Superfluid weight of the superconducting condensate on a mirror asymmetric honeycomb lattice

The superfluid weight is the second derivative of superconducting free energy. A positive definite superfluid weight reflects a stable ground state. We calculate the superfluid weight of the BCS s-wave superconducting condensate as a function of the Rashba spin-orbit coupling in a mirror asymmetric honeycomb lattice. Mirror asymmetry introduces Rashba spin-orbit coupling, leading to the admixture of singlet and triplet order parameters. This model calculation provides insight into the possibility of finite momentum pairing states in mirror asymmetric honeycomb lattice-based 2D superconductors.