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

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.

Main text: 9 pages and 4 figures, SM: 4 pages and 5 figures

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• Mixed higher-order topology: boundary non-Hermitian skin effect induced by a Floquet bulk
• Engineering non-Hermitian Second Order Topological Insulator in Quasicrystals
• Non-Hermitian second-order topological superconductors
• Non-Hermitian higher-Order Weyl semimetal with surface diabolic points
• Entanglement phase transitions in non-Hermitian Floquet systems
• Time evolution of Majorana corner modes in Floquet second-order topological superconductor
• Biorthogonal topological charge pumping in non-Hermitian systems
• Persistent anomaly in dynamical quantum phase transition in long-range non-Hermitian $p$-wave Kitaev chain
• Anomalous Floquet Phases. A resonance phenomena
• Corner modes in non-Hermitian next-nearest-neighbor hopping model
• Majorana zero-modes in a dissipative Rashba nanowire
• Competing topological phases in a non-Hermitian time-reversal symmetry-broken Bernevig-Hughes-Zhang model
• Measuring Non-Hermitian Topological Invariants Directly from Quench Dynamics
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• Measuring topological invariants of even-dimensional line-gapped non-Hermitian systems through quench dynamics
• Generalized Majorana edge modes in a number-conserving periodically driven $p$-wave superconductor
• Adiabatic charge transport through non-Bloch bands
• Tailoring higher-order van Hove singularities in non-Hermitian interface systems via Floquet engineering
• Extended Haldane model -- a modern gateway to topological insulators
• Exceptional flat bands in bipartite non-Hermitian lattices