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 θ=3π/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 θ< πto θ> π, 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.

4 pages, 2 figures, Proceedings of EP2DS-17

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• Anderson Transitions
• Exact relations between multifractal exponents at the Anderson transition
• The Anderson Transition in Two-Dimensional Systems with Spin-Orbit Coupling
• Numerical estimation of the $\beta$-function in 2D systems with spin-orbit coupling
• Magnetic properties of Sr_2Fe_1+xMo_1-xO_6 with -1 <= x <= 0.25
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• Exact exponents for the spin quantum Hall transition in the presence of multiple edge channels
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• Optimisation of multifractal analysis using box-size scaling
• Conformal Invariance and Multifractality at Anderson Transitions in Arbitrary Dimensions
• Surface quantum critical phenomena in disordered Dirac semimetals
• Boundary critical behavior of the Gross-Neveu-Yukawa model