Fractional quantum Hall states at zero magnetic field.
By Titus Neupert, Luiz H Santos, C. Chamon, C. Mudry. Physical Review Letters, 2010
718 citations recorded by the source corpus.
We present a simple prescription to flatten isolated Bloch bands with a nonzero Chern number. We first show that approximate flattening of bands with a nonzero Chern number is possible by tuning ratios of nearest-neighbor and next-nearest-neighbor hoppings in the Haldane model and, similarly, in the chiral-π-flux square lattice model. Then we show that perfect flattening can be attained with further range hoppings that decrease exponentially with distance. Finally, we add interactions to the model and present exact diagonalization results for a small system at 1/3 filling that support (i) the existence of a spectral gap, (ii) that the ground state is a topological state, and (iii) that the Hall conductance is quantized.
Subfields: Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/99dc387ac8c8fcf8582c8d5b84d46e0e4b11c277
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Citations in the corpus
- Band geometry, Berry curvature and superfluid weight (2016, methodology): “Under these parameters, the lower band ( n < 1) is quasiflat with large flatness ratio and the upper band ( n > 1) is strongly dispersive [11], see Fig.”
- Quantum states and intertwining phases in kagome materials (2023, background): “Based on these effects, the flat band, and tuning its filling in the kagome lattice, can generate many non-trivial topological states 50,86–89 , as well as symmetry-breaking quantum states, including charge or spin orders, nematic phases 51,53,54 , ferromagnetism with spin-polarized bands 56,57,90…”
- Artificial flat band systems: from lattice models to experiments (2018, background): “[83] Titus Neupert, Luiz Santos, Claudio Chamon, and Christopher Mudry, “Fractional quantum Hall states at zero magnetic field,” Phys.”
- Fractional Chern Insulator (2011, methodology): “Several Chern insulator models with an approximate flat band have been recently proposed [8, 10, 12].”