Fractional Chern Insulators in Topological Flat Bands with Higher Chern Number

Abstract

Lattice models forming bands with higher Chern number offer an intriguing possibility for new phases of matter with no analogue in continuum Landau levels. Here, we establish the existence of a number of new bulk insulating states at fractional filling in flat bands with a Chern number C = N > 1, forming in a recently proposed pyrochlore model with strong spin-orbit coupling. In particular, we find compelling evidence for a series of stable states at ν = 1/(2N + 1) for fermions as well as bosonic states at ν = 1/(N + 1). By examining the topological ground state degeneracies and the excitation structure as well as the entanglement spectrum, we conclude that these states are Abelian. We also explicitly demonstrate that these states are nevertheless qualitatively different from conventional quantum Hall (multilayer) states due to the novel properties of the underlying band structure.

Elementary formula for the Hall conductivity of interacting systems

“…Equation (3b) predicts the following results for fractional Chern insulators. [11][12][13][14][15][16][17][18][19][20][21] 1. The integral over the Brillouin zone of F (k) ×n(k) equals a rational number p/q, since Laughlin's gauge argument for quantization then applies.…”

Generating many Majorana modes via periodic driving: A superconductor model

“…These results also shed more light on the inherent advantages of driven systems in exploring new topological states of matter, which can be useful for other timely topics related to long-range interactions (e.g., fractional Chern insulators. 49,50 )…”

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] .…”