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Topological effects typically discussed in the context of quantum physics areemerging as one of the central paradigms of physics. Here, we demonstrate therole of topology in energy transport through dimerized micro- andnano-mechanical lattices in the classical regime, i.e., essentially "masses andsprings". We show that the thermal conductance factorizes into topological andnon-topological components. The former takes on three discrete values andarises due to the appearance of edge modes that prevent good contact betweenthe heat reservoirs and the bulk, giving a length-independent reduction of theconductance. In essence, energy input at the boundary mostly stays there, aneffect robust against disorder and nonlinearity. These results bridge twoseemingly disconnected disciplines of physics, namely topology and thermaltransport, and suggest ways to engineer thermal contacts, opening a directionto explore the ramifications of topological properties on nanoscale technology.

Topological quantization of energy transport in micro- and nano-mechanical lattices