Odd-frequency Spin-triplet Superconductivity in Nano-sized Superconductors under a Magnetic Field: Effects of Phonons

We theoretically study spatial variation of odd-frequency superconducting pairs under an external magnetic field. We consider a two dimensional nano-sized superconductor and solve the Eliashberg equation using the finite element method in real space. We investigate the effects of several phonon modes, which is important for odd-frequency Cooper pairs. We confirm that odd-frequency component of the order parameter oscillates and widely exists in the whole system compared to a single phonon mode.