Phonon transport in topological insulators such as bismuth selenide (Bi2Se3) presents a unique interplay between surface and bulk contributions due to their distinct structural and symmetry properties. Unlike conventional insulators, topological insulators possess protected surface states, but their phonon dynamics are less explored compared to electronic properties. The thermal transport in these materials is governed by phonons, which exhibit different behaviors in the bulk and surface regions, leading to complex thermal conductivity mechanisms.

The bulk phonon spectrum of Bi2Se3 consists of acoustic and optical branches arising from its layered rhombohedral crystal structure. The weak van der Waals forces between quintuple layers result in anisotropic phonon dispersion, with lower out-of-plane stiffness compared to in-plane bonding. Longitudinal and transverse acoustic phonons dominate the low-energy thermal transport, while optical phonons contribute minimally due to their low group velocities. The bulk Debye temperature of Bi2Se3 is approximately 180 K, indicating moderate phonon energies. Phonon-phonon scattering, particularly Umklapp processes, becomes significant above 100 K, reducing the bulk thermal conductivity. Point defects and stacking faults further suppress phonon mean free paths, leading to a room-temperature thermal conductivity of around 2 W/mK along the cross-plane direction.

In contrast, surface phonon modes in Bi2Se3 exhibit distinct characteristics due to the termination of the crystal lattice and the presence of topological surface states. Surface acoustic phonons, such as Rayleigh waves, propagate with velocities differing from bulk modes. Measurements using helium atom scattering reveal surface phonon energies in the range of 1-10 meV, with dispersion relations sensitive to surface termination and adsorbates. The surface phonon mean free path is typically shorter than bulk phonons due to enhanced scattering from defects and surface roughness. However, the reduced dimensionality of surface phonons can lead to unconventional thermal transport phenomena, including partially ballistic contributions at nanoscale lengths.

The relative contributions of surface and bulk phonons to total thermal transport depend on sample thickness and temperature. In thick samples (>100 nm), bulk phonons dominate thermal conductivity due to their higher volumetric density. As thickness decreases below 10 nm, surface phonon contributions become increasingly significant, accounting for up to 30% of total heat conduction at room temperature. This size effect follows a non-monotonic trend because surface phonons themselves experience reduced mean free paths in ultra-thin samples. Temperature also plays a critical role—surface phonon contributions are more pronounced at low temperatures where bulk Umklapp scattering is suppressed.

Experimental techniques for probing surface versus bulk phonon transport include time-domain thermoreflectance (TDTR) and frequency-domain thermoreflectance (FDTR). These methods measure thermal conductivity with depth sensitivity, allowing separation of surface and bulk contributions. TDTR studies on Bi2Se3 thin films show that surface phonon thermal conductance ranges from 20-50 MW/m2K at room temperature, depending on surface quality. In comparison, the bulk thermal conductance for a 100 nm film is approximately 200 MW/m2K. Raman thermometry provides additional insights by detecting temperature-dependent shifts in surface phonon peaks, revealing their thermal occupation and coupling to bulk modes.

The anisotropic nature of Bi2Se3 phonon transport manifests differently in surface and bulk regimes. Bulk cross-plane thermal conductivity is typically 2-3 times lower than in-plane values due to the weak interlayer bonding. Surface phonon transport shows less anisotropy within the plane but exhibits strong out-of-plane confinement. This anisotropy affects heat dissipation in device applications, where thermal management must account for directional phonon propagation.

Phonon-surface interactions introduce additional complexity to thermal transport. Surface reconstructions in Bi2Se3 create localized phonon modes that scatter propagating surface waves. Oxidation or contamination layers further modify surface phonon dispersion and scattering rates. Controlled surface functionalization can be used to tune surface phonon transport, with hydrogen termination shown to increase surface thermal conductance by up to 20% compared to bare surfaces. These effects are critical for nanoscale devices where surface-to-volume ratios are high.

Theoretical approaches to modeling phonon transport in topological insulators combine first-principles calculations with Boltzmann transport theory. Density functional theory (DFT) calculations of Bi2Se3 phonon dispersion reveal soft optical modes near the zone center, indicative of strong anharmonicity. Molecular dynamics simulations capture the temperature-dependent evolution of surface phonon populations and their coupling to bulk modes. These models highlight how the unique bonding environment at surfaces alters phonon lifetimes compared to the bulk.

Comparative studies between different topological insulators show material-dependent phonon transport characteristics. For instance, Bi2Te3 exhibits higher bulk thermal conductivity than Bi2Se3 due to its heavier constituent atoms and stronger bonding, while Sb2Te3 shows more pronounced surface phonon effects because of its larger surface state penetration depth. Such variations underscore the importance of material selection for thermal management applications.

Future research directions include exploring phonon transport in heterostructures combining topological insulators with other materials. Interface phonon modes at junctions between Bi2Se3 and conventional dielectrics exhibit hybridized character, potentially enabling new heat conduction pathways. Another promising avenue is investigating non-equilibrium phonon dynamics under ultrafast excitation, where surface and bulk phonon populations may thermalize at different timescales. Advances in nanoscale thermometry techniques will enable more precise mapping of phonon temperature gradients at surfaces.

Understanding surface versus bulk phonon transport in topological insulators has practical implications for thermal management in electronic devices. The low bulk thermal conductivity of Bi2Se3 can be advantageous for thermoelectric applications, while surface phonon engineering may improve heat dissipation in nanoscale devices. Further progress in this field requires coordinated efforts in materials synthesis, characterization, and modeling to fully unravel the complex phonon dynamics in these quantum materials.