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The physics of single nonmagnetic impurity immersed in a two-band $s$-wave superconductor with relative phase $\ensuremath{\delta}\ensuremath{\ne}0$ between its two order parameters is studied and elucidated. It is shown that midgap bound states are always induced by nonmagnetic impurities when $\ensuremath{\delta}=\ensuremath{\pi}$ (${s}_{\ifmmode\pm\else\textpm\fi{}}$-wave superconductors). These bound states emerge as a consequence of the topological nature of the corresponding Bogoliubov-de Gennes equation.

physical review b

In-gap bound states induced by nonmagnetic impurities in two-band<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mo>±</mml:mo></mml:msub></mml:mrow></mml:math>superconductors

In-gap bound states induced by nonmagnetic impurities in two-bands±superconductors