Spatial Dependence of Odd-frequency Spin-triplet Superconducting Order Parameter in Nano-sized s-wave Superconductors Under a Magnetic Field

We theoretically study spatial dependence of odd-frequency Cooper pairs under a magnetic field. We consider a two dimensional nano-sized superconductor and solve the Eliashberg equation, which is a strong coupling theory, using the finite element method. When a magnetic field is applied an even-frequency spin-singlet s-wave nano-sized superconductor, an odd-frequency spin-triplet component uniformly appears in this system. We confirm that the value of odd-frequency order parameter is antisymmetric about the frequency.