Phonon-Dominated Thermal Transport and Large Violation of the Wiedemann-Franz Law in Topological Semimetal CoSi

Abstract

The Wiedemann-Franz (WF) law, relating the electronic thermal conductivity ($κ_{\rm e}$) 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 ($κ_{\rm L}$). 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 ($L_{\rm e}$) instead rises up to $\sim40\%$ 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 $κ_{\rm L}$ is assumed negligible -- as conventional in metals, the resulting $L$ from the total thermal conductivity ($κ_{\rm tot}=κ_{\rm L}+κ_{\rm e}$) deviates from $L_0$ by more than a factor of three. Our work provides deeper insight into the unconventional thermal transport physics in topological semimetals.

Figures (4)

• Figure 1: (a) The crystal structure and the first Brillouin zone of CoSi, (b) the phonon dispersion along with the projected density of states, (c) the calculated $T$-dependent $\kappa_{\rm L}$, (d) cumulative lattice thermal conductivity considering different scattering mechanisms at 300 K, (e) the scattering rates contributed by the 3ph, 4ph, ph-iso, and ph-el processes, and (f) the Eliashberg spectral function $\alpha^2F(\omega)$ and el-ph coupling strength ($\lambda(\omega)$).
• Figure 2: (a) The electrical resistivity, (b) the thermal conductivity ($\kappa_{\rm e}$, $\kappa_{\rm L}$, and $\kappa_{\rm tot}$,), and (c) the Lorenz number with the inset showing the $L$ extracted from $\kappa_{\rm tot}$. The symbols show experimental electrical resistivity taken from Refs.REN20055010.1063/1.307279910.1063/1.5119209PhysRevB.86.064433BURKOV2019540PhysRevB.82.155124, and thermal conductivity taken from Refs.Sun2013.
• Figure 3: (a) Electronic band structure and Orbital-projected density of states (DOS) of CoSi. The DOS decomposition shows contributions from different atomic orbitals: Si $p$ orbitals (green), Co $d_{z^2}$ and $d_{x^2-y^2}$ orbitals (orange), Co $d_{xy}$, $d_{yz}$, and $d_{xz}$ orbitals (red), and total DOS (blue). The energy zero is set to the Fermi level. (b) Zoomed-in band structure near the Fermi level. (c) Band-resolved carrier concentration at 300 K. (d) Schematic illustration of carrier response to an electric field and a temperature gradient.
• Figure 4: The contribution of each band to (a) the electrical conductivity and Seebeck coefficient, (b) the electronic thermal conductivity, and (c) the Lorenz number at $T_{\rm room}$. The blue dashed line in (c) denotes the Lorenz number in the multi-bands case. (d) The carrier thermal conductivity term arising from the Seebeck effect at 300 K.