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Register a new userThe Anderson Transition in Two-Dimensional Systems with Spin-Orbit Coupling
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We report a numerical investigation of the Anderson transition in two-dimensional systems with spin-orbit coupling. An accurate estimate of the critical exponent $ u$ for the divergence of the localization length in this universality class has to our knowledge not been reported in the literature. Here we analyse the SU(2) model. We find that for this model corrections to scaling due to irrelevant scaling variables may be neglected permitting an accurate estimate of the exponent $ u=2.73 pm 0.02$.
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The influence of Rashba spin-orbit interaction on the spin dynamics of a topologically disordered hopping system is studied in this paper. This is a significant generalization of a previous investigation, where an ordered (polaronic) hopping system has been considered instead. It is found, that in the limit, where the Rashba length is large compared to the typical hopping length, the spin dynamics of a disordered system can still be described by the expressions derived for an ordered system, under the provision that one takes into account the frequency dependence of the diffusion constant and the mobility (which are determined by charge transport and are independent of spin). With these results we are able to make explicit the influence of disorder on spin related quantities as, e.g., the spin life-time in hopping systems.
We study the Anderson transition for three-dimensional (3D) $N times N times N$ tightly bound cubic lattices where both real and imaginary parts of onsite energies are independent random variables distributed uniformly between $-W/2$ and $W/2$. Such a non-Hermitian analog of the Anderson model is used to describe random-laser medium with local loss and amplification. We employ eigenvalue statistics to search for the Anderson transition. For 25% smallest-modulus complex eigenvalues we find the average ratio $r$ of distances to the first and the second nearest neighbor as a function of $W$. For a given $N$ the function $r(W)$ crosses from $0.72$ to 2/3 with a growing $W$ demonstrating a transition from delocalized to localized states. When plotted at different $N$ all $r(W)$ cross at $W_c = 6.0 pm 0.1$ (in units of nearest neighbor overlap integral) clearly demonstrating the 3D Anderson transition. We find that in the non-Hermitian 2D Anderson model, the transition is replaced by a crossover.
We report a numerical study of Anderson localization in a 2D system of non-interacting electrons with spin-orbit coupling. We analyze the scaling of the renormalized localization length for the 2D SU(2) model and estimate its $beta$-function over the full range from the localized to the metallic limits.
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=3pi/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.
The probability density function (PDF) for critical wavefunction amplitudes is studied in the three-dimensional Anderson model. We present a formal expression between the PDF and the multifractal spectrum f(alpha) in which the role of finite-size corrections is properly analyzed. We show the non-gaussian nature and the existence of a symmetry relation in the PDF. From the PDF, we extract information about f(alpha) at criticality such as the presence of negative fractal dimensions and we comment on the possible existence of termination points. A PDF-based multifractal analysis is hence shown to be a valid alternative to the standard approach based on the scaling of general inverse participation ratios.
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