Comparing photoemission measurements on Bi2212 with penetration depth data, we show that a description of the nodal excitations of the $d$-wave superconducting state in terms of noninteracting quasiparticles is inadequate, and we estimate the magnitude and doping dependence of the Landau interaction parameter which renormalizes the linear $T$ contribution to the superfluid density. Furthermore, although consistent with $d$-wave symmetry, the gap with underdoping cannot be fit by the simple $\cos k_x-\cos k_y$ form, which suggests an increasing importance of long range interactions as the insulator is approached.

• Received 23 December 1998

DOI:https://doi.org/10.1103/PhysRevLett.83.840