Driven Majorana Modes: A Route to Synthetic $p_x+ip_y$ Superconductivity

TL;DR

This paper proposes a method to create synthetic $p_x+ip_y$ superconductors in one-dimensional topological systems by periodically driving Majorana modes, leading to new topological phases and Majorana modes in a two-dimensional synthetic space.

Contribution

It introduces a Floquet-based protocol to realize $p_x+ip_y$ superconductivity in 1D systems, expanding the possibilities for topological quantum states.

Findings

Realization of Floquet $p_x+ip_y$ superconductors using Kitaev chains.

Identification of a $ ext{pi}$ Majorana mode at the Floquet zone boundary.

Proposal of driven magnetic spiral-superconductor systems as platforms.

Abstract

We propose a protocol to realize synthetic $p_x+ip_y$ superconductors in one-dimensional topological systems that host Majorana fermions. By periodically driving a localized Majorana mode across the system, our protocol realizes a topological pumping of Majorana fermions, analogous to the adiabatic Thouless pumping of electrical charges. Importantly, similar to the realization of a Chern insulator through Thouless pumping, we show that pumping of Majorana zero modes could lead to a $p_x + ip_y$ superconductor in the two dimensions of space and synthetic time. The Floquet theory is employed to map the driven one-dimensional system to a two-dimensional synthetic system by considering frequency as a new dimension. We demonstrate such Floquet $p_x + i p_y$ superconductors using the Kitaev $p$-wave superconductor chain, a prototypical 1D topological system, as well as its more realistic realization in the 1D Kondo lattice model as examples. We further show the appearance of a new $\pi$ Majorana mode at the Floquet zone boundary in an intermediate drive frequency region. Our work suggests a driven magnetic spiral coupled to a superconductor as a promising platform for the realization of novel topological superconductors.