Topological flat band models with arbitrary Chern numbers

Abstract

We report the theoretical discovery of a systematic scheme to produce topological flat bands (TFBs) with arbitrary Chern numbers. We find that generically a multi-orbital high Chern number TFB model can be constructed by considering multi-layer Chern number C = 1 TFB models with enhanced translational symmetry. A series of models are presented as examples, including a twoband model on a triangular lattice with a Chern number C = 3 and an N -band square lattice model with C = N for an arbitrary integer N . In all these models, the flatness ratio for the TFBs is larger than 30 and increases with increasing Chern number. In the presence of appropriate inter-particle interactions, these models are likely to lead to the formation of novel Abelian and Non-Abelian fractional Chern insulators. As a simple example, we test the C = 2 model with hardcore bosons at 1/3 filling and an intriguing fractional quantum Hall (FQH) state is observed. Introduction -The experimental fractional quantum Hall effect (FQHE) arises from the highly degenerate Landau levels of continuum 2D electron systems, and is described by variational wave functions, first proposed by Laughlin for the primary FQHE states [1] and later generalized by Jain for composite fermion states [2], which are analytic functions of the 2D spatial coordinates. Many important properties of the FQHE, e.g., the hierarchy structures and fractionalized excitations [3,4], can be understood within this framework. It even leads to the predictions of intriguing non-Abelian FQH states at certain filling fractions [5][6][7][8]. Moreover, based on a classification of the pattern of zeros of symmetric (analytic) polynomials, a systematic way to classify FQH states [9,10] has been proposed. Thus, our current theoretical knowledge of FQHE is based on the analytic structure the 2D Landau level (LL) Hilbert space.

Repulsive Casimir Effect with Chern Insulators

“…Although close to experimental limits, the resulting Casimir pressure at such a separation is still within observable bounds [36]. Alternatively, multiorbital [29] or multilayer materials [25,28] with possible larger gaps can bring the force even further within measurable values.…”

“…Our results point towards TI thin films and other systems with higher Chern numbers [25][26][27][28][29] as the most promising future route to realize and control Casimir repulsion.…”

Topological Fulde-Ferrell superfluids in triangular lattices

“…To realize topological state with higher Chern number, one can resort to complicated hoppings [28] or lattices [29]. Nonetheless, the simple triangular lattice favors some topologically nontrivial states, it can produce topological state with higher Chern number by merely the nearest-neighbor hoppings [30,31].…”

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

“…1 into one equivalent single-layer square lattice with Chern number two, as engineered in Ref. 10 . Similarly, we stack the other two-component CB lattices H σ CB , σ = 3, 4 in Eq.…”

“…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] .…”