Superfluid stiffness in the 2-d Hubbard model with coexisting antiferromagnetism (AFM) and d-wave superconductivity (d-SC)

Superfluid stiffness allows a superconductor to establish phase coherence and to sustain a supercurrent. Phase coherence may occur at a lower temperature than Cooper pair formation when superfluid stiffness is small, lowering T_c well below its mean-field value.[1] Coexistence with other phases may also lower T_c in underdoped cuprates. We investigate these possibilities using cellular dynamical mean-field theory for the 2-d Hubbard model.[2] We compare the superfluid stiffness and the superconducting d-wave order parameter in the d-wave superconductor with and without coexisting antiferromagnetism. We first establish the formula that allows one to compute c-axis superfluid stiffness in the phase with coexisting antiferromagnetism and superconductivity.

[1] Emery, V. J. and Kivelson, S. A., Nature {\bf 374}, 434 (1995).
[2] Kancharla, S. {\et al.} PRB {\bf 77}, 184516, (2008).