero modes appear at the two ends of the 1D lattice. By calculating energy spectra and topological invariant of the system, we find the interval of the mosaic modulation of the on-site potential, whether it is periodic, quasiperiodic, or randomly distributed, can influence the topological properties significantly. For an even interval of the mosaic potential, the system will exist in the topological superconducting phase for very large or even infinitely strong on-site potentials. When the interval is odd, however, the system undergoes a topological phase transition and enters into the trivial phase as the on-site potentials become stronger than a critical value, except for some special cases in the commensurate lattices. These conclusions are proven and the phase boundaries determined analytically by exploiting the method of transfer matrix. They reveal that robust Majorana zero modes can arise in 1D mosaic lattice independent of the strength of the spatially modulated potentials.