Hall Potential and Current Distribution in Quantum Hall Samples Probed by Scanning Force Microscopy at 1.4 Kelvin

Position shift of the Hall voltage drop at one edge of a two-dimensional electron system with increasing magnetic field. © MPI-FKF / E. Ahlswede

To develop a microscopic picture for the quantum Hall effect on a solid base, in the middle of the 1990’s we started to build up a scanning force microscope operated at 1.4 Kelvin to look into the Hall potential distribution of quantum Hall samples. Meanwhile various samples based on (Al,Ga)As heterostructures and graphene have been investigated. Our experimental results contradict the popular current-carrying edge state model for the quantum Hall effect. Even disorder might not be a prerequisite for the presence of a quantum Hall plateau (see ‘Microscopic picture of the quantum Hall effect’).

Publications

A low-temperature scanning force microscope for investigating buried two-dimensional electron systems under quantum Hall conditions
P. Weitz, E. Ahlswede, J. Weis, K. von Klitzing, K. Eberl
Applied Surface Science 157, 349 (2000)

Hall-potential investigations under quantum Hall conditions using scanning force microscopy
P. Weitz, E. Ahlswede, J. Weis, K. von Klitzing, K. Eberl
Physica E 6, 1 (2000) 

Hall potential profiles in the quantum Hall regime measured by a scanning force microscope
E. Ahlswede, P. Weitz, J. Weis, K. von Klitzing, K. Eberl
Physica B 298, 562 (2001)

Hall potential distribution in the quantum Hall regime in the vicinity of a potential probe contact
E. Ahlswede, J. Weis, K. von Klitzing, K. Eberl
Physica E 12, 165 (2002)        

Adiabatic transport and Hall potential measurements in the integer quantum Hall effect
F. Dahlem, E. Ahlswede, J. Weis, K. v. Klitzing
AIP Conference Proceedings 893, 675 (2007)

Cryogenic scanning force microscopy of quantum Hall samples: Adiabatic transport originating in anisotropic depletion at contact interfaces
F. Dahlem, E. Ahlswede, J. Weis, K. v. Klitzing
Physical Review B 82, 12 (2010)

Current distribution and Hall potential landscape towards breakdown of the quantum Hall effect:
a scanning force microscopy investigation
K. Panos, R.R. Gerhardts, J. Weis, K. von Klitzing
New Journal of Physics 16, 113071(2014)

PhD Theses

Untersuchungen zum Verlauf der Hall-Spannung in einem zweidimensionalen Elektronensystem unter den Bedingungen des Quanten-Hall-Effekts mittels eines Raster-Kraft-Mikroskops
Peter Weitz, Dissertation, Universität Hamburg (1999)

Potential- und Stromverteilung beim Quanten-Hall-Effekt bestimmt mittels Rasterkraftmikroskopie
Erik Ahlswede, Dissertation, Universität Stuttgart (2002)

Adiabatic transport in the quantum Hall regime: Comparison between transport and scanning force microscopy investigations
Franck Dahlem, Dissertation, Universität Stuttgart (2008)

Current Distribution and Hall Potential Landscape within the Quantum Hall Effect in Graphene and towards the Breakdown in a (Al,Ga)As Heterostructure
Konstantinos Panos, Dissertation, Universität Stuttgart (2014)

Annual Reports

Hall potential distribution of a two-dimensional electron system in the quantum Hall regime probed by a scanning force microscope (pdf)
J. Weis, E. Ahlswede, P. Weitz, K. von Klitzing, K. Eberl (2000)

Role of ohmic contacts for the current distribution in quantum Hall samples (pdf)
J. Weis,  F.Dahlem, K. v.Klitzing (2008)

Current-induced asymmetries in narrow quantum Hall systems (pdf)
R.R. Gerhardts, K. Panos, J. Weis, K. v. Klitzing (2012)

Current distribution and Hall potential landscape at the breakdown of the Quantum Hall Effect
K. Panos, J. Weis, R.R. Gerhardts, K. von Klitzing (2013)