Effect of a homogeneous magnetic field on one-dimensional antiferromagnetic superconductors

The effect of an external homogeneous magnetic field, $H_0$, and the staggered magnetic field, $H_Q$ (arising from antiferromagnetism) on superconductivity has been investigated. We have assumed a one-dimensional-like half-filled electron band, a spatially homogeneous order parameter $\Delta$, and temperature independent $H_Q$. In the ground state, we have found a new state having gapless superconductivity and $H_0$-dependent $\Delta$. At finite temperatures, it is found that a variety of interesting phase transitions are possible in different domains of the $H_Q-H_0$ plane. There exists a second-order phase transition into gapless superconductivity in one domain and a first-order phase transition into gapless superconductivity in another domain. There is still another domain where the superconducting state exists only over a certain interval of temperature and a second- (first-) order phase transition occurs at the upper (lower) bound of temperature.