Thermoelectricity of Tin Selenide Monolayers Across a Structural Phase Transition

SnSe monolayers experience a temperature induced two-dimensional Pnm2$_1 \to$ P4/nmm structural transformation precipitated by the softening of vibrational modes. The standard theoretical treatment of thermoelectricity---which relies on a zero temperature phonon dispersion and on a zero temperature electronic structure---is incapable of describing thermoelectric phenomena induced by structural transformations. Relying on structural data obtained from {\em ab initio} molecular dynamics calculations that is utilized in a non-standard way to inform of electronic and vibrational transport coefficients, the present work establishes a general route to understand thermoelectricity across phase transitions. Similar to recent experimental observations pointing to an overestimated thermoelectric figure of merit $ZT$ past the transition temperature, our work indicates a smaller $ZT$ when compared to its value predicted by the standard paradigm. Its decrease is related to the dramatic changes in the electrical conductivity and lattice thermal conductivity as the structural transformation ensues. Though exemplified on a SnSe monolayer, the method does not have any built-in assumptions concerning dimensionality, and thus applicable to arbitrary thermoelectric materials in one, two, and three dimensions.