Non-Hermitian higher-order topological superconductors in two-dimension: statics and dynamics

TL;DR

This paper proposes a non-Hermitian second-order topological superconductor model hosting Majorana zero modes, addressing the breakdown of bulk boundary correspondence and extending static modes to Floquet-driven systems with anomalous $\\pi$-modes.

Contribution

It introduces a non-Hermitian SOTSC model with biorthogonal topological characterization and explores Floquet dynamics, including anomalous $\\pi$-modes, in two-dimensional systems.

Findings

Majorana zero modes inhabit only one corner in the NH SOTSC.

Extension of static MZMs to Floquet systems reveals anomalous $\\pi$-modes.

Biorthogonal nested polarization characterizes Floquet zero modes.

Abstract

Being motivated by intriguing phenomena such as the breakdown of conventional bulk boundary correspondence and emergence of skin modes in the context of non-Hermitian (NH) topological insulators, we here propose a NH second-order topological superconductor (SOTSC) model that hosts Majorana zero modes (MZMs). Employing the non-Bloch form of NH Hamiltonian, we topologically characterize the above modes by biorthogonal nested polarization and resolve the apparent breakdown of the bulk boundary correspondence. Unlike the Hermitian SOTSC, we notice that the MZMs inhabit only one corner out of four in the two-dimensional NH SOTSC. We extend the static MZMs into the realm of Floquet drive. We find anomalous $\pi$-mode following low-frequency mass-kick in addition to the regular $0$-mode that is usually engineered in a high-frequency regime. We further characterize the regular $0$-mode with biorthogonal Floquet nested polarization. Our proposal is not limited to the $d$-wave superconductivity only and can be realized in the experiment with strongly correlated optical lattice platforms.