Theory of band warping and its effects on thermoelectronic transport properties

We define band warping as referring to band structures that do not admit second-order differentiability at critical points in k space and we develop a generally applicable theory, based on radial expansions, and a corresponding definition of angular effective mass. Our theory also accounts for effects of band nonparabolicity and anisotropy, which hitherto have not been precisely distinguished from, if not utterly confused with, band warping. As an application of major significance to thermoelectricity, we use our theory and angular effective masses to generalize derivations of tensorial transport coefficients for cases of either single or multiple electronic bands, with either quadratically expansible or warped energy surfaces. From that theory we discover the formal existence at critical points of transport-equivalent ellipsoidal bands that yield identical results from the standpoint of any transport property.