Zeros of Green functions in topological insulators
Zeros of Green functions in topological insulators
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DOI：
10.1103/physrevresearch.4.023177
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发表时间：
2021-02
影响因子：
4.2
通讯作者：
Takahiro Misawa;Y. Yamaji
中科院分区：
文献类型：
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作者：
Takahiro Misawa;Y. Yamaji
这项研究表明，格林函数对角线分量的零点是可以检测非相互作用拓扑绝缘体的关键量。我们证明了格林函数的零点穿过拓扑相中的带隙。遍历会引起零点的交叉，以及带隙中的零点表面，类似于金属的费米表面。通过计算微观模型的零点，我们发现零点的遍历普遍出现在所有六类传统的非相互作用拓扑绝缘体中。通过利用特征向量-特征值恒等式（线性代数中最近重新发现的关系），我们证明了体格格林函数中零点的遍历是由拓扑相中发生的能带反转保证的。还讨论了零点与检测奇异拓扑绝缘体（例如高阶拓扑绝缘体）的相关性。对于具有最近邻跳跃的哈密顿量，我们还表明无间隙边缘态保证了带隙中的零表面。分析表明，零点可用于检测各种拓扑绝缘体，因此对于寻找新的拓扑材料很有用。
This study demonstrates that the zeros of the diagonal components of Green functions are key quantities that can detect non-interacting topological insulators. We show that zeros of the Green functions traverse the band gap in the topological phases. The traverses induce the crosses of zeros, and the zeros’ surface in the band gap, analogous to the Fermi surface of metals. By calculating the zeros of the microscopic models, we show the traverses of the zeros universally appear in all six classes of conventional non-interacting topological insulators. By utilizing the eigenvector-eigenvalue identity, which is a recently rediscovered relation in linear algebra, we prove that the traverses of the zeros in the bulk Green functions are guaranteed by the band inversions, which occur in the topological phases. The relevance of the zeros to detecting the exotic topological insulators such as the higher-order topological insulators is also discussed. For the Hamiltonians with the nearest-neighbor hoppings, we also show that the gapless edge state guarantees the zeros’ surfaces in the band gap. The analysis demonstrates that the zeros can be used to detect a wide range of topological insulators and thus useful for searching new topological materials.