Microscopic theory for odd-frequency superconductivity in critical region

我们已经发展了奇频超导的基本理论。我们发现，在自发对称性破缺中，通过选择适当的序参数使自由能泛函最小化，可以实现自洽体态。阐明了强耦合局域电子-声子模型和具有临界磁涨落的模型，确定了温度和参数空间的相图。具有对数发散吸引力的临界涨落使其在自能效应下保持稳定。通过求解具有此类边界条件的自洽方程，我们进一步研究了杂质点附近或表面边界上奇频分量出现的机理，并展示了微观和半现象学对有序参数性质的理解之间的关系。

We have developed the fundamental theory for odd-frequency superconductivity. We found that a self-consistent bulk state is possible by choosing an appropriate order parameter that minimizes the free-energy functional in a spontaneous symmetry breaking. We elucidated the strong-coupling local electron-phonon model and the model having a critical magnetic fluctuation, we determined the phase diagram in temperature and parameter space. The critical fluctuation with logarithmically divergent attraction makes it stable against the self-energy effect. We further investigated the mechanism of the appearance of the odd-frequency component near an impurity site or on a surface boundary by solving the self-consistent equations with such boundary conditions, and showed the relationship between the microscopic and semi-phenomenological understandings for the nature of the order parameters.