Theoretical Study of Specific Heat and Density of States of MgB<sub>2</sub> Superconductor in Two Band Model

Abstract

MgB 2 with T c ≈ 40 K, is a record-breaking compound among the s-p metals and alloys. It appears that this material is a rare example of the two band electronic structures, which are weakly connected with each other. Experimental results clearly reveal that boron sub-lattice conduction band is mainly responsible for superconductivity in this simple compound. Experiments such as tunneling spectroscopy, specific heat measurements, and high resolution spectroscopy show that there are two superconducting gaps. Considering a canonical two band BCS Hamiltonian containing a Fermi Surface of π-and σ-bands and following Green's function technique and equation of motion method, we have shown that MgB 2 possess two superconducting gaps. It is also pointed out that the system admits a precursor phase of Cooper pair droplets that undergoes a phase locking transition at a critical temperature below the mean field solution. Study of specific heat and density of states is also presented. The agreement between theory and experimental results for specific heat is quite convincing. The paper is organized in five sections: Introduction, Model Hamiltonian, Physical properties, Numerical calculations, Discussion and conclusions.

Iron-Based Superconductors

“…Like cuprate superconductors, FebSc systems derive their high temperature superconductivity from electron or hole doping of their parent compounds.These parent compounds exhibit long-range AFM static order, which is suppressed by electron or hole doping to induce superconductivity. In contrast to cuprates, magnetism in FebSCs results from a nestinginduced spin density wave [31].…”

“…This increase in positive charge will, in turn, attract another electron. These two electrons are Cooper pairs [31] which are discovered by Cooper [30]. These are also referred to as supperelectrons [8].…”

“…The shape of the electronic band structure depends on the doping level. In electron-doped materials, such as 122 Fe-based superconductor compounds, the Fermi surface contains several quasi-2D warped cylinders centered at Γ point k ¼ 0, 0 ðÞ and M point k ¼ π, π ðÞ in a 2D cross-section, and may also contain a quasi 3D pocket near k z ¼ π as shown in the Figure 6 [15,17,31].…”

“…In weakly and moderately electron-doped materials, the Fermi surface consists of quasi-2D warped cylinders centered at 0, 0 ðÞ and π, π ðÞ in a 2D cross-section. The ones near 0, 0 ðÞ are hole pockets (filled states are outside cylinders), and the ones near π, π ðÞ are electron pockets (filled states are inside cylinders) [17,31].…”

Frequency Dependence of Optical Conductivity in MgB<sub>2</sub> Superconductor

“…Their ratio is estimated to be min max 0.3 -0.4 ∆ ∆ ≈ using several experiments. The two-gap model is shown to consistently describe the optical conductivity and thermodynamic properties of MgB 2 [7]- [9]. However, there is no general agreement whether MgB 2 is an s-wave BCS type superconductor or not.…”