London penetration depth in a tight-binding model of layered narrow-band anisotropic superconductors

Abstract

The London magnetic penetration depth is investigated for the layered narrow tight-binding band anisotropic superconductors. The nearest-neighbor pairing interaction in planes and the tunneling between planes are assumed. The manifestly gauge-invariant expression for the static electromagnetic response kernel is derived within the framework of the ladder-diagram approximation. The out-of-plane penetration depth λ⊥(T) as well as the in-plane one λ∥(T) is calculated as a function of hole density nh and temperature T(<Tc). The resultant λ⊥(0) and λ∥(0) depend symmetrically on hole and electron densities, and are almost not affected by the anisotropy of the order parameter. For both of the extended s-wave and d-wave states, the obtained anisotropy ratio λ⊥(0)/λ∥(0) as well as λ∥(0) and Tc can be in the range of the experimental results for high-Tc superconductors. For the d-wave state, the resultant λ⊥(T)/λ⊥(0) as well as λ∥(T)/λ∥(0) has T-linear behavior at low temperature, and substantially deviates from those for the extended and usual s-wave states for all T<Tc. The in-plane and out-of-plane Ginzburg-Landau (GL) coherence lengths are also calculated by assuming their GL relations with the above penetration depths, and are compared with the experimental results. The case with the out-of-plane tunneling in proportion to carrier density is simply examined.

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