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We introduce and analyze two different scenarios for violation of theWiedemann-Franz law in strongly correlated electron systems of solids, close toa 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 forthe thermal conductivity, thereby enhancing the Lorenz number $L(0)$ relativeto the value $L_0=\pi^2k^2_B/3e^2$ dictated by conventional FL theory. Thesecond 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 insteadto a reduction of the Lorenz number.

Fate of the Wiedemann-Franz law near quantum critical points of electron systems in solids