Abstract
We propose a minimal lattice model for two-dimensional class DIII superconductors with $C_2$-protected higher-order topology. While this class of superconductors cannot be topologically characterized by symmetry eigenvalues at high symmetry momenta, we propose a simple Wannier-orbital-based real-space diagnosis to unambiguously capture the corresponding higher-order topology. We further identify and characterize a variety of conventional topological phases in our minimal model, including a weak topological superconductor and a nodal topological superconductor with chiral-symmetry protection. The disorder effect is also systematically studied to demonstrate the robustness of higher-order bulk-boundary correspondence. Our theory lays the groundwork for predicting and diagnosing $C_2$-protected higher-order topology in class DIII superconductors.
Highlights
Anyons are stable exotic quasiparticles with unconventional statistical braiding properties and serve as the cornerstone for topological quantum computation [1,2,3,4]
Class DIII superconductors with twofold rotational symmetry C2 are special in the sense that they always host the same C2 symmetry eigenvalues at high-symmetry momenta for all possible topologically distinct phases
We prove in Appendix A, for every Kitaev limit, there exists a Kramers pair of maximally localized Bogoliubov–de Gennes (BdG) Wannier orbitals sitting at the center of each bond, whose positions of Wannier centers does not rely on the explicit bonding type
Summary
Anyons are stable exotic quasiparticles with unconventional statistical braiding properties and serve as the cornerstone for topological quantum computation [1,2,3,4]. Several groups have proposed various symmetry indicators to classify such symmetry-protected higher-order TSCs based on symmetry eigenvalues at high-symmetry momenta [25,26,27,28,29] In this context, class DIII superconductors with twofold rotational symmetry C2 are special in the sense that they always host the same C2 symmetry eigenvalues at high-symmetry momenta for all possible topologically distinct phases. The concept of building a higher-order topological superconductor from Kitaev building blocks allows a topology diagnosis based on the real-space distribution of Wannier orbitals and lattice sites—the Majorana counting rule. Motivated by this novel idea, we aim to expand the counting rule to class DIII superconductors with spin degrees of freedom and time-reversal invariance.
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