Thermoelectric properties of GaSb and GaBi monolayers and nanoribbons: Topologically trivial versus nontrivial phases

Utilizing first-principles calculations combined with the non-equilibrium Green's function method, we systematically investigate the thermoelectric (TE) properties of GaSb and GaBi monolayers and their corresponding nanoribbons, with a particular focus on the influences of the edge states on the TE performance. First, the GaBi monolayer is identified as a topologically nontrivial insulator, whereas the GaSb monolayer is a trivial one. Subsequently, we compare the TE figure of merit $ZT$ of the GaSb and GaBi monolayers and nanoribbons. For the two-dimensional monolayers, the GaSb monolayer achieves a substantially higher $ZT$ peak than GaBi, primarily attributed to its wider energy bandgap that induces a larger Seebeck coefficient. In the nanoribbons, the emergence of both the trivial and topological edge states universally suppresses the $ZT$. However, the complete bandgap closing induced by the topologically protected edge states in the GaBi nanoribbons leads to a much more severe suppression of the $ZT$ compared to the preserved bandgap between the edge and bulk states in the GaSb nanoribbons. Finally, the temperature dependence of the $ZT$ peaks, as well as the influence of the nanoribbon width, is examined. The $ZT$ peaks near zero chemical potential exhibit opposite temperature dependences in the GaSb and GaBi monolayers, whereas the peaks far away from zero chemical potential show identical temperature evolution in their nanoribbons. This work not only deepens the understanding of how the topological and trivial edge states differently govern the TE properties, but also provides the crucial guidelines for improving the TE performance via the energy band and edge-state engineering, irrespective of their topological classification.