Nodeless $d$-wave superconducting pairing in antiferromagnetic underdoped Pr$_{2-x}$Ce$_x$CuO$_{4-\delta}$

Experimental results concerning the superconducting pairing symmetry have been contradictory in electron doped cuprates. In particular, penetration depth measurements appear to indicate the presence of an s-wave and/or a d-wave gap in different doping regimes [1]. Here, we discuss the doping and $T$-dependence of the penetration depth in Pr$_{2-x}$Ce$_x$CuO$_{4-\delta}$ (PCCO) and provide a natural explanation for the occurrence of a nodeless superconducting gap and a nonmonotonic gap variation with maximum gap near hot-spots in the underdoped system [2]. Despite the presence of a $d_{x^2-y^2}$ pairing gap, we find a crossover of the low-$T$ penetration depth from a nodeless behavior in the underdoped case to a linear-in-T behavior (characteristic of $d$-wave) as doping increases and a nodal Fermi surface pocket emerges. The present results support the coexistence of antiferromagnetism and superconductivity in the electron doped cuprates [3]. Work supported in part by the USDOE. \newline [1] M.-S. Kim {\it {et. al.,}} PRL, {\bf{91}}, 087001 (2003). \newline [2] T. Das {\it {et. al.,}} PRB, {\bf{74}}, 020506(R) (2006). \newline [3] Y. Dagan {\it {et. al.,}} PRL, {\bf{92}}, 167001 (2004).