Bulk-boundary correspondence (BBC) remains the central topic in modern condensed matter physics and has received a boost of interest with the recent discovery of non-Hermitian skin effects. However, there still exist profound features of BBC that are beyond the existing framework. Here, we report the unexpected behavior of BBC when the Hamiltonian contains terms of the form d0(k)I , which serves as a momentum dependent energy shift. For Hermitian cases, the momentum dependent energy shift can force the system to be metallic, where topological phase transitions can take place with the upper and the lower bands kept untouched. The modified BBC should be reconstructed from the perspective of the indirect band gap. In non-Hermitian cases, skin effects are found to be capable of coexisting with the preserved BBC, of which the process can be greatly facilitated by the complex d0(k)I . Remarkably, such results can be led to a further step, and contrary to the intuition, the modified BBC in Hermitian systems can be restored to be conventional by including extra non-Hermiticity. The physical origin for these phenomena lies in that d0(k)I can drastically change the point gap topology. Finally, the corresponding experimental simulations are proposed via the platforms of electric circuits.

中文翻译：

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具有动量相关能量转移的拓扑系统中的体边界对应

体边界对应（BBC）仍然是现代凝聚态物理学的中心主题，并且随着最近发现的非厄米集肤效应而引起了人们的兴趣。然而，BBC仍然存在着超出现有框架的深刻特征。在这里，我们报告了当哈密顿量包含以下形式的项时 BBC 的意外行为 d0（k）我 ，它作为动量依赖的能量转移。对于厄米特情况，动量相关的能量转移可以迫使系统成为金属性的，其中拓扑相变可以在上能带和下能带保持不变的情况下发生。修改后的BBC应该从间接带隙的角度进行重构。在非厄米特情况下，集肤效应被发现能够与保留的 BBC 共存，该过程可以通过复杂的方法极大地促进 d0（k）我 。值得注意的是，这样的结果可以进一步推进，与直觉相反，厄米系统中修改后的 BBC 可以通过包含额外的非厄米性来恢复为常规系统。这些现象的物理根源在于 d0（k）我 可以极大地改变点间隙拓扑。最后，通过电路平台提出了相应的实验模拟。