Anderson Metal-Insulator Transitions With Classical Magnetic Impurities

Abstract

We study effects of classical magnetic impurities on the Anderson metal-insulator transition numerically. We find that a small concentration of Heisenberg impurities enhances the critical disorder amplitude $W_{\mathrm{c}}$ with increasing exchange coupling strength $J$. The resulting scaling with $J$ is analyzed which supports an anomalous scaling prediction by Wegner due to the combined breaking of time-reversal and spin-rotational symmetry. Moreover, we find that the presence of magnetic impurities lowers the critical correlation length exponent $\nu$ and enhances the multifractality parameter ${\alpha }_0$. The new value of $\nu$ improves the agreement with the value measured in experiments on the metal-insulator transition (MIT) in doped semiconductors like phosphor-doped silicon, where a finite density of magnetic moments is known to exist in the vicinity of the MIT. The results are obtained by a finite-size scaling analysis of the geometric mean of the local density of states which is calculated by means of the kernel polynomial method. We establish this combination of numerical techniques as a method to obtain critical properties of disordered systems quantitatively.

5 pages, 2 figures, 2 tables, submitted to PRB

References in corpus (6)

• Anderson Transitions
• The Kernel Polynomial Method
• Critical exponent for the Anderson transition in the three dimensional orthogonal universality class
• Finite-size scaling and multifractality at the Anderson transition for the three Wigner-Dyson symmetry classes in three dimensions
• Dimensional Dependence of Critical Exponent of the Anderson Transition in the Orthogonal Universality Class
• Critical exponent of metal-insulator transition in doped semiconductors: the relevance of the Coulomb interaction

Cited by in corpus (4)

• Anderson transition of cold atoms with synthetic spin-orbit coupling in two-dimensional speckle potentials
• Multifractal finite-size scaling at the Anderson transition in the unitary symmetry class
• Estimate of the critical exponent of the Anderson transition in the three and four dimensional unitary universality classes
• Towards a Comprehensive Theory of Metal-Insulator Transitions in Doped Semiconductors