Direct comparison of auxiliary and itinerant coherent potential approximations for disordered lattice vibration: Phonon spectral and transport properties

Abstract

The auxiliary and itinerant coherent potential approximations (ACPA and ICPA) have been proposed as effective methods for treating both mass and force-constant disorder in lattice vibration. In this work we make a direct comparison of ACPA and ICPA to identify the differences between these two methods for simulating vibrational properties of disordered materials and devices. We investigate the major approximations in the disorder self-energies of these two methods by using the diagrammatic method. The single-site ACPA neglects the crossing diagrams describing nonlocal correlations, while ICPA utilizes only the single-fluctuation states in the self-consistency and presents extra errors due to a change in the terms with nearest-neighbor fluctuation. To further demonstrate the important differences between the ACPA and ICPA in the phonon spectral and transport properties, we extend ICPA in combination with the Keldysh nonequilibrium Green s function technique to simulate quantum transport and introduce a Green s-function-based spectral unfolding technique to use with molecular ACPA and the supercell methods for comparison. By studying the disordered one- and three-dimensional alloys, we find that ACPA and ICPA agree very well in the weak scattering regime due to weak force-constant disorder or low phonon frequency. However, for the strong scattering of force-constant disorder, it is found that the two methods present important deviations in the linewidth (and height) of disorder-averaged phonon spectra. Compared to the ACPA and exact results, the problematic treatment of the nearest-neighbor fluctuation in ICPA can present unphysical scattering and induce large errors in the phonon transport, presenting important limitations of ICPA for transport simulation.