Auxiliary coherent medium theory for lattice vibrations in random binary alloys with mass and force-constant disorders

Abstract

The inevitable and random impurities or defects can significantly influence the lattice-vibrational properties of materials and devices. Thus, the capability of effectively treating disorder effects is indispensable for theoretical simulations. In this paper, we report an auxiliary coherent medium theory, in the framework of multiple scattering theory, to simulate disordered vibrational systems containing both mass and force-constant disorders. In this method, the physical Green's function is related to an auxiliary Green's function by introducing a separable force-constant model to describe disordered systems. As an important result, the force-constant disorder can be transformed to a diagonal-like disorder in the auxiliary Hamiltonian while maintaining the important force-constant sum rule. In combination with the single-site and cluster coherent potential approximation, the configurational average over the auxiliary Green's function can be performed to obtain the configuration-averaged physical properties. To demonstrate the effectiveness of this method, we apply it to a one-dimensional harmonic chain with atomic disorders and find our calculations agree very well with the exact results for a wide range of mass and force constants. Moreover, we show that the phonon transport property of disordered devices can be derived based on the auxiliary Green's function formalism in combination with vertex corrections. The auxiliary coherent medium theory features easy implementation and feasible incorporation with diagrammatic technique in many-body perturbation and various cluster approximations, providing an important approach to analyze disorder effects on the vibrational properties. Moreover, it is also straightforward to apply the present formalism to treat the general atomic disorder in electronic systems.