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

Abstract

We study the electronic properties of disordered GaAs-AlxGa1−xAs 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) ∝ 1/k (2α−1) , where the exponent α quantifies the strength of the long-range correlations. For a given system size, we find a critical value of the exponent α (αc) for which a metal-insulator transition appears: for α < αc all the states are localized, and for α > αc, 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 αc in the thermodynamic limit, showing that the transition is not a finite-size effect.

Conducting to non-conducting transition in dual transmission lines using a ternary model with long-range correlated disorder

“…Recently, analytical as well as numerical studies revealed that delocalized electronic states can exist in a one-dimensional disordered lattice with short-range [3][4][5][6][7] and long-range [8][9][10][11][12][13][14][15][16][17] correlations. In addition, from the scaling theory [21] it is well known that an infinitesimal disorder can cause localization of all states in one-and two-dimensional systems in the thermodynamic limit.…”

Generación De Bandas De Frecuencias Permitidas en Líneas De Transmisión Dual Con Correlación De Largo Alcance en El Desorden

“…A partir de la secuencia con correlación de largo alcance {v j }, generamos la distribución de tres valores de capacitancias C A , C B y C 0 , según el siguiente mapeo [13]:…”

“…El estudio del grado de localización de la función de onda cuántica, en sistemas desordenados con correlación de corto y largo alcance en el desorden, ha sido objeto de gran atención en el último tiempo [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Recientemente se ha introducido correlación de largo alcance en el desorden a través del proceso de "dilución" de los sistemas desordenados [7][8][9][10][11][12].…”

“…En general, en sistemas unidimensionales existen muy pocos casos en los cuales aparecen bandas de estados extendidos cuando existe correlación de largo alcance en el desorden [1][2][3][4]13,14]. Lo que ocurre es que la existencia de correlación en el desorden es condición necesaria, pero no suficiente, para la aparición de estados extendidos.…”

Metallic phase of disordered graphene superlattices with long-range correlations

“…Experimental evidence for discrete the number of the extended states has been observed in random-dimer semiconductor superlattices as a short-range correlated disorder 25 . Long-range correlated sequences of the potential barriers in semiconductor superlattices, however, could result in a continuum of extended states giving rise the mobility edges [26][27][28] . In this paper, we study the conductance of massless Dirac fermions through graphene superlattices with a long-range correlated disorder on the potentials of the barriers.…”