论文标题
相应磁通量中的对称指标
Symmetry indicators in commensurate magnetic flux
论文作者
论文摘要
我们得出一个框架，以在受磁通量的系统中应用拓扑量子化学。我们首先在均匀的磁场中得出空间对称算子的作用，该磁场将Zak的磁翻译组扩展到所有晶体对称组。最终，磁对称性形成了晶体对称组的投影表示。结果，与非磁理论相比，频带表示获得了一个额外的规格不变阶段。因此，对称指标的理论与非磁性案例不同。我们举例说明出现在$π$通量的新对称指标。最后，我们将结果应用于磁场中有角状态的受阻原子绝缘子。对称指标揭示了有限通量时拓扑到平整的相变，这通过Hofstadter Butterfly计算得到了证实。在某些阻塞的原子绝缘子中，大量相变提供了高阶拓扑的新探针。
We derive a framework to apply topological quantum chemistry in systems subject to magnetic flux. We start by deriving the action of spatial symmetry operators in a uniform magnetic field, which extends Zak's magnetic translation groups to all crystal symmetry groups. Ultimately, the magnetic symmetries form a projective representation of the crystal symmetry group. As a consequence, band representations acquire an extra gauge invariant phase compared to the non-magnetic theory. Thus, the theory of symmetry indicators is distinct from the non-magnetic case. We give examples of new symmetry indicators that appear at $π$ flux. Finally, we apply our results to an obstructed atomic insulator with corner states in a magnetic field. The symmetry indicators reveal a topological-to-trivial phase transition at finite flux, which is confirmed by a Hofstadter butterfly calculation. The bulk phase transition provides a new probe of higher order topology in certain obstructed atomic insulators.
