  At present, topological insulators are the most efficient thermoelectric
materials at room temperature. However, at non-zero temperatures, it seems to
arise a conflict between having time-reversal symmetry, which implies minimal
entropy, and the Seebeck coefficient, which is the entropy carried by each
electric charge unit. This has obliged us to analyze the mathematical and
physical background taking into account relativistic phonons besides the
electrons within quantum field theory. In this search, we found an approximate
expression for the intrinsic topological field b in terms of the Chern number,
the Fermi velocity $v_F$ and the electron effective mass $m$, which allows to
connect the topologically non-trivial insulator with the trivial one, being
consistent with their topological properties and physical robustness. Thanks to
this, we demonstrate that for three-dimensional topological insulators in
thin-film conditions, among others, phonons have chirality coupling in a novel
way to electron dynamics which preserves time-reversal symmetry. This explains
the compatibility of the thermoelectricity within topological insulators and
shows explicitly how it adapts to the family of topological insulators
Bi$_2$Se$_3$.
