Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences


In this work, we study the electronic specific heat $C_e(T)$ of underdoped to overdoped high-$T_c$ cuprates, and identify the nature of anomalies in $C_e(T)$ at the superconducting transition temperature $T_c$ and at temperatures above $T_c$. The doped cuprate superconductor is considered as a multi-carrier model system which is composed of different types of charge carriers. The normal-state electronic specific heat $C_n(T)$ of high-$T_c$ cuprates below a characteristic pseudogap (PG) temperature $T^*$ is calculated taking into account three contributions coming from the excited components of Cooper pairs, the ideal Bose-gas of incoherent Cooper pairs and the unpaired carriers in the impurity band. Above $T^*$, two contributions to $C_n(T)$ coming from the unpaired intrinsic and extrinsic polarons are calculated within the two-component degenerate Fermi-gas model. The total electronic specific heat $C_e(T)=C_n(T)+C_s(T)$ below $T_c$ is calculated by considering the contribution $C_n(T)$ and the contribution $C_s(T)$ coming from the superfluid bosonic carriers. We have shown that our theoretical predictions of the behaviors of $C_e(T)$ near $T_c$ and above $T_c$ are strikingly similar to the behaviors of the electronic specific heat observed below and above $T_c$ in LSCO and YBCO. There is fair quantitative agreement between theoretical predictions about the anomalies in $C_e(T)$ (i.e. a $\lambda$-like anomaly near $T_c$ and a BCS-type anomaly above $T_c$ near $T^*$) and experimental data.

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