Temperature dependence of Liquid density and Magnetic field entrance depth in high-temperature Superconductors

Аннотация

We show that the temperature-dependent superconducting order parameter and related superconducting properties (in particular, the temperature dependences of specific heat, superfluid density and related London penetration depth) of high- cuprates are fundamentally different from those of conventional superconductors and cannot be understood within the existing theories based on the Bardeen-Cooper-Schrieffer (BCS)-type condensation of weakly-bound Cooper pairs into a superfluid Fermi- liquid and on the usual Bose-Einstein condensation (ВЕС) of bosonic Cooper pairs. We examine the validity of an alternative approach to the T  unconventional superconductivity in high- , cuprates and establish that these materials exhibiting a - c like superconducting transition at the critical temperature T are similar to the superfluid 4He and are also T c superfluid Bose systems. We argue that the doped high- cuprates from underdoped to overdoped regime c are unconventional (bosonic) superconductors and the tightly-bound (polaronic) Cooper pairs in these polar materials behave like composite bosons just like4He atoms and condense into a Bose superfluid at T . We c identify the superconducting order parameter in underdoped and optimally doped cuprates as the  SC T coherence parameter of bosonic Cooper pairs, which appears just below and has a kink-like B T  T c temperature dependence near the characteristic temperature . c INTRODUCTION temperature dependences of superfluid density and related magnetic field penetration depth) of high-𝑇 𝑐 cuprates are fundamentally different from those of In conventional metals with weak electron-phonon conventional superconductors and cannot be coupling, the Cooper pairing of electrons and Fermi- understood within the existing theories based on the liquid superconductivity occur simultaneously at the BCS-type condensation of weakly-bound (fermionic) critical temperature 𝑇 of the superconducting 𝑐 Cooper pairs into a superfluid Fermi-liquid and on the transition and these phenomena are well described by usual Bose-Einstein condensation (BEC) of tightly- the Bardeen-Cooper-Schrieffer (BCS) theory [1]. In bound (bosonic) Cooper pairs. The magnetic field contrast, in doped copper oxide (cuprate) penetration depth in superconductors is usually called superconductors, the electron-phonon interaction is the London penetration depth 𝜆 [4] and strong enough and the origin of high-𝑇 𝐿 𝑐 temperaturedependent because, it depends on the superconductivity in these polar materials remains still density 𝜌 of superfluid carriers [3], which decreases controversial [2, 3]. The temperature-dependent 𝑠 with increasing temperature T. The superfluid density superconducting proporties (in particular, the 𝜌 and London penetration depth 𝜆 are the intrinsic power-law temperature dependence of 𝜆 (𝑇) at low 𝑠 𝐿 𝐿 parameters of superconductors closely connected with temperatures in the cuprate superconductors are direct the mechanism of their superconductivity. The consequences of the theory of three-dimensional (3D) temperature dependences of 𝜌 and 𝜆 in Bose-liquid superconductivity. We argue that the doped 𝑠 𝐿 superconductors are sensitive to the form of the hole carriers in a polar crystal of the cuprates interact quasipartical excitation spectrum, which depends on with lattice vibrations (phonons) [7, 8] and they are the fermionic or bosonic nature of Cooper pairs. In self-trapped just like self-trapping holes in ionic particular, the London penetration depth 𝜆 has an crystals of alkali halides [9, 10]. In doped high-𝑇 𝐿 𝑐 exponential temperature dependence in the cuprates the attractive hole-lattice interaction is strong superconductor if the quasiparticle excitation spectrum enough to overcome the Coulomb repulsion between has a finite energy gap, while it has a power-law two self-trapped (polaronic) carriers [11] and the temperature dependence if the excitation spectrum of Cooper pairing of such carriers results in the formation quasiparticles is gapless in the superconductor. of tightly-bound Cooper pairs [12], which behave like For a long time, the different BCS-like theories of bosons just like 𝐻𝑒4 atoms and condense into a 3D Bose Fermi-liquid superconductivity are often used to superfluid [11, 13]. Therefore, we assume that the describe the phenomenon of superconductivity in Bose-liquid superconductivity is realized in high-𝑇 𝑐 doped high-𝑇 cuprates. However, the origins of many cuprates in which the quasiparticle excitations 𝑐 anomalies in the superconducting properties of high-𝑇 characteristic of a superfluid Bose-liquid result into the 𝑐 cuprates have not been well understood yet within the distinctive non-BCS temperature dependences of 𝜌(𝑇) 𝑠 existing theories based on the BCS-like models or the and 𝜆 (𝑇). 𝐿 usual BEC models of an ideal Bose gas [3]. Actually, it According to the theory of the 3D Bose superfluid is found experimentally that the temperature [11], the quasiparticle excitation spectrum 𝐸