Fractional quantum Hall interface induced by geometric singularity

The geometric response, which goes beyond the electromagnetic response, of quantum Hall (QH) liquids is crucial for understanding their topological characteristics. According to the Wen-Zee theory, the topological spin is intricately linked to the curvature of the space in which the electrons exist. The presence of conical geometry offers a local, isolated geometric singularity, making it an ideal setting for exploring geometric responses. In the context of two-dimensional electrons in a perpendicular magnetic field, each Landau orbit occupies the same area. The cone geometry naturally provides a structure where the distances between adjacent orbits vary gradually and can be easily adjusted by modifying the tip angle. The cone tip introduces a geometric singularity that impacts electron density and interacts with electron motion, which has been extensively studied. Additionally, this geometry automatically creates a smooth interface or crossover between the crystalline charge-density-wave state and the liquidlike fractional QH state. In this paper, we investigate the properties of this interface from multiple perspectives, shedding light on the behavior of QH liquids in such geometric configurations.