2 1 M ay 2 01 8 Wigner crystallization in topological flat bands B

B lażej Jaworowski, ∗ Alev Devrim Güçlü, Piotr Kaczmarkiewicz, Micha l Kupczyński, Pawe l Potasz, and Arkadiusz Wójs Department of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wroc law University of Science and Technology, 50-370 Wroc law, Poland Department of Physics, Izmir Institute of Technology, IZTECH, TR35430, Izmir, Turkey Abstract We study the Wigner crystallization on partially filled topological flat bands of kagome, honeycomb and checkerboard lattices. We identify the Wigner crystals by analyzing the Cartesian and angular Fourier transform of the pair correlation density of the many-body ground state obtained using exact diagonalization. The crystallization strength, measured by the magnitude of the Fourier peaks, increases with decreasing particle density. The Wigner crystallization observed by us is a robust and general phenomenon, existing in all three lattice models for a broad range of filling factors and interaction parameters. The shape of the resulting Wigner crystals is determined by the boundary conditions of the chosen plaquette. It is to a large extent independent on the underlying lattice, including its topology, and follows the behavior of classical point particles.