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 nanomechanical lattices in the classical regime, i.e., essentially “masses and springs.” We show that the thermal conductance factorizes into topological and nontopological 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.

中文翻译：

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微观力学和纳米力学晶格中能量传输的拓扑量化

通常在量子物理学的背景下讨论的拓扑效应正在成为物理学的中心范例之一。在这里，我们演示了拓扑在经典方式（即基本上是“质量和弹簧”）中通过二聚化的微机械和纳米机械晶格进行的能量传输中的作用。我们表明，热导分解为拓扑和非拓扑成分。前者具有三个离散值，并且由于边缘模式的出现而出现，这些边缘模式阻止了储热器与主体之间的良好接触，从而导致电导率的长度不依赖于减小。从本质上讲，边界处的能量输入大部分停留在该处，这种作用可有效抵抗无序和非线性。这些结果弥合了两个看似脱节的物理学学科，即拓扑学和热传输学，