Particlelike Phonon Propagation Dominates Ultralow Lattice Thermal Conductivity in Crystalline ${\mathrm{Tl}}_3{\mathrm{VSe}}_4$

We investigate the microscopic mechanisms of ultralow lattice thermal conductivity (${\kappa }_l$) in ${\mathrm{Tl}}_3{\mathrm{VSe}}_4$ by combining a first principles density functional theory based framework of anharmonic lattice dynamics with the Peierls-Boltzmann transport equation for phonons. We include contributions of the three- and four-phonon scattering processes to the phonon lifetimes as well as the temperature dependent anharmonic renormalization of phonon energies arising from an unusually strong quartic anharmonicity in ${\mathrm{Tl}}_3{\mathrm{VSe}}_4$. In contrast to a recent report by Mukhopadhyay et al. [Science 360, 1455 (2018)] which suggested that a significant contribution to ${\kappa }_l$ arises from random walks among uncorrelated oscillators, we show that particlelike propagation of phonon excitations can successfully explain the experimentally observed ultralow ${\kappa }_l$. Our findings are further supported by explicit calculations of the off-diagonal terms of the heat current operator, which are found to be small and indicate that wavelike tunneling of heat carrying vibrations is of minor importance. Our results (i) resolve the discrepancy between the theoretical and experimental ${\kappa }_l$, (ii) offer new insights into the minimum ${\kappa }_l$ achievable in ${\mathrm{Tl}}_3{\mathrm{VSe}}_4$, and (iii) highlight the importance of high order anharmonicity in low-${\kappa }_l$ systems. The methodology demonstrated here may be used to resolve the discrepancies between the experimentally measured and the theoretically calculated ${\kappa }_l$ in skutterides and perovskites, as well as to understand the glasslike ${\kappa }_l$ in complex crystals with strong anharmonicity, leading towards the goal of rational design of new materials.

Figure 1

(a) Calculated temperature-dependent phonon dispersions from $T=0$ to 300 K. The disks at the $\mathrm{\Gamma }$ point depict the experimental measurements at 300 K [16]. (b) and (c) Atom-decomposed phonon density of states at $T=0$ and 300 K, respectively. The shaded gray areas depict the total density of states. (d) Crystal structure of ${\mathrm{Tl}}_3{\mathrm{VSe}}_4$, which features a sublattice formed by ${\mathrm{VSe}}_4^{3-}$ tetrahedral units with loosely bound Tl atoms, visualized using VESTA software [19]. (e) Comparison of theoretical (solid and dashed lines) and experimental (squares) temperature dependent atomic mean square displacements along the [111] direction for Tl (gray), V (blue), and Se (orange) atoms. The dashed lines are calculated in the harmonic approximation, and the solid lines are from the self-consistent phonon approximation. The inset depicts the anisotropic thermal displacement ellipsoids of Tl and Se atoms with the principal ellipses denoted by black solid lines.

Figure 2

(a) A schematic showing the ladder of approximations for calculating ${\kappa }_l$. The levels of theory with accuracy from low to high are $\mathrm{HA}+3\mathrm{ph}$, $\mathrm{SCPH}+3\mathrm{ph}$ and $\mathrm{SCPH}+3,4\mathrm{ph}$, where HA and SCPH denote, respectively, the harmonic (without renormalization) and self-consistent phonon approximations (with renormalization) for calculating phonon energy, and $3/4\mathrm{ph}$ denote three- or four-phonon scattering processes considered in computing phonon scattering rates. (b) Comparison of 3ph scattering rates ($1/{\tau }_{\lambda }$) calculated in the HA (blue) and the SCPH (pink) approximations, respectively. The purple dots depict the calculated 4ph scattering rates in the SCPH approximation. The solid black line assumes the scattering rate to be twice the vibrational frequency, as adopted in the Cahill model [7] to estimate minimum ${\kappa }_l$. (c) Comparison of cumulative (solids lines) and differential (dashed lines) ${\kappa }_l$ calculated using different levels of theory. (d) Same as (c) but for the mean free path cumulative ${\kappa }_l$. All results were obtained at $T=300\mathrm{K}$.

Figure 3

(a) Temperature-dependent ${\kappa }_l$ calculated at three levels of theory in comparison with experimental measurements [16]. (b) Calculated ${\kappa }_l$ (shaped region) considering additional phonon-grain boundary scattering on top of $\mathrm{SCPH}+3,4\mathrm{ph}$. Grain sizes ranging from 50 to 10 000 nm are considered.