Phonon softening near topological phase transitions

Topological phase transitions occur when the electronic bands change their topological properties, typically featuring the closing of the band gap. While the influence of topological phase transitions on electronic and optical properties has been extensively studied, its implication on phononic properties and thermal transport remains unexplored. In this paper, we use first-principles simulations to show that certain phonon modes are significantly softened near topological phase transitions, leading to increased phonon-phonon scattering and reduced lattice thermal conductivity. We demonstrate this effect using two model systems: pressure induced topological phase transition in ${\mathrm{ZrTe}}_5$ and chemical composition induced topological phase transition in ${\mathrm{Hg}}_{1-\mathrm{x}}{\mathrm{Cd}}_{\mathrm{x}}\mathrm{Te}$. We attribute the phonon softening to emergent Kohn anomalies associated with the closing of the band gap. Our paper reveals the strong connection between electronic band structures and lattice instabilities, and opens up a potential direction towards controlling heat conduction in solids.

Figure 1

(a) The crystal structure of ${\mathrm{ZrTe}}_5$ with calculated lattice constants and the corresponding first Brillouin zone, where the band touching points under 5-GPa pressure are labeled with two cones. (b) The supercell structure used and the corresponding Brillouin zone of the ${\mathrm{Hg}}_{1-\mathrm{x}}{\mathrm{Cd}}_{\mathrm{x}}\mathrm{Te}$ alloy system.

Figure 2

(a) The calculated electronic band structure of ${\mathrm{ZrTe}}_5$ under zero pressure. (b) The calculated electronic band structure of ${\mathrm{ZrTe}}_5$ along the $\mathrm{\Gamma }$-Y direction under different hydrostatic pressures. The band gap is closed when ${\mathrm{ZrTe}}_5$ is under 5-GPa pressure. (c) The quadratic electronic energy dispersion along the $a$ and $c$ axis near the band touching points in ${\mathrm{ZrTe}}_5$ under 5-GPa pressure.

Figure 3

(a) The calculated phonon dispersions of ${\mathrm{ZrTe}}_5$ under zero pressure and 5-GPa pressure. (b) The relative changes of the calculated lattice thermal conductivity of ${\mathrm{ZrTe}}_5$ along different directions under 5-GPa pressure compared to those under zero pressure. (c) The phonon-phonon scattering rates in ${\mathrm{ZrTe}}_5$ under zero pressure and 5-GPa pressure, highlighting the increased scattering near the softened phonons in pressured ${\mathrm{ZrTe}}_5$.

Figure 4

(a) The calculated electronic band structure near $\mathrm{\Gamma }$ of the ${\mathrm{Hg}}_{1-\mathrm{x}}{\mathrm{Cd}}_{\mathrm{x}}\mathrm{Te}$ alloys, showing the band closing at the critical composition $x=0.16$. The high-symmetry points correspond to those in the Brillouin zone of the supercell as shown in Fig. 1. (b) The evolution of the calculated band gap of ${\mathrm{Hg}}_{1-\mathrm{x}}{\mathrm{Cd}}_{\mathrm{x}}\mathrm{Te}$ as a function of the composition. (c) The evolution of the calculated TO phonon frequency in ${\mathrm{Hg}}_{1-\mathrm{x}}{\mathrm{Cd}}_{\mathrm{x}}\mathrm{Te}$ as a function of the band gap. The inset shows examples of the calculated optical phonon dispersion. (d) The calculated lattice thermal conductivity of ${\mathrm{Hg}}_{1-\mathrm{x}}{\mathrm{Cd}}_{\mathrm{x}}\mathrm{Te}$ is shown in the left panel. The calculated values are normalized by $v_s^2$ and shown in the right panel.

Figure 5

The calculated mode-resolved phonon scattering rates due to electron-phonon interaction in HgTe (left) and CdTe (right). The color represents the scattering rates of the specific phonon modes.