Imaging the transition from diffusive to Landauer resistivity dipoles

TL;DR

This study visualizes the transition from diffusive to Landauer resistivity dipoles in 2D Bi films, revealing how defect size influences the dipole behavior and enabling estimation of electronic properties.

Contribution

It provides the first direct imaging of the crossover from diffusive to Landauer resistivity dipoles in a two-dimensional conductor.

Findings

Observed a crossover from linear to constant dipole amplitude scaling with defect size.

Quantified the transition parameters to estimate Fermi wave vector and mean free path.

Demonstrated the fundamental limit of resistance imposed by Landauer dipoles.

Abstract

A point-like defect in a uniform current-carrying conductor induces a dipole in the electrochemical potential, which counteracts the original transport field. If the mean free path of the carriers is much smaller than the size of the defect, the dipole results from the purely diffusive motion of the carriers around the defect. In the opposite limit, ballistic carriers scatter from the defect$-$for this situation, Rolf Landauer postulated the emergence of residual resistivity dipoles that are independent of the defect size and thus impose a fundamental limit on the resistance of the parent conductor. Here, we study resistivity dipoles around holes of different sizes in two-dimensional Bi films on Si(111). Using scanning tunneling potentiometry to image the dipoles, we find a crossover from linear to constant scaling behavior of their amplitudes with defect size, manifesting the transition from diffusive to Landauer dipoles. The extracted parameters of the transition allow us to estimate the Fermi wave vector and the carrier mean free path in our Bi films.