Superfluid Stiffness, Nodal Quasiparticles and Quantum Phase Fluctuations in Underdoped Cuprates

We study the low temperature superfluid stiffness $\rho_s(T;x)$ as a function of hole doping $x$ and temperature $T$ for strongly correlated d-wave superconductors. Using Gutzwiller projected wavefunctions and renormalized mean-field theory (RMFT), we calculate $\rho_s(0;x)$ and show that it scales with the quasiparticle spectral weight $Z$. These analytical results are in excellent agreement with earlier variational Monte Carlo studies [1]. We next show that self-consistent inclusion of the zero point motion of phase fluctuations leads to further suppression of $\rho_s(0;x) $, which now vanishes below a doping level of approximately $5\%$. To determine the $T$-dependence of $\rho_s$ we calculate the current carried by nodal quasiparticles (QP) within RMFT and show that the effective charge of the nodal QP is given by $Z m^\ast/m$. Our analytic formula for the effective charge is in excellent agreement with numerical Monte Carlo results of Nave {\it et al.}~[2]. We will conclude by comparing our results with experiments on underdoped cuprates. \\ \noindent [1] A. Paremakanti, M. Randeria and N. Trivedi, Phys. Rev. Lett. {\bf 87}, 217002 (2001) \\ \noindent [2] C. P. Nave, D. A. Ivanov and P. A. Lee, Phys. Rev. B. {\bf 73}, 104502 (2006)