High-temperature transport and polaron speciation in the anharmonic Holstein model

We study the finite-temperature transport of electrons coupled to anharmonic local phonons. Our focus is on the high-temperature incoherent regime, where controlled calculations are possible both for weak and strong electron-phonon coupling. At strong coupling, the dynamics is described in terms of a multiple-species gas of small polarons: this emergent "speciation" is driven by energy conservation. We explicitly compute the dc and ac response in this regime. We discuss the breakdown of the polaron picture, and the onset of localization, in the limit where phonons become quasistatic. Our work exemplifies unusual transport phenomena that can be uncovered even in well-studied models of condensed matter by exploring poorly-explored regimes of parameters, using ideas and techniques sharpened by recent forays into even more exotic settings, such as MBL. Our findings may be realised in the setting of narrow bands engineered in moiré superlattices, where the role of electron-phonon interactions remains debated.