Related Experiment Video
Updated: May 18, 2026

Advanced Experimental Methods for Low-temperature Magnetotransport Measurement of Novel Materials
Published on: January 21, 2016
Metallic phase of the quantum Hall effect in four-dimensional space
J M Edge1, J Tworzydło, C W J Beenakker
1Instituut-Lorentz, Universiteit Leiden, Leiden, The Netherlands.
Abstract:
We study the phase diagram of the quantum Hall effect in four-dimensional (4D) space. Unlike in 2D, in 4D there exists a metallic as well as an insulating phase, depending on the disorder strength. The critical exponent ν≈1.2 of the diverging localization length at the quantum Hall insulator-to-metal transition differs from the semiclassical value ν=1 of 4D Anderson transitions in the presence of time-reversal symmetry. Our numerical analysis is based on a mapping of the 4D Hamiltonian onto a 1D dynamical system, providing a route towards the experimental realization of the 4D quantum Hall effect.
Related Concept Videos
The Hall Effect
Theory of Metallic Conduction
In this theory, Newton's second law of motion is used to determine the acceleration of an electron in the presence of an applied electric field. Then, its velocity is expressed via this acceleration.
An electron moves through the crystal, containing positive ions,...
Crystal Field Theory - Octahedral Complexes
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
Metallic Solids
All metallic solids exhibit high thermal and electrical conductivity, metallic luster, and malleability. Many...
The Pauli Exclusion Principle
Quantum Numbers
