Anatomy of a periodically driven p-wave superconductor

TL;DR

This paper investigates the topological properties and edge modes of a periodically driven p-wave superconductor model, revealing novel gapped and gapless phases with unique edge states, and explores how driving can engineer new topological superconductors.

Contribution

It introduces a toy model of driven Kitaev chains showing how periodic driving can create new topological phases with multiple edge modes and flat edge states, expanding understanding of Floquet topological superconductors.

Findings

Driven Kitaev chains can form a fully gapped $p_x+ip_y$-like superconductor with two chiral edge modes.

A different driving protocol results in a gapless superconductor with flat edge states at quasienergy 0 or π.

Exact computation of the phase bands reveals topological singularities and their relation to edge modes.

Abstract

The topological properties of periodically driven many-body systems often have no static analogs and defy a simple description based on the effective Hamiltonian. To explore the emergent edge modes in driven p-wave superconductors in two dimensions, we analyze a toy model of Kitaev chains (one-dimensional spinless p-wave superconductors with Majorana edge states) coupled by time-periodic hopping. We show that with proper driving, the coupled Kitaev chains can turn into a fully gapped superconductor which is analogous to the $p_x+ip_y$ state but has two, rather than one, chiral edge modes. A different driving protocol turns it into a gapless superconductor with isolated point nodes and completely flat edge states at quasienergy $\omega=0$ or $\pi/T$, with $T$ the driving period. The time evolution operator $U(k_x,k_y,t)$ of the toy model is computed exactly to yield the phase bands. And the "topological singularities" of the phase bands are exhausted and compared to those of a periodically driven Hofstadter model which features counter-propagating chiral edge modes. These examples demonstrate the unique edge states in driven superconducting systems and suggest driving as a potentially fruitful route to engineer new topological superconductors.