Anomalous Chern-Simons orbital magnetoelectric coupling of three-dimensional Chern insulators: gauge-discontinuity formalism and adiabatic pumping
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915160691572736 |
|---|---|
| author | Xue, Yang Liu, Jianpeng |
| author_facet | Xue, Yang Liu, Jianpeng |
| contents | Chern-Simons orbital magnetoelectric (OME) coupling is usually the hallmark of nontrivial band topology in three-dimensional (3D) crystalline insulators. However, if a 3D insulator exhibits nonzero Chern number within any two-dimensional plane of the Brillouin zone, then traditionally the Chern-Simons coupling becomes ill defined for such 3D Chern insulators due to topological obstructions. In this work, by employing a ``gauge-discontinuity" formalism, we resolve this long-standing issue and rigorously derive a quantized layer-resolved OME response in 3D Chern insulators. We demonstrate that the difference of the layer-resolved OME coupling between adjacent layers is universally quantized in unit of $-C e^2/h$, where $C$ is the Chern number. This quantization arises from an anomalous contribution to the Chern-Simons OME coupling, which is closely associated with the Berry curvature of the occupied bands and the hybrid Wannier centers along the direction of the Chern vector $(0,0, C)$. Furthermore, we demonstrate that the anomalous Chern-Simons coupling can be transported by an exact integer quantum from one unit cell to its neighboring cell through an adiabatic cyclic pumping process, accompanied by a quantized displacement of Wannier center along the direction of the Chern vector. Our work provides a rigorous theoretical framework for understanding magnetoelectric response in 3D Chern insulators and opens avenues for designing topological quantum phenomena in layered systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13405 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anomalous Chern-Simons orbital magnetoelectric coupling of three-dimensional Chern insulators: gauge-discontinuity formalism and adiabatic pumping Xue, Yang Liu, Jianpeng Mesoscale and Nanoscale Physics Chern-Simons orbital magnetoelectric (OME) coupling is usually the hallmark of nontrivial band topology in three-dimensional (3D) crystalline insulators. However, if a 3D insulator exhibits nonzero Chern number within any two-dimensional plane of the Brillouin zone, then traditionally the Chern-Simons coupling becomes ill defined for such 3D Chern insulators due to topological obstructions. In this work, by employing a ``gauge-discontinuity" formalism, we resolve this long-standing issue and rigorously derive a quantized layer-resolved OME response in 3D Chern insulators. We demonstrate that the difference of the layer-resolved OME coupling between adjacent layers is universally quantized in unit of $-C e^2/h$, where $C$ is the Chern number. This quantization arises from an anomalous contribution to the Chern-Simons OME coupling, which is closely associated with the Berry curvature of the occupied bands and the hybrid Wannier centers along the direction of the Chern vector $(0,0, C)$. Furthermore, we demonstrate that the anomalous Chern-Simons coupling can be transported by an exact integer quantum from one unit cell to its neighboring cell through an adiabatic cyclic pumping process, accompanied by a quantized displacement of Wannier center along the direction of the Chern vector. Our work provides a rigorous theoretical framework for understanding magnetoelectric response in 3D Chern insulators and opens avenues for designing topological quantum phenomena in layered systems. |
| title | Anomalous Chern-Simons orbital magnetoelectric coupling of three-dimensional Chern insulators: gauge-discontinuity formalism and adiabatic pumping |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2502.13405 |