Linear and quadratic temperature dependence of electronic specific heat for cuprates

TL;DR

This paper models cuprate superconductors as layered structures with paired and unpaired fermions, deriving temperature-dependent electronic specific heat terms that match experimental data near and below the critical temperature.

Contribution

It introduces a layered lattice model with bosonic paired fermions and unpaired fermions, successfully reproducing the temperature dependence of electronic specific heat in cuprates.

Findings

Derived linear and quadratic specific heat terms consistent with experiments.

Reproduced the total specific heat curve near Tc, matching experimental values.

Quantified model parameters using the specific heat jump at Tc.

Abstract

We model cuprate superconductors as an infinite layered lattice structure which contains a fluid of paired and unpaired fermions. Paired fermions, which are the superconducting carriers, are considered as noninteracting zero spin bosons with a linear energy-momentum dispersion relation, which coexist with the unpaired fermions in a series of almost two dimensional slabs stacked in their perpendicular direction. The inter-slab penetrable planes are simulated by a Dirac comb potential in the direction in which the slabs are stacked, while paired and unpaired electrons (or holes) are free to move parallel to the planes. Paired fermions condense at a BEC critical temperature at which a jump in their specific heat is exhibited, whose values are assumed equal to the superconducting critical temperature and the specific heat jump experimentally reported for YBaCuO_(7-x) to fix our model parameters: the plane impenetrability and the fraction of superconducting charge carrier. We straightforwardly obtain, near and under the superconducting temperature Tc, the linear (\gamma_e T) and the quadratic (\alpha T^2) electronic specific heat terms, with \gamma_e and \alpha, of the order of the latest experimental values reported. After calculating the lattice specific heat (phonons) Cl from the phonon spectrum data obtained from inelastic neutron scattering experiments, and added to the electronic (paired plus unpaired) Ce component, we qualitatively reproduce the total specific heat below Tc, whose curve lies close to the experimental one, reproducing its exact value at Tc.