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arXiv 2401.04656cond-mat.mes-hall
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二维手征类中受保护的外尔半金属

Protected Weyl semimetals within 2D chiral classes

Faruk Abdulla

AI总结:

本研究修正了二维手征类外尔半金属的K理论分类结论,证明5个手征类中均存在由Z缠绕数表征的稳定外尔节点,且存在零能无色散的受保护费米弧边缘态。

摘要:

三维中的外尔半金属可独立于平移之外的任何对称性而存在。相比之下,二维中的外尔半金属需要额外的对称性(包括晶体对称性)才能存在。此前基于K理论分类的研究表明,手征对称性可以保护二维中的外尔节点。根据K理论,稳定的外尔节点可存在于四个手征类——AIII、BDI、CII和DIII——中,并由$\boldsymbol{\rm Z}$(AIII、BDI、DIII)和$\boldsymbol{\rm Z}_2$(CII)不变量分类。然而后来发现,K理论预测的$\boldsymbol{\rm Z}_2$和平凡指标并不能可靠地指示二维中外尔节点的存在与否。本研究证明,稳定的外尔节点存在于全部五个手征类中,且在二维中可由一个$\boldsymbol{\rm Z}$缠绕数表征。我们通过求解与该对称性类一致的最普遍哈密顿量的显式解,支撑了这一结论。我们还讨论了受保护的费米弧边缘态,它们总是连接具有相反拓扑荷的外尔节点的投影。与三维外尔半金属中的表面态不同,手征类二维外尔半金属中的边缘态完全无色散,且由于受手征对称性保护而保持在零能态。

英文摘要:

Weyl semimetals in three dimensions can exist independently of any symmetry apart from translations. In contrast, in two dimensions, Weyl semimetals require additional symmetries, including crystalline symmetries, to exist. Previous research, based on K-theory classification, suggested that chiral symmetry can protect Weyl nodes in two dimensions. According to K-theory, stable Weyl nodes can exist in four chiral classes-AIII, BDI, CII, and DIII-and are classified by $\mathbb{Z}$ (AIII, BDI, DIII) and $\mathbb{Z}_2$ (CII) invariants. However, it was later found that the $\mathbb{Z}_2$ and trivial indices predicted by K-theory do not reliably indicate the presence or absence of Weyl nodes in two dimensions. In this study, we demonstrate that stable Weyl nodes exist in each of the five chiral classes and can be characterized by a $\mathbb{Z}$ winding number in two dimensions. Our conclusion is supported by the explicit solution of the most general Hamiltonian consistent with the symmetry class. We also discuss protected Fermi arc edge states, which always connect the projections of Weyl nodes with opposite topological charges. Unlike the surface states in three-dimensional Weyl semimetals, the edge states in two-dimensional Weyl semimetals within chiral classes are completely dispersionless and remain at zero energy due to the protecting chiral symmetry.

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