The edges of a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime are divided into alternating metallic and insulating strips, with their widths determined by the energy gaps of the QHE states and the electrostatic Coulomb interaction. Local probing of these submicrometer features, however, is challenging due to the buried 2DEG structures. Using a newly developed microwave impedance microscope, we demonstrate the real-space conductivity mapping of the edge and bulk states. The sizes, positions, and field dependence of the edge strips around the sample perimeter agree quantitatively with the self-consistent electrostatic picture. The evolution of microwave images as a function of magnetic fields provides rich microscopic information around the ν=2 QHE state. © 2011 American Physical Society.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-F1-033-02
Acknowledgements: We would like to thank Steve A. Kivelson, Shoucheng Zhang, David Goldhaber-Gordon, and Bertrand I. Halperin for the helpful discussion. The work is supported by NSF grants DMR-0906027 and Center of Probing the Nanoscale PHY-0425897; DOE-DE-FG03-01ER45929-A001 for the equipment; NSF grants ECCS-1001719, DMR-1033046, and DOE-DE-FG02-00-ER45841 for the 2DEG materials; and King Abdullah University of Science and Technology Fellowship (KUS-F1-033-02).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.