# Quantum Hall effect of interacting electrons in a periodic potential

@article{Pfannkuche1997QuantumHE, title={Quantum Hall effect of interacting electrons in a periodic potential}, author={Daniela Pfannkuche and Allan H. MacDonald Department of Physics and Indiana University and Bloomington and Usa and Max-Planck-Institut fuer Festkoerperforschung and Stuttgart and H Germany}, journal={Physical Review B}, year={1997}, volume={56} }

We consider the influence of an external periodic potential on the fractional quantum Hall effect. For many electrons on a torus, we find that at finite system sizeL the splitting of incompressible ground-state degeneracies by a weak external potential is proportional to exp(2L/j). We present numerical results consistent with a scenario in which j diverges at a continuous phase transition from fractional to integer quantum Hall states which occurs at a critical periodic potential strength…

## 14 Citations

Fractional quantum Hall effect in Hofstadter butterflies of Dirac fermions.

- Physics, MedicineJournal of physics. Condensed matter : an Institute of Physics journal
- 2015

The influence of a periodic potential on the fractional quantum Hall effect (FQHE) states in monolayer graphene is reported on and it is shown that for one-half flux quantum the emergent gaps are due entirely to the electron-electron interaction, whereas for the one-third flux quantum per unit cell these are due to both non-interacting electrons (Hofstadter butterfly pattern) and the electrons-electrons interaction.

Evidence for a fractional fractal quantum Hall effect in graphene superlattices

- Physics, MedicineScience
- 2015

Measurements of high-mobility graphene superlattices where the complete unit cell of the Hofstadter spectrum is accessible are reported and coexistence of conventional fractional quantum Hall effect (QHE) states together with the integer QHE states associated with the fractal HofstadTER spectrum is observed.

Observation of fractional Chern insulators in a van der Waals heterostructure

- Physics, MedicineScience
- 2018

The observation of gapped states at fractional fillings of Harper-Hofstadter bands arising from the interplay of a magnetic field and a superlattice potential in a bilayer graphene–hexagonal boron nitride heterostructure is reported.

Thermodynamic measurements of ultra-clean van der Waals heterostructures

- Physics
- 2019

Author(s): Zibrov, Alexander A | Advisor(s): Young, Andrea F | Abstract: When interactions between electrons dominate over their kinetic energies, this can lead to emergent collective states with new…

Emergent Multi-Flavor
QED3
at the Plateau Transition between Fractional Chern Insulators: Applications to Graphene Heterostructures

- PhysicsPhysical Review X
- 2018

Recent experiments in graphene heterostructures have observed Chern insulators - integer and fractional Quantum Hall states made possible by a periodic substrate potential. Here we study…

Mobility gap in fractional quantum Hall liquids: Effects of disorder and layer thickness

- Physics
- 2005

We study the behavior of two-dimensional electron gas in the fractional quantum Hall regime in the presence of finite layer thickness and correlated disordered potential. Generalizing the Chern…

Rotating electrons in quantum dots: Classical limit

- Physics
- 2007

We solve the problem of a few electrons in a two-dimensional harmonic confinement using a quantum mechanical exact diagonalization technique, on the one hand, and classical mechanics, on the other.…

Fractal butterflies of Dirac fermions in monolayer and bilayer graphene

- Physics, Computer ScienceIET Circuits Devices Syst.
- 2015

An overview of the theoretical understanding of Hofstadter butterflies in monolayer and bilayer graphene is presented and the future prospects of butterfly search are discussed, especially for interacting Dirac fermions in graphene.

Moiré butterflies in twisted bilayer graphene

- Physics
- 2011

The Hofstadter butterfly spectral patterns of lattice electrons in an external magnetic field yield some of the most beguiling images in physics. Here we explore the magnetoelectronic spectra of…

A Model for Separation and Melting of Deoxyribonucleic Acid in Replication and Transcription Processes

- Chemistry, MedicineJournal of biomolecular structure & dynamics
- 2008

A dynamical model on the basis of structure and motion of DNA under the actions of energy released in hydrolysis of adenosine triphosphate (ATP) and enzymes is proposed to understand mechanism and essence of the replication or transcription process and promote quantitative description of these processes.