The Wiedemann-Franz (WF) law, relating the electronic thermal conductivity (${\kappa }_{\mathrm{e}}$) to the electrical conductivity, is vital in numerous applications such as in the design of thermoelectric materials and in the experimental determination of the lattice thermal conductivity (${\kappa }_{\mathrm{L}}$). While the WF law is generally robust, violations are frequently observed, typically manifesting in a reduced Lorenz number ($L$) relative to the Sommerfeld value ($L_0$) due to inelastic scattering. Here, we report a pronounced departure from the WF law in the topological semimetal CoSi, where the electronic Lorenz number ($L_{\mathrm{e}}$) instead rises up to $\sim 40\%$ above $L_0$. We demonstrate that this anomaly arises from strong bipolar diffusive transport, enabled by topological band-induced electron-hole compensation, which allows electrons and holes to flow cooperatively and additively enhance the heat current. Concurrently, we unveil that the lattice contribution to thermal conductivity is anomalously large and becomes the dominant component below room temperature. As a result, if ${\kappa }_{\mathrm{L}}$ is assumed negligible—as conventional in metals—the resulting $L$ from the total thermal conductivity (${\kappa }_{\mathrm{tot}}={\kappa }_{\mathrm{L}}+{\kappa }_{\mathrm{e}}$) deviates from $L_0$ by more than a factor of 3. Our work provides deeper insight into the unconventional thermal transport physics in topological semimetals.

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• Electrical conductivity
• Thermal conductivity
• Transport phenomena
• Topological materials
• Density functional calculations