Related Experiment Video
Updated: Jul 7, 2026

Advanced Experimental Methods for Low-temperature Magnetotransport Measurement of Novel Materials
Published on: January 21, 2016
Microscopic theory of the quantum Hall hierarchy
E J Bergholtz1, T H Hansson, M Hermanns
1Department of Physics, Stockholm University, AlbaNova University Center, SE-106 91 Stockholm, Sweden.
Abstract:
We solve the quantum Hall problem exactly in a limit and show that the ground states can be organized in a fractal pattern consistent with the Haldane-Halperin hierarchy, and with the global phase diagram. We present wave functions for a large family of states, including those of Laughlin and Jain and also for states recently observed by Pan et al., and show that they coincide with the exact ones in the solvable limit. We submit that they establish an adiabatic continuation of our exact results to the experimentally accessible regime, thus providing a unified approach to the hierarchy states.
Related Concept Videos
The de Broglie Wavelength
The Uncertainty Principle
The Quantum-Mechanical Model of an Atom
The Bohr Model
The Hall Effect
The Principle of Superposition and the Gravitational Field

