Two distinctive temperature dependences of the London penetration depth in high-Tc cuprate superconductors as support for the theory of Bose-liquid superconductivity

Abstract

In the framework of the theory of Bose-liquid superconductivity, we show that in high-Tc cuprate superconductors the magnetic field penetration depth (known as the London penetration depth λL(T)) decreases first exponentially below the superconducting transition temperature Tc with decreasing the temperature T and then λL(T) decreases like a certain power of T at lower temperatures due to the vanishing of the energy gap Δg(T) in the excitation spectrum of a superfluid Bose-liquid at a characteristic temperature Tc⁎ lower than Tc. Below Tc, the London penetration depth λL(T) has an exponential temperature dependence down to Tc⁎, which is different from a BCS- like exponential temperature dependence, and then λL(T) will follow a power law temperature dependence down to T=0, which is also different from power-law temperature dependences predicted by some BCS-like (d-wave) pairing theories. In unconventional (bosonic) cuprate superconductors characterized by the strong interboson coupling constant (γB≳1), λL(T) exhibits the distinctly different temperature dependences in different temperature intervals 0≤T≤Tc⁎<<Tc and Tc⁎<T<Tc when the energy gap Δg(T) vanishes at a temperature Tc⁎ well below Tc. In the weak interboson coupling (γB<<1) the energy gap Δg(T) vanishes at a temperature Tc⁎ close to Tc and the reduced London penetration depth λL(T)/λL(0) has an unusual Tn power-law temperature dependence in a wide temperature range 0<T<Tc⁎ below Tc, i.e. the expression λL(T)/λL(0)≃[1−aL(T)(T/Tc)n]−1/2 (where n≳4 and aL(T)≲1) is valid only below Tc⁎ and is similar to the well-known empirical Gorter-Casimir law. Our theoretical predictions of the distinctive power-law and exponential temperature dependences of λL(T)/λL(0) are in good agreement with the experimental results reported for GdBa2Cu3O7−δ ceramics and YBa2Cu3O7−δ films. The peculiar temperature dependences of λL(T)/λL(0) observed in these high-Tc materials at low and high temperatures do not follow the predictions of the s- and d-wave BCS-like theories of Fermi-liquid superconductivity and give evidence for the predictions of the theory of Bose-liquid superconductivity.