The effects of spin independent hybridization potential and spin orbit coupling on two band superconductor with equal time s-wave inter band pairing order parameter is investigated theoretically. To study symmetry classes in two band superconductors the Gorkov equations are solved analytically. By defining spin singlet and spin triplet s wave order parameter due to two band degree of freedom the symmetry classes of Cooper pair are studied. For spin singlet case it is shown that spin independent hybridization generates Cooper pair belongs to even frequency spin singlet even momentum even band parity (ESEE) symmetry class for both intraband and interband pairing correlations. For spin triplet order parameter, intraband pairing correlation generates odd frequency spin triplet even momentum even band parity (OTEE) symmetry class whereas, interband pairing correlation generates even frequency spin triplet even momentum odd band parity ETEO) class. For the spin singlet, spin orbit coupling generates pairing correlation that belongs to odd frequency spin singlet odd momentum even band parity (OSOE) symmetry class and even frequency spin singlet even momentum even band parity (ESEE) for intraband and interband pairing correlation respectively. In the spin triplet case for itraband and interband correlation, spin orbit coupling generates even-frequency spin triplet odd momentum even band parity (ETOE) and even frequency spin triplet even momentum odd band parity (ETEO) respectively.
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