Anomalous thermoelectricity at the two-dimensional structural transition of SnSe monolayers

The thermoelectric figure of merit $ZT$ comprises electronic and vibrational contributions that drastically change across phase transitions, and the most common theoretical ab initio approach to thermoelectricity fails to describe the evolution of $ZT$ across finite-temperature structural transitions in its entirety. Furthermore, while the thermoelectric behavior of bulk SnSe has been extensively studied, SnSe monolayers have been experimentally realized only recently, and the existent prediction of thermoelectricity on this two-dimensional material is unreliable because it misses its structural transition altogether. SnSe monolayers (and similar GeS, GeSe, GeTe, SnS, and SnTe monolayers) experience a temperature-induced two-dimensional $Pnm{2}_{1}\ensuremath{\rightarrow}P4/nmm$ structural transition precipitated by the softening of vibrational modes, and we describe their thermoelectric properties across the phase transition, using molecular dynamics data to inform both electronic and vibrational coefficients directly and within the same footing. Similar to recent experimental observations pointing to an overestimated $ZT$ past the transition temperature in bulk SnSe, we find a smaller $ZT$ on SnSe monolayers when compared to its value predicted by the standard paradigm, due to the dramatic changes in the electrical conductivity and lattice thermal conductivity as the structural transition ensues. The process described here lends a strong focus to both the vibrational and electronic evolutions throughout the structural transition, and it applies to thermoelectric materials undergoing thermally driven solid-to-solid structural phase transitions in one, two, and three dimensions.