Nonlinear Coherent Transport in 2D Thermal Metamaterials: From Solitons and Topological Defects to Quantum Computing

TL;DR

This paper develops a unified theoretical framework for 2D thermal metamaterials, revealing a two-channel heat transport mechanism involving nonlinear coherent excitations and incoherent modes, with implications for thermal management and quantum regimes.

Contribution

It introduces minimal models for 2D thermal transport, linking microscopic nonlinearity and geometry to heat channeling, and connects classical and quantum regimes beyond standard simulations.

Findings

Experimental results in PdSSe monolayers show ultra-low thermal conductivity with high mobility.

Silicon phononic structures exhibit anisotropic heat flow consistent with the two-channel model.

Theoretical predictions align with recent computational studies, validating the framework.

Abstract

Understanding heat transport in low-dimensional and nano-architectured materials remains a central challenge in nonequilibrium statistical physics due to persistent deviations from Fourier's law. These deviations are driven by anharmonicity, reduced dimensionality, and the emergence of long-lived coherent excitations. In this work, we develop a unified theoretical framework for two-dimensional thermal metamaterials that combines nonlinear lattice dynamics, soliton-based effective field theories, and geometrically organized defect networks as guiding structures for energy flow. We introduce minimal discrete and continuum-inspired models suitable for controlled benchmarking of thermal transport in patterned two-dimensional architectures and identify a two-channel transport mechanism in which coherent nonlinear excitations coexist with incoherent hydrodynamic modes. The interplay between these channels is shown to be highly sensitive to geometry, nonlinearity, and temperature, offering new avenues for thermal management. We establish rigorous connections between microscopic nonlinearity, geometry-driven channeling of heat in two dimensions, and quantum-enabled exploration of both high-occupation classical regimes and genuinely quantum regimes beyond the reach of standard simulation strategies. The theoretical predictions are corroborated by recent experimental and computational results in Stone-Wales-defected PdSSe monolayers and silicon phononic crystal nanostructures, which exhibit ultra-low thermal conductivity coexisting with high carrier mobility and strong anisotropy -- direct manifestations of the two-channel mechanism. This synthesis provides actionable guidance for the design of engineered heat-spreading architectures and positions quantum simulation as a transformative tool for advancing the theory of nonlinear heat transport.