Interlayer penetration depth in the pseudogap phase of cuprate superconductors

The opening of a pseudogap in the electronic structure of the underdoped high Tc cuprates has a profound effect on superconducting properties. Here we consider the c-axis penetration depth. A phenomenological model of the pseudogap due to Yang, Rice, and Zhang (YRZ) is used. It is based on the idea of a resonating valence bond spin liquid. A simplifying limit, the arc model, is also considered as it provides useful analytic formulas. The zero temperature value of the superfluid density n(s)(T = 0) is greatly reduced with increasing values of the pseudogap (Δpg). This value reflects the reconstruction of the Fermi surface from the large contour of Fermi liquid theory to ever smaller Luttinger pockets as Δpg becomes larger. Also, as temperature is increased the ratio n(s)(T)/n(s)(0) as a function of the reduced temperature t = T/T(c) decreases more rapidly than in the corresponding Fermi liquid (Δpg = 0) as states which have both superconducting and pseudogap become more significantly sampled.