Pseudo-Band-Structure in a Disordered Quantum Wire Array

Abstract

Transport properties of quantum-wire arrays with disorder in the period are studied theoretically within a self-consistent Born approximation. Although no band gap opens to the lowest order because of the flat average potential, a pseudo-band-structure is recovered in higher order due to effects of strong diffuse Bragg scattering as long as the disorder remains small. A pseudo-band-gap manifests itself in the density of states, the spectral function, and the anisotropic conductivities, and modifies the conductivity in the quantum-wire direction qualitatively in the vicinity of the zone boundary.

Pseudo-Band-Structure of Disordered Lateral Superlattice in Magnetic Field

“…These parameters are the same as those in the previous study. [10][11][12][13] As a basis, we take into account Landau levels lying in the energy range " N =" 0 2. The finite cutoff causes an inappropriate behavior in the results in the vicinity of E=" 0 % 2 as will be shown in the following section.…”

“…5,6) Later calculations with effects of diffuse Bragg scattering in a self-consistent Born approximation have shown that this system has a pseudo-band-structure. 10,11) In fact, the density of states has a dip and the equi-energy lines in the wavevector space have a characteristic feature near the energy corresponding to the first-Brillouin-zone boundary in a perfectly periodic system. The dynamical conductivity also shows the presence of pseudo-interband-transition.…”

Dynamical Conductivity in Disordered Quantum Wire Array

“…In fact, it was successful in demonstrating the opening of a pseudo band gap in the present quantum wire arrays with disorder in their period. 10) In this approximation the self-energy is given by…”

“…Because the huge diffuse Bragg peaks present in the correlation function, the scattering probability has strongly dependent on the electron wave vector. 8,10) Because the number of k points is limited due to computational time, impurities have to be introduced for the purpose of making actual calculations possible. In the following explicit calculations, the largest mean free path for which the sufficient convergence is achieved so far is l=a ¼ 16.…”

“…8,9) Later calculations with effects of higher order scattering included in a self-consistent Born approximation have shown that this system has a pseudo-band-structure. 10) In fact, the density of states has a dip and the equi-energy lines in the wave-vector space have a characteristic feature near the energy corresponding to the Brillouin-zone boundary in a perfectly periodic system.…”