After limits on layer thickness, a 20-cell silicon–germanium stack, about 10 nanometres long, still leaves more than 786,000 arrangements. A 2026 study used machine learning to seek opposite properties: stacks that impede heat and stacks that let it travel more readily. The results are simulations at 200 K (about −73°C), where coherent heat transport dominates.[1]
Heat can travel through a crystal as vibrations called phonons. Experiments published in Science in 2012 supplied evidence that those vibrations can preserve their wave behaviour across a layered structure. Between 30 and 150 K, measured thermal conductivity increased with the structure’s total thickness, consistent with coherent transport. Calculations supported that interpretation. The finding established an experimental basis for treating layers as a system through which heat-carrying waves propagate.[2]
That perspective complicates the familiar idea that disorder must always obstruct heat. In a separate 2022 silicon–germanium study, researchers first simulated 300 randomly generated arrangements. All conducted heat less effectively than their corresponding periodic references. An iterative machine-learning search nevertheless found exceptional arrangements that reversed that comparison. A non-repeating stack could preserve useful local patterns, even though the whole sequence lacked a regular beat.[3]
The new search began with 800 calculated structures and checked promising candidates with fresh transport calculations. Its lowest conductivity was 0.378 W/mK, versus 0.466 W/mK for a comparison matched in composition, interface count and length: about 19% lower. Its highest value was 1.848 W/mK, roughly 33% above the best periodic reference.[1]
The 2022 analysis connects that behaviour to the spacing of interfaces. When vibrations lose their phase relationship before reaching another boundary, a particle-like scattering description becomes useful. When they retain it across closely spaced boundaries, interference and collective wave modes matter. Counting boundaries alone cannot describe all those relationships. The sequence determines which interfaces a vibration encounters, and at what spacing.[3]
Closely grouped interfaces suppressed transmission through repeated weak reflections. Sparse arrangements supported more extended vibrations. The calculations isolate coherent, elastic transport; they do not demonstrate these gains in a fabricated room-temperature cooling device.[1]
The important distinction is between global regularity and local arrangement. A non-repeating stack can still contain stretches that support collective waves. Disorder describes the overall pattern; it does not by itself specify what heat does at each boundary.[3]
Sources & further reading
- Coherent thermal transport in Si-Ge stacks npj Computational Materials · 4 Jun 2026 · Accessed 20 Oct 2026
- Coherent phonon heat conduction in superlattices Science / CaltechAUTHORS · 16 Nov 2012 · Accessed 20 Oct 2026
- Aperiodic superlattice thermal enhancement npj Computational Materials · 21 Jan 2022 · Accessed 20 Oct 2026