Chiral topologically ordered insulating phases in arrays of interacting integer quantum Hall islands

Abstract

We study arrays of Coulomb-blockaded integer quantum Hall islands with even fillings ν = 2k (k being an integer). Allowing only spin-current interactions between the islands (i.e., without any charge transfer), we obtain solvable models leading to a rich set of insulating SU (2) k topologically ordered phases. The case with k = 1 is dual to the Kalmeyer-Laughlin phase, k = 2 to Kitaev's chiral spin liquid and the Moore-Read state, and k = 3 contains a Fibonacci anyon that may be utilized for universal topological quantum computation. Additionally, we show how the SU (2) k topological phases may be obtained also in an array of islands with ν = 2k integer quantum Hall states and critical spin chains in a checkerboard pattern. We discuss the stability of these topologically ordered phases, their bulk excitations, and show that their thermal Hall conductance is universal, reflecting the central charge c = 3k/(k + 2) of the chiral edge modes.