Dynamical generation of Floquet Majorana flat bands in s-wave superconductors

TL;DR

This paper introduces quantum control methods to generate Floquet Majorana flat bands in s-wave superconductors, expanding the possibilities for realizing topological states beyond equilibrium conditions.

Contribution

It presents two control strategies to engineer Floquet Majorana flat bands by dynamically inducing or activating chiral symmetry in superconductors.

Findings

Periodic modulation of chemical potential creates Majorana flat bands.

Effective parity kicks generate chiral symmetry dynamically.

Time-dependent control broadens access to gapless topological phases.

Abstract

We present quantum control techniques to engineer flat bands of symmetry-protected Majorana edge modes in s-wave superconductors. Specifically, we show how periodic control may be employed for designing time-independent effective Hamiltonians, which support $Floquet$ $Majorana$ $flat$ $bands$, starting from equilibrium conditions that are either topologically trivial or only support individual Majorana pairs. In the first approach, a suitable modulation of the chemical potential simultaneously induces Majorana flat bands and dynamically $activates$ a pre-existing chiral symmetry which is responsible for their protection. In the second approach, the application of effective parity kicks dynamically $generates$ a desired chiral symmetry by suppressing chirality-breaking terms in the static Hamiltonian. Our results demonstrate how the use of time-dependent control enlarges the range of possibilities for realizing gapless topological superconductivity, potentially enabling access to topological states of matter that have no known equilibrium counterpart.