Ordered state of one-dimensional antiferromagnetic superconductors in the presence of a homogeneous magnetic field

Assuming a one-dimensional electron band and examining the free energy difference F (=F_S–F_N) for an antiferromagnetic superconductor in the presence of a homogeneous magnetic field H₀, it is shown that (i) for temperatureT=0, the spatially varying order parameter _Q (having the same period as the antiferromagnetic fieldH_Q) and the BCS order parameter coexist when |–H_QH₀<+H_Q (here, the pairing coupling constant for _Q is assumed small), and (ii) forT near the second-order phase transition temperature the coexistence of _Q and is always realized whenH₀0.Work supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada.On leave of absence from Physics Department, Tohoku University, Sendai, Japan.