  We introduce and analyze two different scenarios for violation of the
Wiedemann-Franz law in strongly correlated electron systems of solids, close to
a topological quantum critical point (TQCP) where the density of states $N(0)$
diverges. The first, applicable to the Fermi-liquid (FL) side of the TQCP,
involves a transverse zero-sound collective mode that opens a new channel for
the thermal conductivity, thereby enhancing the Lorenz number $L(0)$ relative
to the value $L_0=\pi^2k^2_B/3e^2$ dictated by conventional FL theory. The
second mechanism for violation of the WF law, relevant to the non-Fermi-liquid
(NFL) side of the TQCP, involves the formation of a flat band and leads instead
to a reduction of the Lorenz number.
