Thermal Transport Mechanisms in Low-Dimensional Systems

In low-dimensional materials such as nanowires, two-dimensional sheets and one-dimensional chains, heat propagates through vibrational and electronic excitations in ways that diverge markedly from bulk behaviour. At the nanoscale, phonon mean free paths, confinement and boundary scattering become dominant, giving rise to ballistic, diffusive and anomalous heat transport regimes. Ballistic transport occurs when energy carriers traverse the system without scattering, yielding length-independent thermal conductance, whereas diffusive transport adheres to Fourier’s law, with conductivity scaling inversely with length. Between these extremes, integrability, long-range interactions and nonlinearities often induce superdiffusive or subdiffusive behaviour, manifesting as size-dependent conductivity and non-local temperature responses. The interplay of conserved quantities such as momentum and energy underpins these anomalies, while surface roughness and dimensional crossover further modulate thermal flow. Understanding these mechanisms is pivotal for thermal management in nanoelectronics, for the design of phononic devices and for optimising energy conversion processes in low-dimensional systems.

Research from Nature Portfolio

Recent studies have challenged the universality of anomalous Fourier’s law in one-dimensional momentum-conserving fluids. By employing novel scaling analyses of hydrodynamic profiles in diatomic hard-point models, researchers have demonstrated that heat conductivity anomalies can collapse onto a single master curve across diverse gradients, densities and system sizes. This finding reveals that even deep into the nonlinear regime, anomalous conduction need not conform to conventional universality classes, suggesting new bounds on heat current in terms of internal pressure and prompting a re-examination of renormalisation-group predictions for low-dimensional transport.

Thermal Transport Mechanisms in Low-Dimensional Systems publication trend

The graph below shows the total number of articles in thermal transport mechanisms in low-dimensional systems across all publications each year (not limited to Nature Index journals).

Technical terms

Fourier’s law: Macro-scale linear relation between heat flux and temperature gradient.

Ballistic transport: Heat conduction regime with negligible scattering, independent of system length.

Diffusive transport: Conductive regime where thermal conductivity is constant and follows Fourier’s law.

Anomalous transport: Non-Fourier conduction characterised by size-dependent conductivity and non-local effects.

Phonon: Quantised lattice vibration acting as an energy carrier in crystalline solids.

Integrability: Property of certain systems permitting exact solutions and ballistic-like behaviour.

Long-range interaction: Force between particles that decays slowly with distance, affecting collective transport.

References

1. A violation of universality in anomalous Fourier’s law. Scientific Reports (2016).
2. Non-Fourier heat transport in nanosystems. La Rivista del Nuovo Cimento (2023).
3. Observation of thermal transport close to diffusive in a weak long-ranged Fermi-Pasta-Ulam-Tsingou-type model. Physical Review Research (2024).
4. Heat and charge transport in interacting nanoconductors driven by time-modulated temperatures. SciPost Physics (2024).