Topological defects in flat geometry: The role of density inhomogeneity

Topological defects are found in particles confined to planar disks interacting via the 1/r Coulomb potential. The total interior topological charge is found to monotonically converge to a negative value as the energy decreases during the relaxation process regardless of initial configurations; it is more negative in a larger cluster. The comparison with a uniform hyperbolic tessellation reveals an underlying hyperbolic structure in a low-energy configuration where the particle density increases from the center of the disk to its boundary. An elliptic structure is identified in an opposite particle distribution where the particle density decreases from the center to the edge of the disk. The novel mechanism of density inhomogeneity driven topological defects as well as the underlying geometric structure may shed light in understanding a wide variety of relevant systems.