Spatial correlations in chaotic nanoscale systems with spin-orbit coupling

We investigate the statistical properties of wave functions in chaotic nanostructures with spin-orbit coupling (SOC), focusing in particular on spatial correlations of eigenfunctions. Numerical results from a microscopic model are compared with results from random matrix theory in the crossover from the Gaussian orthogonal to the Gaussian symplectic ensembles (with increasing SOC); one-and two-point distribution functions were computed to understand the properties of eigenfunctions. It is found that correlations of wave-function amplitudes are suppressed with SOC; nevertheless, eigenfunction correlations play a more important role in the two-point distribution function(s), compared to the case with vanishing SOC. Experimental consequences of our results are discussed.