Higher-order topological superconductors characterized by Fermi level crossings

Abstract

We demonstrate that level crossings at the Fermi energy serve as robust indicators for higher-order topology in two-dimensional superconductors of symmetry class D. These crossings occur when the boundary condition in one direction is continuously varied from periodic to open, revealing the topological distinction between opposite edges. The associated Majorana numbers acquire nontrivial values whenever the system supports two Majorana zero modes distributed at its corners. Owing to their immunity to perturbations that break crystalline symmetries, Fermi level crossings are able to characterize a wide range of higher-order topological superconductors. By directly identifying the level-crossing points from the bulk Hamiltonian, we establish the correspondence between gapped bulk and Majorana corner states in higher-order phases. In the end, we illustrate this correspondence using two toy models. Our findings suggest that Fermi level crossings offer a possible avenue for characterizing higher-order topological superconductors in a unifying framework.

7+6 pages, 4+6 figures

References in corpus (11)

• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Reflection symmetric second-order topological insulators and superconductors
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Realization of a minimal Kitaev chain in coupled quantum dots
• Bulk-corner correspondence of time-reversal symmetric insulators: deduplicating real-space invariants
• High-throughput Investigations of Topological and Nodal Superconductors
• Faithful derivation of symmetry indicators: A case study for topological superconductors with time-reversal and inversion symmetries
• Topological classification of intrinsic 3D superconductors using anomalous surface construction
• Perfectly localized Majorana corner modes in fermionic lattices

Cited by in corpus (3)

• Direct demonstration of bulk-boundary correspondence in higher-order topological superconductors with chiral symmetry
• Characterization of higher-order topological superconductors using Bott indices
• Scattering theory of higher order topological phases