Hopping tunneling through a quasiperiodic potential.

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Abstract

In this work, we have developed a one-dimensional tight-binding model to investigate the conductivity of tunneling through a quasiperiodic or slowly-varying potential. Our study focuses on the hopping tunneling properties of a tight-binding model in which the on-site potential is replaced by both quasiperiodic and periodic functions. By comparing the hopping transport in scenarios involving a periodic potential and an slowly-varying model, the latter being the only known case of a 1D potential with a mobility edge and a metal-insulator transition, we gain valuable insights. In our analysis, we consider a proposed device situated between two quantum reservoirs in both quasiperiodic and periodic cases. Remarkably, we find that the tunnel transport through the lattice completely diminishes at the band center. This intriguing phenomenon is likely to hold fundamental importance in the interpretation of experimental data.