Strong-coupling anisotropic superconductivity in hexagonal HfRuAs from anisotropic Migdal-Eliashberg theory

TL;DR

This study uses anisotropic Migdal-Eliashberg theory combined with ab initio calculations to reveal that hexagonal HfRuAs is a strong-coupling, anisotropic, phonon-mediated superconductor with a single s-wave gap and significant multiband anisotropy.

Contribution

It provides a detailed theoretical analysis of HfRuAs's superconducting properties, highlighting strong electron-phonon coupling and anisotropic multiband effects using advanced first-principles methods.

Findings

Electron-phonon coupling constant λ ≈ 1.56

Superconducting gap Δ ≈ 2.9 meV with anisotropy

Gap ratio 2Δ(0)/k_B T_c ≈ 4.2 exceeding BCS limit

Abstract

We present a comprehensive theoretical investigation of the superconducting (SC) properties of hexagonal HfRuAs ($h$-HfRuAs) by solving anisotropic Migdal--Eliashberg (ME) equations with the inputs from \textit{ab initio} calculations of electronic structure, phonon dispersion and electron phonon coupling matrix elements. The calculated Eliashberg spectral function reveals strong electron--phonon coupling (EPC) with a constant $\lambda \approx 1.56$, dominated by low-frequency phonon modes associated primarily with Hf and Ru vibrations. The SC state is characterized by a single anisotropic gap with overall $s$-wave symmetry, as evidenced by the fully gapped quasiparticle density of states. The momentum-resolved EPC and SC gap exhibit pronounced anisotropy across different Fermi surface sheets, with the largest variations occurring on the hole-like bands. The SC gap is centered around $\Delta \approx 2.9$ meV with a spread of $\sim 0.8$ meV, indicating significant multiband anisotropy. The resulting gap ratio $2\Delta(0)/k_B T_c \approx 4.2$ exceeds the BCS weak-coupling limit, establishing $h$-HfRuAs as a strong-coupling superconductor. The calculated transition temperature, $T_c$, agrees in the order of magnitude with experiments. Overall, our results identify $h$-HfRuAs as a phonon-mediated, strongly coupled anisotropic superconductor and provide detailed insights into the role of momentum-dependent electron--phonon interactions in determining its SC properties.