拓扑超导系统中的第二Chern数和非Abel Berry相位
Second Chern Number and Non-Abelian Berry Phase in Topological Superconducting Systems
摘要：
拓扑学最终揭示了在复杂系统中观察到的完美量子化的根源。二维量子霍尔效应是著名的原型。值得注意的是，拓扑甚至可以在控制参数扮演额外合成维度角色的高维空间中表现出来。然而，到目前为止，已经提出了非常有限数量的高维拓扑系统的实现，一个值得注意的例子是所谓的4D量子霍尔效应。在这里，我们表明，介观超导系统可以实现高维拓扑结构，并表示一个强大的平台来研究一个纯粹的非平凡的第二陈数的量子系统。我们证明了所设计的微波光谱中的积分吸收强度是量子化的，其整数与第二陈数直接相关。最后，我们表明，这些系统也承认一个非阿贝尔贝瑞阶段。因此，他们也实现了一个启发性的范式拓扑非阿贝尔系统在更高的维度。
英文摘要：
Topology ultimately unveils the roots of the perfect quantization observed in complex systems. The 2D quantum Hall effect is the celebrated archetype. Remarkably, topology can manifest itself even in higher-dimensional spaces in which control parameters play the role of extra, synthetic dimensions. However, so far, a very limited number of implementations of higher-dimensional topological systems have been proposed, a notable example being the so-called 4D quantum Hall effect. Here we show that mesoscopic superconducting systems can implement higher-dimensional topology and represent a formidable platform to study a quantum system with a purely nontrivial second Chern number. We demonstrate that the integrated absorption intensity in designed microwave spectroscopy is quantized and the integer is directly related to the second Chern number. Finally, we show that these systems also admit a non-Abelian Berry phase. Hence, they also realize an enlightening paradigm of topological non-Abelian systems in higher dimensions.
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