Abstract
While the symmetry-based diagnosis of topological insulators and semimetals has enabled large-scale discovery of topological materials candidates, the extension of these approaches to the diagnosis of topological superconductors remains a major open question. One important new ingredient in the analysis of topological superconductivity is the presence of $\mathbb Z_2$-valued Pfaffian invariants associated with certain high-symmetry momenta. Such topological invariants lie beyond the conventional scope of symmetry representation theory for band structures, and as such they are nontrivial to incorporate into the systematic calculations of the symmetry indicators of band topology. Here, we overcome this challenge and report the full computation of the $\mathbb Z_2$-enriched symmetry indicators for superconductors in all symmetry settings. Our results indicate that incorporating the $\mathbb Z_2$ band labels enhance the diagnostic power of the scheme in roughly $60\%$ of the symmetry settings. Our framework can also be readily integrated with first-principles calculations to elucidate on the possible properties of unconventional superconductivity in a given compound. As a demonstration, we analyze explicitly the interplay between pairing symmetry and topological superconductivity in the recently discovered superconductors CaPtAs and CaSb$_2$.
Highlights
While spatial symmetries have always been a critical component in the analysis of unconventional pairing, their role in protecting distinct classes of topological materials has only been understood in the past decade
We have computed exhaustively the Z2-enriched symmetry indicators for symmetry classes relevant for superconductors, and found that the diagnostic power of the symmetry indicator scheme is improved in about 60% of the symmetry classes
We illustrate how the symmetry indicator analysis can be integrated with density functional theory (DFT) calculations to diagnose the topological and nodal features of unconventional superconductors using CaPtAs [58] and CaSb2 [59] as concrete examples
Summary
While spatial symmetries have always been a critical component in the analysis of unconventional pairing, their role in protecting distinct classes of topological materials has only been understood in the past decade. Such Z2-valued symmetry data could be related to the number of filled bands in the normal-state band structure under the weak-pairing assumption [50,51,52,54,55,56], they correspond to a new set of band labels which cannot be readily analyzed using the original framework of symmetry-indicators designed for nonsuperconducting band structure Such Z2 band labels were not incorporated into the systematic calculation in Ref. Despite the significant progress reported in these earlier works, there is still a lack of a systematic way to treat the Z2-nature of Pfaffian invariants, which undermines comprehensive computations Such comprehensive computations represent a first step towards performing a systematic survey on the materials candidates for topological superconductors, similar to what has been achieved for insulators and semimetals [31,32,33]. We illustrate the diagnosis algorithm using two recently discovered superconductors CaPtAs [58] and CaSb2 [59] as concrete examples, and discuss how the symmetrybased analysis allows one to readily constrain the possible nodal features in the superconducting gap for various pairing symmetries
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