Anharmonicity-driven phonon avoided crossing and anomalous thermal transport in nodal-line semimetal ZrSiS

TL;DR

This work uses first-principles calculations to dissect both phonon- and electron-driven transport in the topological nodal-line semimetal ZrSiS. By incorporating temperature-dependent anharmonic phonon renormalization, the authors find substantial phonon softening and a Γ–Z optical-mode avoided crossing, which together reduce phonon group velocities and suppress the lattice thermal conductivity κ_L, most notably along the c-axis where κ_L can drop by ~16% at room temperature. They also reveal an anomalously large lattice contribution to thermal transport along the c-axis, causing the Lorenz number L to exceed the Sommerfeld value L0 by up to ~3×, while Dirac states support exceptionally high electrical conductivity σ due to high Fermi velocities and weak el–ph coupling. The results underscore the vital role of APR in metallic lattice dynamics and thermal transport, and provide a framework for understanding heat conduction in topological semimetals where lattice and electronic degrees of freedom are strongly intertwined.

Abstract

Understanding thermal and electrical transport in topological materials is essential for advancing their applications in quantum technologies and energy conversion. Herein, we employ first-principles calculations to systematically investigate phonon and charge transport in the prototypical nodal-line semimetal ZrSiS. The results unveil that anharmonic phonon renormalization results in the pronounced softening of heat-carrying phonons and suppressed lattice thermal conductivity ($κ_{\rm L}$). Crucially, anharmonic effects are found to noticeably weaken Zr-S interactions, triggering avoided-crossing behavior of low-frequency optical phonons. The combination of phonon softening and avoided crossing synergistically reduces phonon group velocities, yielding a 16\% suppression in $κ_{\rm L}$ along the $c$-axis at room temperature. Contrary to conventional metals, we discover that the lattice contribution to thermal conductivity in ZrSiS is abnormally large, even dominating heat conduction along the $c$-axis. This unusual behavior results in a substantial deviation of the Lorenz number from the Sommerfeld value -- exceeding it by up to threefold -- thereby challenging the validation of standard Wiedemann-Franz law for thermal conductivity estimation. Moreover, our calculations demonstrate that ZrSiS exhibits exceptional electrical conductivity, attributed to its topological electronic Dirac states that account for both high Fermi velocities and weak electron-phonon coupling. This study provides critical insights into the electrical and thermal transport mechanisms in ZrSiS and highlights the importance of anharmonic effects in the lattice dynamics and thermal transport of metallic materials.

Figures (7)

• Figure 1: (a) Lattice structure of ZrSiS, the bond length for Zr-Si, Zr-S, and Si-Si are marked. (b) The first Brillouin zone of ZrSiS. (c) ICOHP for various chemical bonds represented in (a).
• Figure 2: (a) Phonon spectra of ZrSiS obtained from harmonic approximation (HA) and room temperature (300 K) second-order IFCs. The pink dotted line marks the phonon avoided-crossing characteristic. (b) Phonon vibration mode of the sixth phonon branch at $\Gamma$ point ($\Gamma_{6}$) in the first BZ. (c) Mean square displacement (MSD) of Zr, S, and Si obtained using HA and RT second-order IFCs. (d) Phonon dispersion at 0 K with Gr$\rm{\ddot{u}}$neisen parameters projection. (e) Modulus of second-order IFC ($|\rm{\Phi^{(2)}}|$) in ZrSiS. Bonds from d$_{1}$ to d$_{4}$ are defined in Fig. \ref{['fig1']}(a). (f) Compare the phonon dispersion relation obtained from our toy model with that calculated using the HA.
• Figure 3: The lattice thermal conductivity ($\kappa_{\rm L}$) of ZrSiS along the (a) $a$-axis and (b) $c$-axis, as well as (c) the ratio of $\kappa_{\rm L}$, calculated using different computational approaches. The dotted lines in (c) denote the corresponding ratios of $\kappa_{\rm L}$ along the $a$-axis.
• Figure 4: The spectral $\kappa_{\rm L}$ ($\kappa_{\rm sp}$) and cumulative $\kappa_{\rm L}$ of ZrSiS along (a) $a$-axis and (b) $c$-axis using HA and TD IFCs, respectively.
• Figure 5: (a) The zoom-in plot of phonon dispersions highlighting the phonon softening and avoided crossing behavior. Phonon group velocity of ZrSiS along the (b) $a$-axis, and (c) $c$-axis. (d) The harmonic component of $\kappa_{\rm L}$ ($\kappa_{\mathrm{HA}}$), with the inset illustrating the ratio of $\kappa_{\mathrm{HA}}$ obtained with and without using TD IFCs. (e) Three-phonon (3ph) scattering rates obtained with and without using HA and TD IFCs, as well as the ph-el scattering rates at 300 K. (f) The path-dependent ph-el scattering rates.