Corner Multifractality for Reflex Angles and Conformal Invariance at 2D Anderson Metal-Insulator Transition with Spin-Orbit Scattering

TL;DR

This paper demonstrates that boundary multifractality at the 2D Anderson transition with spin-orbit scattering obeys conformal invariance, extending previous results to larger corner angles and refining symmetry relations.

Contribution

It provides numerical evidence linking corner and boundary multifractality through conformal symmetry at the 2D Anderson transition with spin-orbit scattering.

Findings

Multifractal exponents at corners relate to boundary exponents via conformal symmetry.

Extension of corner multifractality results to angles greater than pi.

Refinement of symmetry relations for corner multifractality.

Abstract

We investigate boundary multifractality of critical wave functions at the Anderson metal-insulator transition in two-dimensional disordered non-interacting electron systems with spin-orbit scattering. We show numerically that multifractal exponents at a corner with an opening angle \theta=3\pi/2 are directly related to those near a straight boundary in the way dictated by conformal symmetry. This result extends our previous numerical results on corner multifractality obtained for \theta < \pi to \theta > \pi, and gives further supporting evidence for conformal invariance at criticality. We also propose a refinement of the validity of the symmetry relation of A. D. Mirlin et al., Phys. Rev. Lett. \textbf{97} (2006) 046803, for corners.