Superconductivity with Finite-Momentum Pairing in Zero Magnetic Field

TL;DR

This paper demonstrates that in certain superconductors with nearest neighbor attraction, stable finite-momentum pairing states can form, leading to coexistence with charge order, differing from traditional zero-momentum pairing in BCS theory.

Contribution

It reveals the possibility of finite-momentum pairing in superconductors with momentum-dependent interactions, expanding the understanding beyond conventional BCS assumptions.

Findings

Finite-momentum pairing states coexist with zero-momentum states.

Strong interactions favor finite-momentum pairing as ground state.

Finite-momentum pairing is linked with charge order at wave vector 2q.

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 q and -q coexist and, for a sufficiently strong interaction, one of these states becomes the groundstate of the superconductor. This finite-momentum pairing state is accompanied by a charge order with wave vector 2q. For a weak pairing interaction, the groundstate is a d-wave superconductor.