Zoology of fractional Chern insulators

Abstract

We study four different models of Chern insulators in the presence of strong electronic repulsion at partial fillings. We observe that all cases exhibit a Laughlin-like phase at filling fraction 1/3. We provide evidence of such a strongly correlated topological phase by studying both the energy and the entanglement spectra. In order to identify the key ingredients of the emergence of Laughlin physics in these systems, we show how they are affected when tuning the band structure. We also address the question of the relevance of the Berry curvature flatness in this problem. Using three-body interactions, we show that some models can also host a topological phase reminiscent of the ν = 1/2 Pfaffian Moore-Read state. Additionally, we identify the structures indicating cluster correlations in the entanglement spectra.

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.…”

D-algebra structure of topological insulators

“…Evidence for their existence has been provided in a series of analytical and numerical works in twodimensional Chern insulators [3][4][5][6][7][8][9][10][11] and time-reversal invariant topological insulators [12][13][14]. The plethora of new experimental facts and theoretical ideas discovered in the non-interacting topological insulators suggests that their fractional (i.e.…”

Flat bands with Berry curvature in multilayer graphene

“…Thus far, attention has been focused on systems where the Berry curvature is nearly uniform [11][12][13][14][15][16][17][18][19][20]. However, it is apparent from (1) that non-trivial quantum geometry effects do not require a uniform Berry curvature.…”

“…Recently, a strong interest has emerged in flat band systems as playgrounds for investigating the interplay of strong correlation effects and non-trivial quantum geometry. However, attention has been mostly focused on systems with non-zero integrated Berry curvature, [11][12][13][14][15][16][17][18][19][20], while the effect of the Fubini-Study metric has largely been ignored.…”