Metal-insulator transition in random Kronig-Penney superlattices with long-range correlated disorder

Abstract

We study the electronic properties of disordered $\mathrm{Ga}\mathrm{As}\text{\ensuremath{-}}{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ semiconductor superlattices with structural long-range correlations. The system consists of quantum barriers and wells with different thicknesses and heights which fluctuate around their mean values randomly, following a long-range correlated pattern of fractal type characterized by a power spectrum of the type $S(k)\ensuremath{\propto}1∕{k}^{(2\ensuremath{\alpha}\ensuremath{-}1)}$, where the exponent $\ensuremath{\alpha}$ quantifies the strength of the long-range correlations. For a given system size, we find a critical value of the exponent $\ensuremath{\alpha}$ $({\ensuremath{\alpha}}_{c})$ for which a metal-insulator transition appears: for $\ensuremath{\alpha}<{\ensuremath{\alpha}}_{c}$ all the states are localized, and for $\ensuremath{\alpha}>{\ensuremath{\alpha}}_{c}$, we find a continuous band of extended states. We also show that the existence of extended states causes a strong enhancement of the dc conductance of the superlattice at finite temperature, which increases in many orders of magnitude when crossing from the localized to the extended regime. Finally, we perform finite size scaling and we obtain the value of the critical exponent ${\ensuremath{\alpha}}_{c}$ in the thermodynamic limit, showing that the transition is not a finite-size effect.