Superconducting state with a finite-momentum pairing mechanism in zero external magnetic field

Abstract

In the BCS theory of superconductivity, one assumes that all Cooper pairs have the same center-of-mass momentum. This is indeed enforced by self-consistency if the pairing interaction is momentum independent. Here, we show that for an attractive nearest-neighbor interaction, this is different. In this case, stable solutions with pairs with momenta $\mathbf{q}$ and $\ensuremath{-}\mathbf{q}$ coexist and, for a sufficiently strong interaction, one of these states becomes the ground state of the superconductor. The possibility for a finite-momentum pairing state emerges only for nodal superconductors and is accompanied by a charge order with wave vector $2\mathbf{q}$. For a weak pairing interaction, the ground state is a $d$-wave superconductor.