  The effective transport coefficients and figure of merit ZT for anisotropic
systems are derived from a macroscopic formalism. The full tensorial structure
of the transport coefficients and the effect of the sample boundaries are
included. Induced transverse fields develop which can be larger than the
applied fields and which reduce the effective transport coefficients. A
microscopic model relevant for multi-valleyed materials is introduced which
utilizes the effective-mass and relaxation-time approximations. The thermopower
and Lorentz number are independent of the tensorial structure of the transport
coefficients in this case and are therefore isotropic. ZT is also isotropic for
vanishing lattice thermal conductivity \kappa_\ell. For non-vanishing but
sufficiently isotropic \kappa_\ell, ZT is maximal along the direction of
highest electrical conductivity \sigma. Numerical calculations suggest that
maximal ZT generally occurs along the principal direction with the largest
\sigma/\kappa_\ell. An explicit bound on ZT is derived. Several results for
specific systems are obtained: (1) Bulk n-type Bi_2Te_3 exhibits easily
observable induced transverse fields and anisotropic ZTs. (2) Increased
anisotropy in HgTe/ Hg_{1-x}Cd_xTe superlattices (SLs) is associated with
larger induced fields. (3) The valley degeneracy is split and the bulk masses
modified in isolated Bi_2Te_3 quantum wells, resulting in optimal ZTs for wells
grown along the trigonal direction. (4) Non-parabolic dispersion in SLs has
little effect on the thermopower at the carrier concentrations which maximize
ZT.
