Fractional Chern Insulator

By N. Regnault, Bogdan Andrei Bernevig. 2011

448 citations recorded by the source corpus.

Chern insulators are band insulators exhibiting a nonzero Hall conductance but preserving the lattice translational symmetry. We conclusively show that a partially filled Chern insulator at 1/3 filling exhibits a fractional quantum Hall effect and rule out charge-density wave states that have not been ruled out by previous studies. By diagonalizing the Hubbard interaction in the flat-band limit of these insulators, we show the following: The system is incompressible and has a 3-fold degenerate ground state whose momenta can be computed by postulating an generalized Pauli principle with no more than 1 particle in 3 consecutive orbitals. The ground state density is constant, and equal to 1/3 in momentum space. Excitations of the system are fractional statistics particles whose total counting matches that of quasiholes in the Laughlin state based on the same generalized Pauli principle. The entanglement spectrum of the state has a clear entanglement gap which seems to remain finite in the thermodynamic limit. The levels below the gap exhibit counting identical to that of Laughlin 1/3 quasiholes. Both the 3 ground states and excited states exhibit spectral flow upon flux insertion. All the properties above disappear in the trivial state of the insulator - both the many-body energy gap and the entanglement gap close at the phase transition when the single-particle Hamiltonian goes from topologically nontrivial to topologically trivial. These facts clearly show that fractional many-body states are possible in topological insulators.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/d5c9d0080821b4087c1cbaf1765b83b035caa9c8

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In Atomic and Molecular Physics, and Optics

1. Shizeng Lin
2. Umesh Kumar
3. Heqiu Li
4. K. Sun

Citations in the corpus

• Gapless Surface Dirac Cone in Antiferromagnetic Topological Insulator MnBi2Te4 (2019, background): “[4] N.”
• Flat bands, strange metals and the Kondo effect (2023, unknown): “For multi-orbital systems such as the iron pnictides or chalcogenides, the Mott transition can become orbitally selective, allowing metallic behaviour to survive at the largest values of U / W .”
• Fractional quantum Hall physics in topological flat bands (2013, unknown): “The small system size means that this choice can be delicate; see [18] for details.”
• Spontaneous fractional Chern insulators in transition metal dichalcogenide moiré superlattices (2021, background): “However Δ should vanish if only one of N1 or N2 approaches infinity, because this limit is a one-dimensional system which should not support FCI [47].”