We investigate the effect of anti-ferromagnetic (AF) quantum criticality on the magnetic penetration depth $\lambda(T)$ in line-nodal superconductors, including the cuprates, the iron pnictides, and the heavy-fermion superconductors. The critical magnetic fluctuation renormalizes the current vertex and drastically enhances zero-temperature penetration depth $\lambda(0)$, which is more remarkable in the iron-pnictide case due to the Fermi-surface topology. Additional temperature ($T$) dependence of the current renormalization makes the expected $T$-linear behavior at low temperatures approaching to $T^{ 1.5}$ asymptotically. These anomalous behaviors are well consistent with experimental observations. We stress that $\lambda(T)$ is a good probe to detect the AF quantum critical point in the superconducting state.
Categories: cond-mat.supr-con cond-mat.str-el