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Updated: May 30, 2026
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Advanced Experimental Methods for Low-temperature Magnetotransport Measurement of Novel Materials
Published on: January 21, 2016
Fractional quantum Hall states at zero magnetic field
Titus Neupert1, Luiz Santos, Claudio Chamon
1Condensed Matter Theory Group, Paul Scherrer Institute, Villigen PSI, Switzerland.
Physical Review Letters
|July 21, 2011
Summary
We developed a method to flatten isolated Bloch bands with a nonzero Chern number using tunable hoppings. This approach ensures a spectral gap, a topological ground state, and quantized Hall conductance in interacting systems.
Area of Science:
- Condensed Matter Physics
- Topological Materials
Background:
- Bloch bands with nonzero Chern numbers are crucial for topological phenomena.
- Achieving flat bands is key to realizing strongly correlated topological states.
Purpose of the Study:
- To present a simple prescription for flattening isolated Bloch bands with a nonzero Chern number.
- To investigate the role of interactions in these flattened band systems.
Main Methods:
- Tuning ratios of nearest-neighbor and next-nearest-neighbor hoppings in lattice models.
- Introducing further-range hoppings that decay exponentially with distance.
- Employing exact diagonalization for small interacting systems at 1/3 filling.
Main Results:
- Approximate band flattening achieved by tuning hopping parameters in Haldane and chiral-π-flux models.
- Perfect band flattening realized with exponentially decaying long-range hoppings.
- Exact diagonalization confirms a spectral gap, a topological ground state, and quantized Hall conductance in the interacting system.
Conclusions:
- The proposed prescription effectively flattens Bloch bands with a nonzero Chern number.
- The flattened bands support topological phases even with the inclusion of interactions.
- This work provides a pathway for designing novel topological materials.
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