Fermi Surface Nesting and Phonon Frequency Gap Drive Anomalous Thermal Transport

The lattice thermal conductivity, $k_L$, of typical metallic and nonmetallic crystals decreases rapidly with increasing temperature because phonons interact more strongly with other phonons than they do with electrons. Using first principles calculations, we show that $k_L$ can become nearly independent of temperature in metals that have nested Fermi surfaces and large frequency gaps between acoustic and optic phonons. Then, the interactions between phonons and electrons become much stronger than the mutual interactions between phonons, giving the fundamentally different $k_L$ behavior. This striking trend is revealed here in the group V transition metal carbides, vanadium carbide, niobium carbide, and tantalum carbide, and it should also occur in several other metal compounds. This work gives insights into the physics of heat conduction in solids and identifies a new heat flow regime driven by the interplay between Fermi surfaces and phonon dispersions.

Figure 1

Fermi surface of (a) NbC and (b) TiC calculated from first principles. Images prepared using XCrySDen [41]. The red arrows show the three nesting vectors with lengths 0.66 (in units of $2\pi /a$) along $\mathrm{\Gamma }\text{−}X$, 0.71 along $\mathrm{\Gamma }\text{−}K$, and at the $L$ point for NbC. Possible nesting vector for TiC also shown.

Figure 2

Phonon dispersions of (a) NbC and (b) TiC calculated from first principles and compared to measured data from Refs. [42, 43], respectively. Blue arrows in (a) show the phonon anomalies for NbC. No anomalies occur for TiC acoustic phonons.

Figure 3

Comparison of phonon-phonon (blue points) and phonon-electron (red points) scattering rates for (a) NbC and (b) TiC at 300 K.

Figure 4

Lattice thermal conductivity $k_L$ as a function of $T$ for NbC limited by (i) phonon-phonon and phonon-isotope scattering (dashed blue curve), (ii) phonon-phonon, phonon-isotope, and phonon-electron scattering (solid blue curve). Same for TiC with red curves.

Figure 5

Lattice thermal conductivity as a function of temperature for the group IV transition metal carbides, TiC, ZrC, and HfC (dashed curves), which show strong temperature dependence, and for the group V transition metal carbides, VC, NbC, and TaC, which show very little temperature dependence.