Origins of anomalies in the temperature dependences of specific heat and superfluid density in doped high-Tc cuprates: Signatures of Bose-liquid superconductivity

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-[Formula: see text] 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 (BEC) of bosonic Cooper pairs. We examine the validity of an alternative approach to the unconventional superconductivity in high-[Formula: see text] cuprates and establish that these materials exhibiting a [Formula: see text]-like superconducting transition at the critical temperature [Formula: see text] are similar to the superfluid 4 He and are also superfluid Bose systems. We argue that the doped high-[Formula: see text] cuprates, from underdoped to overdoped regime, are unconventional (bosonic) superconductors and the tightly bound (polaronic) Cooper pairs in these polar materials behave like composite bosons just like 4 He atoms and condense into a Bose superfluid at [Formula: see text]. We identify the superconducting order parameter [Formula: see text] in underdoped and optimally doped cuprates as the coherence parameter [Formula: see text] of bosonic Cooper pairs, which appears just below [Formula: see text] and has a kink-like temperature dependence near the characteristic temperature [Formula: see text]. We find that the [Formula: see text]-like specific heat anomaly in high-[Formula: see text] cuprates near [Formula: see text] predicted by the theory of Bose-liquid superconductivity is similar to that observed both in superfluid 4 He near [Formula: see text] and in Hg-based cuprate superconductor HgBa 2 Ca 2 Cu 3 O 8 near [Formula: see text][Formula: see text]K. We demonstrate that in high-[Formula: see text] superconductor YBa 2 Cu 3 [Formula: see text] the superfluid density [Formula: see text] exhibits distinctly different temperature dependences in the temperature ranges [Formula: see text] and [Formula: see text]. In this superconductor, a pronounced anomaly in [Formula: see text] exists near [Formula: see text] and the temperature dependence of [Formula: see text] below [Formula: see text] deviates downwards from the high-temperature behavior. Our results for the normalized superfluid density [Formula: see text] are in good agreement with the experimental data on the temperature dependence of [Formula: see text] in YBa 2 Cu 3 [Formula: see text]. The anomalous temperature dependences of specific heat and superfluid density observed in Hg- and Y-based high-[Formula: see text] superconductors are clear signatures of Bose-liquid superconductivity.