Nonlocal effects on the magnetic penetration depth in d-wave superconductors

We show that, under certain conditions, the low temperature behavior of the magnetic penetration depth lambda(Tau) of a pure d-wave superconductor is determined by nonlocal electrodynamics and, contrary to the general belief, the deviation Delta lambda(Tau) = lambda(Tau)- lambda(0) is proportional to Tau(2) and not Tau. We predict that the Delta lambda(Tau) alpha Tau(2) dependence, due to nonlocality, should be observable experimentally in nominally clean high-Tau(c), superconductors below a crossover temperature Tau(*) = (zeta(0)/lambda(0))Delta(0) similar to 1 K. Possible complications due to impurities, surface quality, and crystal axes orientation are discussed.