论文标题
非高铁三维两波型霍夫夫绝缘子
Non-Hermitian three-dimensional two-band Hopf insulator
论文作者
论文摘要
HOPF绝缘子是拓扑绝缘子标准分类之外的三维拓扑绝缘子。在这里，我们考虑了两种类型的非热型HopF绝缘子，一种没有且具有非铁皮皮肤效应的类型。在非热门模型中，Hermitian模型的孤立无间隙点被扩展到有限的方案中。但是，HOPF指数的模量仍在间隙区域中进行量化。没有非铁皮皮肤效应的模型可以准确评估其广义HOPF指数和能量谱，显示出具有周期性和开放边界条件的系统的无间隙 - 政权估计之间的一致性。在零能量平面附近，每当将HOPF指数定量以非零值量化时，就可以观察到费米环，并且Hopf指数的模量与费米环的数量之间存在巨大的边界对应关系。另一个模型表现出广义的布里渊区中的非富甲皮肤效应，并显示了散装状态的偏斜曲线。在存在非铁皮皮肤效应的情况下，HOPF指数和能量谱对边界条件敏感。
The Hopf insulator is a three-dimensional topological insulator outside the standard classification of topological insulators. Here we consider two types of non-Hermitian Hopf insulators, one without and one with the non-Hermitian skin effect. The isolated gapless points of the Hermitian model are broadened into finite regimes in the non-Hermitian models. However, the modulus of the Hopf index remains quantized in the gapped regions. The model without the non-Hermitian skin effect allows an accurate evaluation of its generalized Hopf index and energy spectrum, showing an agreement between the gapless-regime estimations from the systems with periodic- and open- boundary conditions. Near the zero-energy plane, Fermi rings can be observed whenever the Hopf index is quantized at nonzero values, and there is a bulk-boundary correspondence between the modulus of the Hopf index and the number of Fermi rings. The other model manifests the non-Hermitian skin effect in the generalized Brillouin zone and shows the skewed profiles of the bulk states. The Hopf index and energy spectrum are shown to be sensitive to the boundary condition in the presence of the non-Hermitian skin effect.
