Fractional quantum Hall interface induced by geometric singularity

The geometric response of quantum Hall liquids is an important aspect to understand their topological characteristics in addition to the electromagnetic response. According to the Wen-Zee theory, the topological spin is coupled to the curvature of the space in which the electrons reside. The presence of conical geometry provides a local isolated geometric singularity, making it suitable for exploring the geometric response. 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 in which the distances between two adjacent orbits gradually change and can be easily adjusted by altering the tip angle. The presence of a cone tip introduces a geometric singularity that affects the electron density and interacts with the motion of electrons, which has been extensively studied. Furthermore, this type of geometry can automatically create a smooth interface or crossover between the crystalline charge-density-wave state and the liquid-like fractional quantum Hall state. In this work, the properties of this interface are studied from multiple perspectives, shedding light on the behavior of quantum Hall liquids in such geometric configurations.