陈绝缘体边界临界性
Chern insulator boundary criticality
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中文总结 AI 辅助
本文研究存在边界时陈绝缘体相变的手性特征，通过狄拉克质量畴壁结构分析边界临界性，确定相关模式的反常系数，结果可推广至多类拓扑相变。
中文摘要 AI 辅助
我们研究存在边界时陈绝缘体相变中的手性特征。平庸绝缘体与陈数 $C=1$ 的陈绝缘体之间的相变由无质量狄拉克费米子描述，其宇称反常给出临界霍尔电导率 $\u03c3_{xy}=\ rac{1}{2}\ rac{e^2}{h}$。利用狄拉克质量畴壁结构，我们证明手性边缘模式在临界时离域进入体态，但边界费米子关联函数仍保留手性结构并获得体态费米子的标度维数。我们计算电流关联函数，证明体态霍尔响应的反常与边界附近离域手性模式匹配。仅利用半空间中 $(2+1)$ 维共形场论（CFT）的剩余共形对称性，我们确定电流和能量-动量张量关联函数中编码这些模式的宇称奇项，并确定其电磁和引力反常系数。因此，我们的分析适用于一般的时间反演对称性破缺的 $(2+1)$ 维 CFT，超出了自由狄拉克相变的范围。我们还将结果推广到更高陈数相变，以及 $(3+1)$ 维拓扑绝缘体与平庸绝缘体之间的相变。
英文摘要
We investigate signatures of chirality at Chern insulator transitions in the presence of a boundary. The transition between a trivial insulator and a Chern insulator with Chern number $C=1$ is described by a massless Dirac fermion whose parity anomaly gives a critical Hall conductivity $σ_{xy}=\frac{1}{2}\frac{e^2}{h}$. Using a Dirac mass domain wall construction, we show that the chiral edge mode delocalizes into the bulk at criticality, but the boundary fermion correlation function retains a chiral structure and acquires the scaling dimension of the bulk fermion. We compute current correlation functions and demonstrate that the anomaly of the bulk Hall response is matched by delocalized chiral modes near the boundary. Using only the residual conformal symmetry of a (2+1)d conformal field theory (CFT) in a half-space, we identify parity-odd terms in current and energy-momentum tensor correlation functions that encode these modes and determine their electromagnetic and gravitational anomaly coefficients. Our analysis therefore applies to general time-reversal breaking (2+1)d CFTs, beyond the free Dirac transition. In particular, the analysis of the gravitational anomaly is also applicable to the free Majorana CFT governing the transition between a trivial superconductor and a topological superconductor. We also extend our results to more general Chern number changing transitions and to the transition between a (3+1)d topological insulator and a trivial insulator.
发表机构
- Department of Physics and Anthony J. Leggett Institute for Condensed Matter Theory, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校物理系和安东尼·J·莱格特凝聚态理论研究所）
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