发表机构
Vocational School, Atlas University（阿特拉斯大学职业学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文以量子电容为统一探针，揭示量子霍尔效应与拓扑绝缘体共享的拓扑边界态密度，并阐明量子化平台下体态并非均匀绝缘的场依赖本质。
AI 中文摘要
量子霍尔效应、拓扑绝缘体和量子电容通常被视为不同的课题，但它们有着共同的主线。体拓扑决定了一个受保护的边界态，而量子电容是少数能够检测态密度的静电方法之一。本文考察了这一联系。整数量子霍尔效应表明，量子化的边界输运具有由陈数给出的拓扑起源，后来扩展到零场下的Z2拓扑绝缘体，其具有螺旋边缘和狄拉克表面态。量子电容最初是为二维电子气开发的，此后已成为绘制量子霍尔效应背后的朗道能级态密度以及拓扑表面态的线性狄拉克态密度的关键技术。这一图景因自洽屏蔽理论而变得复杂，该理论表明量子霍尔体被分割成可压缩和不可压缩区域，这些区域随场移动。局部量子电容测量证实，即使平台保持量子化，体在量子化平台上也不是均匀绝缘的。本文认为，量子电容不是这些现象的次要特征，而是拓扑所强加的边界态密度最清晰的窗口之一，并且它揭示了量子霍尔效应与拓扑绝缘体之间类比所依据的绝缘体假设的局部、场依赖性本质。
英文摘要
The quantum Hall effect, topological insulators and quantum capacitance are usually treated as distinct topics, yet they share a common thread. Bulk topology determines a protected boundary state, and quantum capacitance is one of the few electrostatic methods able to detect the density of states. This paper examines that connection. The integer quantum Hall effect showed that quantised boundary transport has a topological origin given by the Chern number, later extended to zero field in Z2 topological insulators with helical edge and Dirac surface states. Quantum capacitance, developed for two-dimensional electron gases, has since become a key technique for mapping the Landau level density of states underlying the quantum Hall effect and the linear Dirac density of states of topological surface states. This picture is complicated by self-consistent screening theory, which shows that the quantum Hall bulk splits into compressible and incompressible regions that shift with field. Local quantum capacitance measurements confirm that the bulk is not uniformly insulating across a quantised plateau, even though the plateau stays quantised. The paper argues that quantum capacitance is not a secondary feature of these phenomena but one of the clearest windows into the boundary density of states that topology imposes, and that it reveals the local, field-dependent nature of the insulating bulk assumption underlying the analogy between the quantum Hall effect and topological insulators.
