Carrier mobility in Holstein–Peierls models of organic materials: A tensor-train HEOM approach

We present a comprehensive theoretical study of charge transport in organic materials on the basis of the one-dimensional dispersive Holstein–Peierls model. The hierarchical equations of motion in tensor-train format (HEOM-TT) method is employed to accurately describe both local Holstein-type and nonlocal Peierls-type electron–phonon couplings in the presence of low-frequency dispersive phonons. Linear response formulation of carrier mobility is obtained by employing the generating functional method. We demonstrate the capability of the method by calculating current correlation functions, diffusivities, and mobilities for various transport regimes. Our results provide new insights into the mechanisms underlying charge transport in organic semiconductors and establish HEOM-TT as a powerful tool for studying complex vibronic quantum dynamics and transport properties in condensed matter systems.