Revealing anharmonic contributions and numerical symmetry-breaking effects in the temperature-dependent phonon properties of 2D TMDC/hBN heterostructures

Accurate prediction of phonon propagation is crucial for modeling temperature-dependent properties in solid-state systems—particularly in two-dimensional (2D) materials and their heterostructures, where interfacial effects strongly influence vibrational and thermal behavior. Here, we employ density functional theory to investigate the impact of anharmonicity on thermal expansion and temperature-dependent phonon frequencies in semiconducting monolayers of transition metal dichalcogenides (TMDCs), specifically MoS2 and WS2, and their vertical heterostructures with insulating hexagonal boron nitride. We specifically examine the often-overlooked rotational invariance condition (RIC) of interatomic force constants, a fundamental symmetry requirement. Our results show that thermal expansion significantly affects all geometric parameters in monolayers and heterostructures, including in-plane lattice constants, monolayer thickness, and interlayer separation (with the expansion of the latter reaching ∼2.1 × 10−5 K−1 at 300 K). We also provide first-principles predictions of the temperature dependence of prominent Raman-active E′-like and A1′-like phonon modes in TMDC-based systems, highlighting the roles of thermal expansion and phonon–phonon interactions. Notably, we find that anharmonicity alone can alter the frequency difference of a given Raman-active phonon mode between monolayer and heterostructure forms—by ⩾0.4 cm−1 at 300 K. Furthermore, we demonstrate that neglecting RIC leads to incorrect phonon redshifts, with errors ⩾0.5 cm−1 in monolayers and ⩾0.1 cm−1 in heterostructures at 300 K—potentially exceeding Raman spectroscopy resolution. It also distorts thermal expansion coefficients, with deviations of up to ∼30%. These discrepancies arise primarily from the mischaracterization of out-of-plane acoustic (ZA) phonons, which may exhibit unphysical imaginary frequencies or erroneous quasi-linear dispersion, instead of the symmetry-preserving quadratic behavior. The framework enables accurate modeling of temperature-dependent vibrational and thermal phenomena in a range of 2D systems.