A two-dimensional electron gas in a static external magnetic field exhibits two distinct collective excitation modes. The lower frequency mode propagates along the periphery of the domain almost freely with an extended lifetime, which is referred to as edge magnetoplasmons. Peculiar phenomena caused by a capacitive interaction between nearest neighbor domains are known, such as the emergence of Tomonaga-Luttinger liquid and charge density fractionalization. Meanwhile, the number of coupled domains investigated in the past has been limited to a small number. Here, we performed calculations using a continuum model of edge magnetoplasmons, the band structures of planar crystals composed of an arbitrary number of domains, including a chain, ladder, and honeycomb network, with the general interaction strength. We explain the band structures in terms of the fundamental collective modes of a molecule composed of two equivalent domains. These are the extended chiral propagation modes that yield a linear dispersion band and the standing wave modes localized in the coupled regions that cause a flat band. The chain's band structures resemble the miniband structures calculated from the Kronig-Penny model for the electron in a semiconductor superlattice. We point out that a geometrical deformation of the chain does not change the band structures as it can be expressed as a gauge degree of freedom that only causes a shift in the wavenumber.

31 pages, 9 figures