Acoustic phonon-restricted four-phonon interactions: Impact on thermal and thermoelectric transport in monolayer h-NbN

TL;DR

This work addresses heat and charge transport in the 2D buckled h-NbN monolayer, where mirror-symmetry breaking and a large acoustic–optical gap amplify higher-order phonon processes. Using first-principles density functional theory and Boltzmann transport theory, it shows that four-phonon scattering, especially among acoustic modes and ZA phonons, severely limits the lattice thermal conductivity $\kappa_l$. Tensile strain reduces anharmonicity, modestly increasing $\kappa_l$ while also narrowing the electronic gap and enhancing electrical conductivity, leading to a thermoelectric figure of merit of about $zT \approx 0.7$ at high temperatures when four-phonon effects are included. Overall, the results highlight the necessity of incorporating multi-phonon processes and strain effects for accurate predictions of thermal and thermoelectric performance in low-dimensional materials.

Abstract

To explore the thermal and thermoelectric potential of 2D materials, we study the h-NbN monolayer, which lacks mirror symmetry and features a large acoustic-optical phonon gap and quadratic flexural mode. First-principles calculations and the Boltzmann transport formalism reveal a complex interplay of multi-phonon scattering processes, where flexural phonons and four-phonon interactions play a significant role in heat transport, primarily dominated by acoustic phonons. Notably, the four-phonon interactions are predominantly confined to acoustic phonons. Tensile strain preserves the underlying scattering mechanisms while reducing anharmonicity, consequently, the scattering rates, enhancing thermal conduction. Simultaneously, competing modifications in thermal and electrical transport shape the strain-dependent thermoelectric response, achieving a figure of merit approaching 1 at elevated temperatures, a testament to its thermoelectric promise. Our findings underscore the critical role of microscopic transport modeling in accurately capturing thermal and thermoelectric properties, paving the way for advanced applications of 2D materials.

Figures (6)

• Figure 1: Crystal structure of h-NbN. (a) Top view shows a hexagonal lattice. (b) Side view reveals significant buckling that breaks reflection symmetry, likely influencing heat transport. The short Nb-N bond length indicates strong covalent bonding.
• Figure 2: (a) The phonon dispersion of h-NbN confirms dynamic stability, featuring a quadratic ZA mode near $\Gamma$, a wide A-O gap, and nearly non-dispersive acoustic branches along $M-K$. PDOS analysis shows that acoustic modes are dominated by Nb vibrations, while N contributes mainly to optical modes. (b) The calculated lattice thermal conductivity ($\kappa_l$) shows a significant reduction when four-phonon scattering is included. The mode-resolved $\kappa_l^{\rm mode}$ at 300 K (inset) reveals that this suppression affects all acoustic branches, with the ZA mode being the most severely affected. (c) Scattering rates involving acoustic modes calculated at 300 K indicate that four-phonon processes are weaker at low frequencies, but become comparable to three-phonon scatterings in the intermediate frequency range. Cumulative $\kappa_{l}$ corresponding to total scattering rates are also shown. (d) Mode-resolved acoustic scattering rates show that the ZA mode predominantly governs phonon scattering. Although TA and LA modes exhibit stronger scattering at higher frequencies, their contributions to $\kappa_l$ remain limited.
• Figure 3: (a) Three-phonon (3ph) (b) four-phonon (4ph) scattering rates are presented. At 300K, both three-phonon and four-phonon scattering in monolayer h-NbN are predominantly governed by normal processes rather than Umklapp scattering. Moreover, phonon scattering is primarily driven by all-acoustic processes, specifically the AAA and AAAA channels.
• Figure 4: (a) The h-NbN monolayer remains dynamically stable under tensile strain $\epsilon = 3\%$, with phonon dispersion showing overall softening, a reduced A-O phonon gap, and a transition to nearly linear ZA dispersion near the Brillouin zone centre. (b) Lattice thermal conductivity ($\kappa_l$) increases under tensile strain across all temperatures. Similar to the unstrained case, four-phonon scattering remains equally significant under strain. (c) Phonon softening under strain reduces the group velocity $v_\text{g}$ of all acoustic modes, except for the ZA mode below 1THz, due to its transition toward linear dispersion. Mode-resolved Grüneisen parameter $\gamma$ reveals that anharmonicity is primarily governed by the ZA mode, whose contribution is significantly suppressed under tensile strain.
• Figure 5: (a) Three-phonon $\tau^{-1}_{\rm 3ph}$ and (b) four-phonon $\tau^{-1}_{\rm 4ph}$ scattering rates and their mode-resolved contributions, in the strained monolayer, exhibit a pronounced reduction in the low frequency range, which plays a dominant role in heat conduction. Mode-resolved $\kappa_l$ for (c) ${\rm 3ph}$ and (d) ${\rm 3ph} + {\rm 4ph}$ processes shows that the modest enhancement is primarily driven by the weakening of four-phonon scattering under strain. All results presented are computed at 300K.