Dice Lattice in Ribbons and their Topological Properties

The existence of nearly flat bands with non-zero Chern numbers in a two-dimensional dice lattice has been studied [1] in the presence of Rashba spin-orbit coupling and a magnetic field. In this work, we studied the topological properties of the dice lattice defined using ribbons both with open and periodic boundary conditions. We found that the Chern numbers [2] are finite even for narrow systems such as Nx3 [3]. We also observed spin currents moving along the edges at half filling, when ribbons are in a cylindrical geometry with open conditions in the long direction. Understanding these topological properties in ribbon-like geometry is important because of computationally exact techniques like DMRG can be used to investigate the effect of Hubbard interactions on dice lattices.

[1] F. Wang and Y. Ran, Phys. Rev. B 84, 241103 (2011)
[2] T. Fukui, Y. Hatsugai, and H. Suzuki, J. Phys. Soc. Jpn. 74 (2005)
[3] R. Soni, N. Kaushal, S. Okamoto, and E. Dagotto (in preparation)