Critical behaviour at the metal-insulator transition in 3-dimensional disordered systems in a strong magnetic field

TL;DR

This study analyzes spectral fluctuations in 3D disordered systems under strong magnetic fields, revealing that certain critical behaviors at the metal-insulator transition are unaffected by time reversal symmetry.

Contribution

It demonstrates that the critical behavior at the metal-insulator transition is independent of time reversal symmetry in 3D disordered systems with strong magnetic fields.

Findings

Large s behavior of P(s) and Δ3(L) are symmetry-independent.

Small s behavior of P(s) depends on magnetic field presence.

Metal-insulator transition symmetry is unaffected by magnetic field strength.

Abstract

The critical behaviour of 3-dimensional disordered systems in a strong magnetic field is investigated by analysing the spectral fluctuations of the energy spectrum. The level spacing distribution $P(s)$ as well the Dyson-Mehta statistics $\Delta_{3}(L)$ are considered. Except for the small $s$ behaviour of $P(s)$, which depends on the presence or absence of a magnetic field but not on its strength, the other quantities, large $s$ behaviour of $P(s)$ and $\Delta_{3}(L)$, turn out to be independent of its presence or absence and therefore of the time reversal symmetry. This suggests that the metal-insulator transition, which is defined by the symmetry of the system {\it at} the critical point, is independent of the presence or absence of the time reversal symmetry.