The effect of interorbital scattering on superconductivity in doped Dirac materials

Abstract

Unconventional superconductivity has been discovered in a variety of doped materials, including topological insulators, semimetals and twisted bilayers. A unifying property of these systems is strong orbital hybridization, which involves pairing of states with non-trivial Bloch wave functions. In contrast to naive expectation, many of these superconductors are relatively resilient to disorder. Here we study the effects of a generic disorder on superconductivity in doped 3D Dirac systems, which serve as a paradigmatic example for the dispersion near a band crossing point. We argue that due to strong orbital hybridization, interorbital scattering processes are naturally present and must be taken into account. We calculate the reduction of the critical temperature for a variety of pairing states and scattering channels using Abrikosov-Gor'kov theory. In that way, the role of disorder is captured by a single parameter $\Gamma$, the pair scattering rate. This procedure is very general and can be readily applied to different band structures and disorder configurations. Our results show that interorbital scattering has a significant effect on superconductivity, where the robustness of different pairing states highly depends on the relative strength of the different interorbital scattering channels. Our analysis also reveals a protection, analogous to the Anderson's theorem, of the odd-parity pairing state with total angular momentum zero (the B-phase of superfluid ${}^3$He). This odd-pairty state is a singlet of partners under $\mathcal{C}\mathcal{T}$ symmetry (rather than $\mathcal{T}$ symmetry in the standard Anderson's theory), where $\mathcal{C}$ and $\mathcal{T}$ are chiral and time-reversal symmetries, respectively. As a result, it is protected against any disorder potential that respects $\mathcal{C}\mathcal{T}$ symmetry, which includes a family of time-reversal odd (magnetic) impurities.

arXiv comment14 pages, 5 figures, 5 appendices; Including mass term in the Hamiltonian. Extensive revisions in Appendix A. New figure 4

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• General theory of robustness against disorder in multi-band superconductors
• Symmetries, Length Scales, Magnetic Response and Skyrmion Chains in Nematic Superconductors
• Magnetic response of nematic superconductors: skyrmion stripes and their signatures in muon spin relaxation experiments
• Time-reversal-symmetry Breaking in the Superconducting State of ScS
• Lifshitz transition in dirty nematic superconductor
• Bound states around impurities in a superconducting bilayer
• Andreev bound states at nonmagnetic impurities in superconductor/antiferromagnet heterostructures
• Unconventional superconductivity from electronic dipole fluctuations
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