Topological effects typically discussed in the context of quantum physics are
emerging as one of the central paradigms of physics. Here, we demonstrate the
role of topology in energy transport through dimerized micro- and
nano-mechanical lattices in the classical regime, i.e., essentially "masses and
springs". We show that the thermal conductance factorizes into topological and
non-topological components. The former takes on three discrete values and
arises due to the appearance of edge modes that prevent good contact between
the heat reservoirs and the bulk, giving a length-independent reduction of the
conductance. In essence, energy input at the boundary mostly stays there, an
effect robust against disorder and nonlinearity. These results bridge two
seemingly disconnected disciplines of physics, namely topology and thermal
transport, and suggest ways to engineer thermal contacts, opening a direction
to explore the ramifications of topological properties on nanoscale technology.Comment: 6 pages, 3 figures; Supplemental information included as an ancillary
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