Higher-order topological superconductors from Weyl semimetals

Abstract

We propose that doped Weyl semimetals with four Weyl points are natural candidates to realize higher-order topological superconductors, which exhibit a fully gapped bulk while the surface hosts robust gapless chiral hinge states. We show that in such a doped Weyl semimetal, a featureless finite-range attractive interaction favors a $p+ip$ pairing symmetry. By analyzing its topological properties, we identify such a chiral pairing state as a higher-order topological superconductor, which depending on the existence of a four-fold roto-inversion symmetry ${\mathsf{R}}_{4z}$, is either intrinsic (meaning that the corresponding hinge states can only be removed by closing the bulk gap, rather than modifying the surface states) or extrinsic. We achieve this understanding via various methods recently developed for higher-order topology, including Wannier representability, Wannier spectrum, and defect classification approaches. For the ${\mathsf{R}}_{4z}$ symmetric case, we provide a complete classification of the higher-order topological superconductors. We show that such second-order topological superconductors exhibit chiral hinge modes that are robust in the absence of interaction effects but can be eliminated at the cost of introducing surface topological order.

20 pages, 14 figures

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Cited by in corpus (14)

• Intrinsic first and higher-order topological superconductivity in a doped topological insulator
• Corner- and sublattice-sensitive Majorana zero modes on the kagome lattice
• Nodal higher-order topological superconductivity from a ${\mathcal{C}}_4$-symmetric Dirac semimetal
• Surface Bogoliubov-Dirac cones and helical Majorana hinge modes in superconducting Dirac semimetals
• Hinge mode dynamics of periodically driven higher-order Weyl semimetals
• Sublattice-sensitive Majorana Modes
• Dephasing enhanced strong Majorana zero modes in 2D and 3D higher-order topological superconductors
• Higher-order topological superconductivity in a topological metal 1T${}^{\prime }$-MoTe${}_2$
• Higher-order topological superconductivity in monolayer WTe${}_2$ from repulsive interactions
• Edge and corner superconductivity in a 2D topological model
• Majorana corner states in an attractive quantum spin Hall insulator with opposite in-plane Zeeman energy at two sublattice sites
• Higher-order topological phases for time-reversal-symmetry breaking superconductivity in UTe${}_2$
• Anomalous gapped boundaries between surface topological orders in higher-order topological insulators and superconductors with inversion symmetry
• Euler band topology in superfluids and superconductors