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Materials with ring-shaped electronic bands are promising thermoelectriccandidates, since their unusual dispersion shape is predicted to give largepower factors. While previous calculations of these materials have relied onthe assumption of a constant mean-free-path or relaxation time, recentfirst-principles modeling of electron-phonon scattering suggests that thescattering rates may be better approximated by the electron density-of-states(so-called DOS scattering model). In this work, we use density functionaltheory to investigate single and double quintuple-layer Bi$_2$Te$_3$,Bi$_2$Se$_3$ and Sb$_2$Te$_3$, with a focus on understanding how the threeaforementioned scattering approximations impact thermoelectric performance --emphasis is placed on the DOS scattering model. The single quintuple-layermaterials possess two ring-shaped valence band maxima that provide an abruptincrease in conducting channels, which benefits the power factor. Additionally,below the band edge a ring-shaped minimum, located between the two maxima, isfound to further enhance the thermoelectric performance but only with the DOSscattering model. This comes from a sharp drop in the DOS, and thus scattering,just below the ring-shaped minimum. An analytic octic dispersion model isintroduced and shown to qualitatively capture the observed features. The doublequintuple-layer materials display notably worse thermoelectric properties,since their dispersions are significantly modified compared to the singlequintuple-layer case. The benefits of ring-shaped bands are sensitive to thealignment of the two ring maxima and to the degree of ring anisotropy. Overall,single quintuple-layer Bi$_2$Te$_3$ and Bi$_2$Se$_3$ are most promising, withthe DOS scattering model giving the highest power factors.

physical review. b./physical review. b

Thermoelectric calculations of ring-shaped bands in two-dimensional  Bi$_2$Te$_3$, Bi$_2$Se$_3$ and Sb$_2$Te$_3$: a comparison of simple  scattering approximations