It is commonly believed that time reversal symmetry breaking perturbations such as magnetic field or scattering on magnetic impurities destruct superconductivity and suppress the critical temperature of the superconducting phase transition. However, in recent experimental studies, significant enhancement of superconducting critical temperature by parallel magnetic field was found for several thin superconducting systems [H. J. Gardner et al., Nat. Phys. 7, 895 (2011); T. Asaba et al., Sci. Rep. 8, 6520 (2018)]. Here we present a possible explanation of the observed phenomenon showing that combination of interfacial spin-orbit interaction and external magnetic field can cause the increase of the superconducting critical temperature of thin superconducting film in a wide range of magnetic fields. We use the Ginzburg-Landau formalism, taking into account Lifshitz invariant originated from Rashba spin-orbit interaction, which is also responsible for the superconducting diode effect. We also calculate the modification of the Little-Parks oscillations of the critical temperature of hollow superconducting cylinder at the presence of Rashba interfacial spin-orbit interaction.

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• Magnetism
• Spin-orbit coupling
• Superconducting phase transition
• Superconductivity