Mixed-state penetration depths in s-wave and d-wave superconductors

We report on a microscopic calculation of the current and magnetic field distribution in the mixed state of model s-wave and d-wave superconductors. For the d-wave case, we find that corrections to London theory are important at fields small compared to Hc2. The field distribution is influenced by both superfluid-velocity dependence and non-locality in the current response function of the mixed state. We compare our calculations with recent muon spin rotation measurements in high temperature superconductors. PACS numbers: 74.60.Ec, 74.72.-h Typeset using REVTEX 1 The Meissner effect, in which weak external magnetic fields are exponentially screened from the bulk, is a basic property of superconducting metals. It is a consequence of the linear relationship between circulating currents (J) and the magnetic flux density (h) in a superconductor expressed by the London equation: h + 4πλ c ∇× J = 0. (1) In Eq.(1) λ, the penetration depth, determines the spatial extent of magnetic fields near the surface of a superconductor in the Meissner state. Measurements of this parameter in a particular material provide important information on the microscopic nature of its superconducting state. For example, recent measurements [1,2] of the temperature dependence of λ, which microscopic theory relates to the quasiparticle energy spectrum [3], have provided important evidence for d-wave pairing [4] in high-temperature superconductors. Both nuclear magnetic resonance (NMR) and muon spin rotation (μSR) measurements of λ are based on the relationship between magnetic field inhomogeneity in the mixed state of a type-II superconductor and the penetration depth. In the mixed state, Eq.(1) applies only outside the vortex cores and the London equation becomes, h+ 4πλ c ∇× J = ẑΦ0 ∑