Ab initio study of orbital-selective superconductivity in $γ$-BiPd

TL;DR

This paper addresses the origin of superconductivity in γ-BiPd by combining fully relativistic ab initio electronic/phonon structure with anisotropic Migdal-Eliashberg theory to obtain $T_c$, gap anisotropy, and the quasiparticle DOS. The authors find a complex Fermi surface with three pockets and demonstrate that pairing is orbital-selective and predominantly Bi $p$-orbital in character, while Pd $d$-orbitals contribute on the hole sheet. The calculated gap $oldsymbol\Delta_{f k}$ is anisotropic but forms a single spin-singlet $s$-wave gap, with $T_c \approx 2.0$ K and a U-shaped $N_s(\\omega)$; the EPC constant is $oldsymbol\lambda \approx 0.46$, and the coherence length is $oldsymbol\xi \approx 0.72\ b00\bm$. The results link Bi$ p$-orbital contributions to EPC and gap anisotropy, providing a microscopic mechanism for orbital-selective pairing in a SOC-influenced, multiband superconductor and establishing a framework for predicting such behavior in similar materials.

Abstract

We investigate the superconducting (SC) properties of experimentally realised $γ$-BiPd by solving the anisotropic Migdal-Eliashberg equations in conjunction with {\it ab initio} relativistic calculations of the electron and phonon band structures as well as electron-phonon coupling (EPC) matrix elements. Our study reveals that $γ$-BiPd possesses a complex Fermi surface (FS), consisting of two electron pockets and one hole pocket, each characterised by distinct atomic orbitals. Our key finding is that the superconductivity in $γ$-BiPd is primarily orbital-selective, arising from Bi $p$-orbitals, and distributed anisotropically on the FS, although contribution from Pd $d$-orbitals, particularly on the hole pocket, is also discernable. While our results show an anisotropic nature of the {\bf k}-dependent SC gap $Δ_{\bf k}$ and EPC strength $λ_{\bf k}$ across the FS, calculated superconducting quasiparticle density of states $N_S$ spectra exhibit a U-shaped gap and $Δ_{\bf k}$ distribution forms a single peak, being consistent with the spin-singlet $s$-wave superconductivity observed in this material. The calculated $T_c$ is $\sim$2.0 K, agreeing in order of magnitude with the experimental value of 3.3 K in $γ$-BiPd thin films. The predicted EPC-enhanced Sommerfeld coefficient $γ_n$ of $0.141$ mJ/K$^2$cm$^3$ is similar to the experimental $γ_n$ value ($0.119$ mJ/K$^2$cm$^3$) of the isoelectronic and isostructural Bi(Pd$_{0.5}$Pt$_{0.5}$) alloy.

Figures (10)

• Figure 1: (a) A side-view and (b) the $z$-axis view of crystal structure of $\gamma$-BiPd. In (b), the 2$\times$2$\times$1 supercell is shown. The associated BZ is illustrated in (c).
• Figure 2: (a) Phonon dispersion, (b) phonon DOS (PhDOS), (c) Eliashberg spectral function ($\alpha^{2}F$), and accumulative electron-phonon coupling constant ($\lambda(\omega)$) of $\gamma$-BiPd.
• Figure 3: (a) Orbital-projected fat plot of the band structure, with the orbital weights being proportional to the sizes of the corresponding colored dots and (b) orbital-projected DOSs of $\gamma$-BiPd. In (a), one band labelled H1 represents the hole pocket, and two bands labelled E1 and E2 form the two electron pockets.
• Figure 4: Momentum ${\bf k}$-dependent magnitude of the Fermi velocity $v_f$ on the Fermi surface of $\gamma$-BiPd on (a) hole pocket H1, (b) electron pocket E1, and (c) electron pocket E2.
• Figure 5: Total and band-resolved normalized density distribution of (a) the EPC strength $\lambda_{n{\bf{k}}}$, $g(\lambda_{n{\bf k}})$, and of (b) SC gap $\Delta_{n{\bf{k}}}$, $g(\Delta_{n{\bf k}})$, on the FS of $\gamma$-BiPd.