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Using Green’s function method, the frequency dependence of optical conductivities of high-quality MgB
_{2} film is calculated in the framework of the single- and two-band model. By comparing the numerical and experimental results, it is shown that the single-gap isotropic model is insufficient to understand consistently optical behaviors. Also, it is concluded that the two-band model consistently describes the optical behaviors. In the two-gap model, we consider that the both components of optical conductivity are a weighted sum of the contribution from σ and π bonds and hybridization between them is negligible.

The discovery of MgB_{2} superconductor [

There have been several studies to detect the MgB_{2} gaps. The isotope effect of boron has suggested that MgB_{2} is a BCS-type superconductor [_{2} [_{2} is an s-wave BCS type superconductor or not. In conventional s-wave superconductors, there is no quasiparticle excitation at low energies and the thermodynamic and transport coefficients decay exponentially at low temperatures. In this superconductors, the deviation of penetration depth

Pronin et al. measurements [_{2} film has a

Kaindl et al. [_{2} film as a function of frequency for different temperatures. They compared their results with conventional superconductors and concluded that their results were inconsistent with BCS calculations. This disagreement with BCS calculations could be caused by an additional absorption.

In this paper we introduce the new view of the frequency dependence of optical properties of MgB_{2} . Numerical calculations of frequency dependence of optical conductivities are carried out by proposing different kinds of energy gaps. We show that the optical conductivities are well described by a two-band superconductor model with different anisotropies in k-space. First, we conclude that the single-gap model is insufficient to understand consistently the optical behaviors. Then, it will be shown that the two-gap model with different symmetries in k-space is sufficient to understand optical properties. In this model the larger gap

Our model of MgB_{2} by a Hamiltonian has two bands, labeled

where

Here, c and d are referred to

We can write the similar equations for

where

We assume that the hybridization between

Optical conductivity describes the linear response of a material, which is exposed to an electromagnetic field. This field induces shielding currents

where

The real and imaginary parts of the optical conductivity are given by

where

where V is the volume of the system and the current expression in the case of noninteracting particle is given by

By using Equation (16), Equation (15) can be written as

where

Here, we consider thin film satisfying

Then in the isotropic case we obtain the Mattis-Bardeen formula from Equations (13) and (14):

where

states that generalized to

surface.

Now, we present the numerical solutions of complex conductivity of MgB_{2} film in the frequency range

The anisotropy of d-wave gap considered in this paper is

Here, θ is the angular deviation of

where

integral of the first kind.

In

Here, a two-band model with different anisotropies is investigated. We assume that the hybridization between

In this curves, the best fit to the experimental data are obtained if we assign the ratio of the weights of the

By using Green’s function method and linear response theory we have calculated the frequency dependence of the real and imaginary parts of optical conductivity of MgB_{2} film in the framework of two-band theory. We have shown that a single-gap model is insufficient to describe the optical behaviors, but the two-band model with different symmetries can explain the experimental results consistently. Also, we have shown that the electrons in

AdelShojaei,MohammadMoarrefi-Romeileh,AsadollahJoata-Bayrami, (2015) Frequency Dependence of Optical Conductivity in MgB_{2} Superconductor. World Journal of Condensed Matter Physics,05,353-360. doi: 10.4236/wjcmp.2015.54036