Assessing Phonon Spectral Functions in Disordered Binary Alloys within the Dynamical Cluster Approximation

Efficient and accurate treatment of disorder effects on vibrational observables is essential for understanding a wide range of experiments. This work focuses on the effect of mass disorder in harmonic binary isovalent alloys (i.e., NiPd and AuCu) using Green's-function-based mean-field approaches, benchmarked against numerically exact solutions. Specifically, we assess the phonon spectral function using the Average T-matrix Approximation (ATA), the Coherent Potential Approximation (CPA), and the Dynamical Cluster Approximation (DCA), in comparison to exact diagonalization and spectral-phonon-unfolding (SPU) calculations. An interesting phenomenon we examine is the emergence and evolution of local modes in the phonon spectra, which can be traced back to single-impurity resonances. Our study demonstrates that the CPA provides a remarkably robust description of most features of the phonon spectral function, offering a baseline understanding of disorder in real materials at a small computational cost.