Nodal higher-order topological superconductivity from a C4-symmetric Dirac semimetal

Abstract

We analyze the topological properties of the possible superconducting states emerging from a Cd3As2-like, C4-symmetric Dirac semimetal, with two fourfold-degenerate Dirac points separated in the kz direction. Unlike the simplest Weyl semimetal for which all pairing orders are topologically obstructed and nodal, we show that the topological obstruction for pairing in Dirac semimetals crucially only exists for certain pairing symmetries. In particular, we focus on odd-parity B1u and B2u pairing states, both of which can be induced by Ising ferromagnetic fluctuations. The B1u and B2u pairing states inherit the topological obstruction from the normal state, which dictates that these states necessarily host four Bogoliubov–de Gennes (BdG) Dirac point nodes protected by a Z2 monopole charge. By a Wannier state analysis, we show that the topological obstruction in the superconducting states is of higher-order nature. As a result, in a rod geometry with gapped surfaces, arcs of higher-order Majorana zero modes exist in certain kz regions of the hinges between the BdG Dirac points. Unlike Fermi arcs in Weyl semimetals, the higher-order Majorana arcs are stable against self-annihilation due to an additional Z-valued monopole charge of the BdG Dirac points protected by C4 symmetry. We find that the same Z-valued charge is also carried by B1g and B2g channels, where the BdG spectrum hosts bulk “nodal cages,” i.e., cages formed by nodal lines, that are stable against symmetry-preserving perturbations.

Source-reported materials — not catalogue approval

Similar papers