Abstract Body

We theoretically study the appearance of bound states around impurities in a superconducting bilayer. We focus on the unconventional s-wave pairing that includes odd-parity states permitted by the layer degree of freedom. Applying numerical mean-field and analytical T-matrix methods [1], we survey the bound state spectrum produced by momentum-independent impurity potentials. For even-parity s-wave pairing, bound states are only found for impurities that break time-reversal symmetry. For odd-parity s-wave states, in contrast, bound states are generically found for all impurity potentials, and fall into six distinct categories. This categorization remains valid for nodal gaps. Our results are conveniently understood in terms of the "superconducting fitness'' concept [2, 3], and show an interplay between the pair-breaking effects of the impurity and the normal-state band structure. Our approach [4] is suitable for general multi-band superconductors with one band crossing the Fermi surface.

References

1. A. V. Balatsky, I. Vekhter, and Jian-Xin Zhu, Rev. Mod. Phys. 78, 373–433 (2006)
2. A. Ramires et. al., Phys. Rev. B 94, 104501 (2016); Phys. Rev. B 98, 024501 (2018)
3. D. C. Cavanagh and P. M. R Brydon, Phys. Rev. B 101, 054509 (2020); Phys. Rev. B 104,014503 (2021)
4. Y. Zhu, N. A. Hackner and P. M. R Brydon, Phys. Rev. B 107, 134514 (2023)

Acknowledgment

Y.Z. and P.M.R.B were supported by the Marsden Fund Council from Government funding, managed by Royal Society Te Ap\={a}rangi, Contract No. UOO1836. The authors acknowledge useful discussions with D. C. Cavanagh, J. Schmalian, S. Rachel, A. Ramires, B. Zinkl, and J.-X. Zhu.
Y.Z. and N.A.H. contributed equally to this work.