Exploring 4D quantum Hall physics with a 2D topological charge pump
Exploring 4D quantum Hall physics with a 2D topological charge pump
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DOI：
10.1038/nature25000
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发表时间：
2018-01-04
期刊：
影响因子：
64.8
通讯作者：
Bloch, Immanuel
中科院分区：
文献类型：
--
作者：
Lohse, Michael;Schweizer, Christian;Bloch, Immanuel
物质拓扑态的发现极大地提高了我们对物理系统相变的理解。拓扑相不是用局部序参数来描述的，而是用全局拓扑不变量来描述的，因此对扰动具有很强的鲁棒性。一个突出的例子是二维(2D)整数量子霍尔效应(1)：它的特征是第一陈数，这体现在由外电场诱导的量子化霍尔响应(2)。将量子霍尔效应推广到四维(4D)系统，产生了一个附加的量子化霍尔响应，但它是非线性的，由一个四维拓扑不变量描述--第二陈数(3，4)。在这里，我们报道了具有本征4D拓扑的体响应的观测，并通过测量相关的第二陈氏数来演示它的量子化。通过在有角度的光学超晶格中利用超冷玻色子原子实现二维拓扑电荷泵，我们实现了4D整数量子霍尔效应的动力学版本(5，6)。利用一小团原子云作为局域探针，通过原位成像和现场分辨能带映射，充分表征了系统的非线性响应。我们的发现为实验探索高维量子霍尔系统铺平了道路，在该系统中预测了额外的强关联拓扑相、奇异的集体激发和边界现象，如孤立的Weyl费米子(4)。
The discovery of topological states of matter has greatly improved our understanding of phase transitions in physical systems. Instead of being described by local order parameters, topological phases are described by global topological invariants and are therefore robust against perturbations. A prominent example is the two-dimensional (2D) integer quantum Hall effect(1): it is characterized by the first Chern number, which manifests in the quantized Hall response that is induced by an external electric field(2). Generalizing the quantum Hall effect to four-dimensional (4D) systems leads to the appearance of an additional quantized Hall response, but one that is nonlinear and described by a 4D topological invariant-the second Chern number(3,4). Here we report the observation of a bulk response with intrinsic 4D topology and demonstrate its quantization by measuring the associated second Chern number. By implementing a 2D topological charge pump using ultracold bosonic atoms in an angled optical superlattice, we realize a dynamical version of the 4D integer quantum Hall effect(5,6). Using a small cloud of atoms as a local probe, we fully characterize the nonlinear response of the system via in situ imaging and site-resolved band mapping. Our findings pave the way to experimentally probing higher-dimensional quantum Hall systems, in which additional strongly correlated topological phases, exotic collective excitations and boundary phenomena such as isolated Weyl fermions are predicted(4).