Higher-Order Topological Dirac Superconductors

TL;DR

This paper introduces higher-order topological Dirac superconductors (HOTDSC), a new 3D gapless topological phase with hinge Majorana modes protected by symmetries, and proposes a practical realization via unconventional pairing in Dirac semimetals.

Contribution

It defines the HOTDSC phase, characterizes it with topological indices, constructs a minimal lattice model, and explores its relation to higher-order topological phases and Weyl superconductors.

Findings

HOTDSC features hinge Majorana modes protected by symmetries.

A minimal lattice model for HOTDSC is constructed and verified.

Breaking inversion symmetry leads to a higher-order Weyl superconductor.

Abstract

We introduce higher-order topological Dirac superconductor (HOTDSC) as a new gapless topological phase of matter in three dimensions, which extends the notion of Dirac phase to a higher-order topological version. Topologically distinct from the traditional topological superconductors and known Dirac superconductors, a HOTDSC features helical Majorana hinge modes between adjacent surfaces, which are direct consequences of the symmetry-protected higher-order band topology manifesting in the system. Specifically, we show that rotational, spatial inversion, and time-reversal symmetries together protect the coexistence of bulk Dirac nodes and hinge Majorana modes in a seamless way. We define a set of topological indices that fully characterizes the HOTDSC. We further show that a practical way to realize the HOTDSC phase is to introduce unconventional odd-parity pairing to a three-dimensional Dirac semimetal while preserving the necessary symmetries. As a concrete demonstration of our idea, we construct a corresponding minimal lattice model for HOTDSC obeying the symmetry constraints. Our model exhibits the expected topological invariants in the bulk and the defining spectroscopic features on an open geometry, as we explicitly verify both analytically and numerically. Remarkably, the HOTDSC phase offers an example of a higher-order topological quantum critical point, which enables realizations of various higher-order topological phases under different symmetry-breaking patterns. In particular, by breaking the inversion symmetry of a HOTDSC, we arrive at a higher-order Weyl superconductor, which is yet another new gapless topological state that exhibits hybrid higher-order topology.