Landauer conductance of tunnel junctions: Strong impact from boundary conditions

TL;DR

This paper investigates how boundary conditions significantly influence the Landauer conductance calculations for tunnel junctions, revealing that using periodic models can lead to overestimations due to resonant scattering effects.

Contribution

It demonstrates that applying the Landauer formula to periodic lattice models for tunneling conductance can be inaccurate, emphasizing the importance of boundary conditions.

Findings

Resonant scattering causes overestimation of conductance by about 1/t.

Periodic models overestimate conductance compared to finite barrier models.

Boundary conditions critically affect tunneling conductance calculations.

Abstract

We present model calculations for the Landauer conductance of tunnel junctions. The tunneling of free electrons through a rectangular potential barrier is considered. The conductance of a finite number of barriers was calculated using a transfer matrix method. The periodic arrangement of the same barriers was described by a Kronig-Penney model to calculate the band structure and from that the conductance of a point contact in the ballistic limit. The comparison of both results elucidated the importance of the boundary conditions. Caused by resonant scattering in the superlattice the conductance is overestimated by the order of 1/t, the transmission coefficient of the single barrier. In the case of metallic multilayers these interferences are of minor importance. In conclusion, the application of the Landauer formula to periodic lattices to describe the tunneling conductance of a single barrier is not correct.