Corner multifractality for reflex angles and conformal invariance at 2D Anderson metal-insulator transition with spin-orbit scattering

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. 97 (2006) 046803, for corners.