The superconductor $\beta \text{−}{\mathrm{Bi}}_2\mathrm{Pd}$ is well known for its inconsistent experimental indications of single versus multiple superconducting (SC) gaps, while simultaneously being considered a promising candidate for topological superconductivity. To clarify its SC behavior, we investigate the SC gap, the quasiparticle density of states (DOS), and $T_c$ in the frameworks of superconducting density functional theory and density functional perturbation theory. We explicitly consider the $\mathbf{k}$-dependent dynamical screened Coulomb pseudopotential, spin-fluctuation, and electron-phonon coupling in a fully first-principles way by incorporating the relativistic spin-orbit coupling (SOC). The strong SOC increases the electronic DOS near the Fermi level and enhances the electron-phonon coupling strength, which in turn leads to a larger SC gap and $T_c$ values that more closely match with recent experiments. The Fermi surface (FS) size of the $\alpha$ band, which is linked to the ${\mathrm{\Gamma }}_6^{-}$ irreducible representation and originates from Bi $p_{1/2}$-orbitals, is notably reduced with the SOC. This FS size reduction leads to isotropic and strong pairing strength, primarily driven by the coupling between the $\alpha$ band and $A_{1g}$ phonons. As a result, distinct SC gaps emerge that are characterized by the SOC-splitted Bi $p_{1/2}$ and $p_{3/2}$ states. This is further consistent with observed kinks in the quasiparticle DOS spectra, agreeing with the recently observed experimental multigap behavior. The average gap values of $\sim 0.75\mathrm{meV}$ and $T_c\sim 4.2\mathrm{K}$ are both consistent with experimental reports. Additionally, our calculated heat capacity jump ratio $\mathrm{\Delta }C/{\gamma }_n{T}_c\simeq 1.9$ suggests that $\beta \text{−}{\mathrm{Bi}}_2\mathrm{Pd}$ is a strongly coupled superconductor.

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• Electronic structure
• Multiband superconductivity
• Pairing mechanisms
• Phonons
• Spin-orbit coupling
• Superconducting fluctuations
• Superconducting gap
• Superconductivity
• Superconductors
• Density functional theory
• Methods in superconductivity