Multifractal properties of critical eigenstates in two-dimensional systems with symplectic symmetry

TL;DR

This paper numerically investigates the multifractal characteristics of critical eigenstates at the metal-insulator transition in a 2D disordered system with spin-orbit interaction, revealing specific relationships between spectral and eigenstate dimensions.

Contribution

It provides new numerical evidence on the multifractal properties and their interrelations in 2D symplectic systems at criticality.

Findings

Relation D₂=2D̃₂ between eigenstate and spectral measure dimensions

Energy correlation exponent η=0.35±0.05

Verification of η=2−D₂ relation

Abstract

The multifractal properties of electronic eigenstates at the metal-insulator transition of a two-dimensional disordered tight-binding model with spin-orbit interaction are investigated numerically. The correlation dimensions of the spectral measure $\widetilde{D}_{2}$ and of the fractal eigenstate $D_{2}$ are calculated and shown to be related by $D_{2}=2\widetilde{D}_{2}$. The exponent $\eta=0.35\pm 0.05$ describing the energy correlations of the critical eigenstates is found to satisfy the relation $\eta=2-D_{2}$.