Specific heat of underdoped cuprate superconductors from a phenomenological layered Boson–Fermion model

• We present a superconductivity model which includes the Boson–Fermion model and extend it to layered structures.
• The model straightforwardly predicts and reproduces the electronic specific heat of underdoped cuprates.
• The linear component of the electronic specific heat, and the quadratic and cubic behaviors for low temperatures are obtained.
• The total specific heat is built giving very satisfactory results.
• The mass anisotropy is explained through this model.

We adapt the Boson–Fermion superconductivity model to include layered systems such as underdoped cuprate superconductors. These systems are represented by an infinite layered structure containing a mixture of paired and unpaired fermions. The former, which stand for the superconducting carriers, are considered as noninteracting zero spin composite-bosons with a linear energy–momentum dispersion relation in the CuO2 planes where superconduction is predominant, coexisting with the unpaired fermions in a pattern of stacked slabs. The inter-slab, penetrable, infinite planes are generated by a Dirac comb potential, while paired and unpaired electrons (or holes) are free to move parallel to the planes. Composite-bosons condense at a critical temperature at which they exhibit a jump in their specific heat. These two values are assumed to be equal to the superconducting critical temperature Tc and the specific heat jump reported for YBa2Cu3O6.80 to fix our model parameters namely, the plane impenetrability and the fraction of superconducting charge carriers. We then calculate the isochoric and isobaric electronic specific heats for temperatures lower than Tc of both, the composite-bosons and the unpaired fermions, which matches the latest experimental curves. From the latter, we extract the linear coefficient (γn) at Tc, as well as the quadratic (αT2) term for low temperatures. We also calculate the lattice specific heat from the ARPES phonon spectrum, and add it to the electronic part, reproducing the experimental total specific heat at and below Tc within a 5% error range, from which the cubic (ßT3) term for low temperatures is obtained. In addition, we show that this model reproduces the cuprates mass anisotropies.