Abstract
The metal-insulator phase transition that arises in the Integer Quantum Hall Effect has been characterized through the multifractal nature of extended states near the center of the Lowest Landau Level. In this work, we obtain numerical solutions for the one-electron Hamiltonian with disorder, where the correlation dimension of extended states in the first two Landau Levels is obtained, by taking into account the Rashba spin-orbit coupling in the Hamiltonian. Although, spin-orbit coupling at moderate field intensities has been determined experimentally, there is no theoretical evidence for the nature of the transition in this case. The correlation dimension of extended states for the resolved spin levels is obtained, and within the statistical error, it is found that the Rashba Hamiltonian in presence of disorder, belongs to the same universality class of spin unresolved systems.
Highlights
After the experimental confirmation of the Integer Quantum Hall Effect (IQHE) by Klaus Von Klitzing [1], the main concern was to find a localization theory for two dimensional electron systems (2DES) in presence of disorder
We obtain numerical solutions for the one-electron Hamiltonian with disorder, where the correlation dimension of extended states in the first two Landau Levels is obtained, by taking into account the Rashba spin-orbit coupling in the Hamiltonian
In this work, it has been shown that extended states are present near the center of each spin resolved Landau level
Summary
After the experimental confirmation of the Integer Quantum Hall Effect (IQHE) by Klaus Von Klitzing [1], the main concern was to find a localization theory for two dimensional electron systems (2DES) in presence of disorder. With numerical simulations it is possible to find a solution to the one-electron Hamiltonian with disorder and understand the electronic transport in the 2DES, as a phase transition between localized and extended states. There is a major interest to study 2DES with zero field spin splitting, where it is possible to control the spin-orbit coupling (SOC) parameter by tuning the gate voltage. We study the nature of the phase transition on 2DES with Rashba SOC, in presence of disorder. The Rashba SOC term in the Hamiltonian, couples adjacent Landau levels; we are able to obtain for different SOC parameters, the correlation dimension of extended states near the center of each spin split level.
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