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We investigate the effect of the Rashba interaction on two dimensional superconductivity. The presence of the Rashba interaction lifts the spin degeneracy and gives rise to the spectrum of two bands. There are intraband and interband pairs scattering which result in the coupled gap equations. We find that there are isotropic and anisotropic components in the gap function. The latter has the form of cos  φ   k   where. The former is suppressed because the intraband and the interband scatterings nearly cancel each other. Hence, −the system should exhibit the  p -wave superconductivity. We perform a detailed study of electron-phonon interaction for 2DEG and find that, if only normal processes are considered, the effective coupling strength constant of this new superconductivity is about one-half of the  s -wave case in the ordinary 2DEG because of the angular average of the additionalin the anisotropic gap function. By taking into account of Umklapp processes, we find they are the major contribution in the electron-phonon coupling in superconductivity and enhance the transition temperature  T   c  .

The p-wave superconductivity in the presence of Rashba interaction in 2DEG