Metal-insulator transition in an aperiodic ladder network: an exact result

TL;DR

This paper analytically demonstrates a metal-insulator transition in a quasiperiodic ladder network, revealing multiple mobility edges and confirming results with numerical conductance calculations.

Contribution

It provides an exact analytical solution for the metal-insulator transition in a quasiperiodic ladder network, complemented by numerical conductance analysis.

Findings

Multiple mobility edges identified in the spectrum.

Exact analytical conditions for transition at specific hopping parameters.

Numerical conductance results support the analytical predictions.

Abstract

We show, in a completely analytical way, that a tight binding ladder network composed of atomic sites with on-site potentials distributed according to the quasiperiodic Aubry model can exhibit a metal-insulator transition at multiple values of the Fermi energy. For specific values of the first and second neighbor electron hopping, the result is obtained exactly. With a more general model, we calculate the two-terminal conductance numerically. The numerical results corroborate the analytical findings and yield a richer variety of spectrum showing multiple mobility edges.