Unconventional superconductivity and Surface pairing symmetry in Half-Heusler Compounds

TL;DR

This paper classifies the gap functions and topological properties of bulk and surface states in half-Heusler superconductors using a six-band Kane model, highlighting the role of topological surface states from band inversion.

Contribution

It introduces a systematic classification based on the six-band Kane model, extending beyond previous four-band models to better understand surface states in half-Heusler superconductors.

Findings

Topological surface states originate from band inversion between Gamma}6 and Gamma}8 bands.

Surface states significantly influence surface properties in the superconducting regime.

The six-band Kane model provides new insights into the topological nature of these compounds.

Abstract

Signatures of nodal line/point superconductivity have been observed in half-Heusler compounds, such as LnPtBi (Ln = Y, Lu). Topologically non-trivial band structures, as well as topological surface states, has also been confirmed by angular-resolved photoemission spectroscopy in these compounds. In this work, we present a systematical classification of possible gap functions of bulk states and surface states in half-Heusler compounds and the corresponding topological properties based on the representations of crystalline symmetry group. Different from all the previous studies based on four band Luttinger model, our study starts with the six-band Kane model, which involves both four p-orbital type of {\Gamma}8 bands and two s-orbital type of {\Gamma}6 bands. Although the {\Gamma}6 bands are away from the Fermi energy, our results reveal the importance of topological surface states, which originate from the band inversion between {\Gamma}6 and {\Gamma}8 bands, in determining surface properties of these compounds in the superconducting regime by combining topological bulk state picture and non-trivial surface state picture.