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arXiv:2605.08162

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

R. A. C. Correa, K. N. M. Sharma, P. Lolur, J. van Velzen

cond-mat.mes-hallcond-mat.mtrl-scihep-thquant-phSubmitted May 4, 2026• Announced May 5, 2026
v1 · May 4, 2026v2 · May 13, 2026
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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.

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Thermal fluctuations, the microscopic fluctuations of things due to their temperature, counteract order in many-body systems. Thermal fluctuations often lead to high-temperature disordered phases and low-temperature ordered ones. In lower dimensions, thermal fluctuations are relatively stronger with two-dimensional materials being just on the brink of thermal fluctuations destroying their order. Twodimensional materials therefore display unique behaviour, for example undergoing a superfluid phase transition driven by point-like topological defects. In this work, we realise two-dimensional bosonic quantum gases of the isotope Rb-87 in precisely controlled potentials to study how quantum-tunnelling and spatially disordered potentials affect the phases of matter they form. We also present a new scheme for cooling quantum gases directly in the finely tuned radiofrequency-dressed traps confining the gases in our experiments. To study tunnel-coupled gases, this work utilises a novel method to read out information from bilayer quantum gas experiments by analysing noise patterns arising from interference effects. We find that quantum-tunnelling between the two layers in a bilayer system can cause both layers to remain superfluid at higher temperatures than without quantum tunnelling. We compare our results to predictions using renormalisation-group theory and numerical simulations. We experimentally observe the predicted double-layer superfluid phase, a novel phase where the U(1) symmetry of the relative phase is broken and relative excitations are suppressed. Separately, we investigate the topological Berezinskii-Kosterlitz-Thouless phase transition in disordered two-dimensional Bose gases. We find that such systems can be driven across this phase transition by increasing the strength of an applied disordered potential. We experimentally map out the phase diagram for a continuous 2D Bose gas in the presence of disorder, which has not previously been carried out to the best of our knowledge. We find that the presence of disorder increases the number of topological defects at a given temperature while reducing the rate at which the number of defects increases with temperature. The experimental results for 2D disordered Bose gases are in qualitative agreement with numerical simulations for the parameter regime studied.