A modified simplified coherent potential approximation model of band gap energy of III-V ternary alloys

Based on the modification of the simplified coherent potential approximation （SCPA）, a model is developed to calculate the composition dependence of the band gap energy of Ⅲ-V ternary alloys with the same anion. The derived equation is used to fit the experimental band gap energy of InxAl1-xN, InxGa1-xN and A1xGal xN with x from 0 to 1. It is found that the fitting results are better than those done by using SCPA. The fitting results are also better than those obtained by using the formula with a small bowing coefficient, especially for InxAl1-xN. In addition, our model can also be used to describe the composition de- pendence of band gap energy of other Ⅲ-V ternary alloys.

Graphene as Gas Sensors

The triatomic and tetratomic gas molecule adsorption effects on the electrical conductivity of graphene areinvestigated by the tight-binding model,Green’s function method,and coherent potential approximation.We find thatthe electrical conductivity of graphene sheet is sensitive to the adsorption of these gases.

Low Frequency Dispersion Law for Two-Dimensional Metallic Photonic Crystals

Using the rigorous multiple-scattering theory, we study the dispersion relation of electromagnetic （EM） waves in two dimensional dielectric photonic crystals （PCs） and metallic photonic crystals （MPCs） in the low-frequency limit. Analytic formula for the effective velocity of EM waves in PCs and MPCs is obtained. Accuracy of our formula is checked by comparing the results with rigorous calculations. For PCs, our result is exactly the same as the coherent potential approximation （CPA）, which is accurate even when the filling fraction is high. But for MPCs, our approach demonstrates special advantages, while the CPA theory fails, in predicting the effective velocity of EM waves in MPCs at low frequency.

Full counting statistics of phonon transport in disordered systems

The coherent potential approximation(CPA)within full counting statistics(FCS)formalism is shown to be a suitable method to investigate average electric conductance,shot noise as well as higher order cumulants in disordered systems.We develop a similar FCS-CPA formalism for phonon transport through disordered systems.As a byproduct,we derive relations among coefficients of different phonon current cumulants.We apply the FCS-CPA method to investigate phonon transport properties of graphene systems in the presence of disorders.For binary disorders as well as Anderson disorders,we calculate up to the 8-th phonon transmission moments and demonstrate that the numerical results of the FCS-CPA method agree very well with that of the brute force method.The benchmark shows that the FCS-CPA method achieves 20 times more speedup ratio.Collective features of phonon current cumulants are also revealed.