London penetration depth in the tight binding approximation: Orthorhombic distortion and oxygen isotope effects in cuprates

TL;DR

This paper derives a new expression for superfluid density in superconductors with tight binding dispersion, analyzes isotope effects in cuprates considering orthorhombic distortion, and estimates key parameters from experimental data.

Contribution

It provides a novel derivation of superfluid density expression for tight binding superconductors and applies it to analyze isotope effects in cuprates with structural distortions.

Findings

Superfluid density expression differs from that of parabolic dispersion superconductors.

Isotope effects on London penetration depth are quantified in cuprates.

The temperature dependence of 1/λ² is highly sensitive to the gap ratio 2Δₘ(0)/k_B T_c.

Abstract

We present a simple derivation of an expression for the superfluid density $ n_s \propto 1/\lambda^2 $ in superconductors with the tight binding energy dispersion. The derived expression is discussed in detail because of its distinction from the known expressions for ordinary superconductors with parabolic energy dispersion. We apply this expression for the experimental data analysis of the isotope effect in London penetration depth parameter $ \lambda $ in the BiSrCuO and YBaCuO family compounds near optimal doping, taking into account the orthorhombic distortion of crystal structure, and estimate the isotopic change of hopping parameters from the experimental data. We point out that $1/\lambda^2$ temperature behaviour is very sensitive to the ratio $ 2\Delta_m(T=0)/ k_B T_c $ and estimate this quantity for a number of compounds.