Biswas Rudro R, Son Dam Thanh
Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907;
Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL 60637
Proc Natl Acad Sci U S A. 2016 Aug 2;113(31):8636-41. doi: 10.1073/pnas.1609470113. Epub 2016 Jul 19.
The quest for universal properties of topological phases is fundamentally important because these signatures are robust to variations in system-specific details. Aspects of the response of quantum Hall states to smooth spatial curvature are well-studied, but challenging to observe experimentally. Here we go beyond this prevailing paradigm and obtain general results for the response of quantum Hall states to points of singular curvature in real space; such points may be readily experimentally actualized. We find, using continuum analytical methods, that the point of curvature binds an excess fractional charge and sequences of quantum states split away, energetically, from the degenerate bulk Landau levels. Importantly, these inter-Landau-level states are bound to the topological singularity and have energies that are universal functions of bulk parameters and the curvature. Our exact diagonalization of lattice tight-binding models on closed manifolds demonstrates that these results continue to hold even when lattice effects are significant. An important technological implication of these results is that these inter-Landau-level states, being both energetically and spatially isolated quantum states, are promising candidates for constructing qubits for quantum computation.
对拓扑相通用性质的探索至关重要，因为这些特征对于特定于系统的细节变化具有鲁棒性。量子霍尔态对平滑空间曲率的响应方面已得到充分研究，但在实验上难以观测。在此，我们超越这一普遍范式，获得了量子霍尔态对实空间中奇异曲率点响应的一般结果；此类点可在实验中轻易实现。我们使用连续分析方法发现，曲率点束缚了一个额外的分数电荷，并且量子态序列从简并的体朗道能级在能量上分裂开来。重要的是，这些朗道能级间的态与拓扑奇点相关联，其能量是体参数和曲率的通用函数。我们在封闭流形上对晶格紧束缚模型进行的精确对角化表明，即使晶格效应显著，这些结果仍然成立。这些结果的一个重要技术意义在于，这些朗道能级间的态作为能量和空间上都孤立的量子态，是构建用于量子计算的量子比特的有前景的候选者。
