Superconductivity under a ferromagnetic molecular field

Superconductivity under a ferromagnetic molecular field is investigated theoretically based on a one-dimensional electron-band model. By using an exact solution which takes into account infinite numbers of higher harmonics for the Bogoliubov---de Gennes equation, it is demonstrated that the spatially modulated superconducting state with a distorted sinusoidal wave is stabilized in the highfield region. A key feature of the solution is a soliton lattice structure which has a two-energy-gap structure and is accompanied by a spin-density polarization of the conduction electrons. The coexistence phase observed in ErRh₄{B}₄$ which consists of ferromagnetism, superconductivity, and a sinusoidally modulated magnetic state, is successfully interpreted in terms of this modulated superconducting state.