Series of Abelian and non-Abelian states inC>1fractional Chern insulators

Abstract

We report the observation of a new series of Abelian and non-Abelian topological states in fractional Chern insulators (FCI). The states appear at bosonic filling ν = k/(C + 1) (k, C integers) in several lattice models, in fractionally filled bands of Chern numbers C ≥ 1 subject to on-site Hubbard interactions. We show strong evidence that the k = 1 series is Abelian while the k > 1 series is non-Abelian. The energy spectrum at both groundstate filling and upon the addition of quasiholes shows a low-lying manifold of states whose total degeneracy and counting matches, at the appropriate size, that of the Fractional Quantum Hall (FQH) SU (C) (color) singlet k-clustered states (including Halperin, non-Abelian spin singlet(NASS) states and their generalizations). The groundstate momenta are correctly predicted by the FQH to FCI lattice folding. However, the counting of FCI states also matches that of a spinless FQH series, preventing a clear identification just from the energy spectrum. The entanglement spectrum lends support to the identification of our states as SU (C) color-singlets but offers new anomalies in the counting for C > 1, possibly related to dislocations that call for the development of new counting rules of these topological states.

Topological bands with a Chern numberC=2by dipolar exchange interactions

“…The prime example is the fractional quantum Hall effect, where strong magnetic fields generate Landau levels [3]. Furthermore, lattice models without Landau levels have been proposed for the realization of topological bands [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Notably, spinorbit coupling has emerged as an experimentally promising tool for band structures with topological invariants [22][23][24][25][26][27].…”

Topological flat band models with arbitrary Chern numbers

“…However, both the band gap and the flatness ratio in this model vanish as the Chern number increases. After the submission of the present Letter, another work [42] observes FQH states in our C = 3 triangular lattice model, and C = 4, 5 square lattice models.…”

SU(N) fractional quantum Hall effect in topological flat bands

“…In analogy to the Laughlin fractional quantum Hall (FQH) states in two-dimensional Landau levels 7 , recent numerical studies suggest that a rich series of Abelian FCI emerges when single-component particles partially occupy topological flat bands with higher Chern number C > 1 at fillings ν = 1/(M C + 1) (M = 1 for hardcore bosons and for M = 2 spinless fermions) [8][9][10][11][12][13][14] . For C = 2, these FCIs are believed to be color-entangled lattice versions of two-component Halperin (mmn) FQH states 15 , and the corresponding Haldane pseudopotential Hamiltonians for these FCIs can be constructed [16][17][18] .…”