# Scanning Tunneling Potentiometry, Charge Transport and Landauer's Resistivity Dipole from the Quantum to the Classical Transport Regime

## TL;DR

This paper explores how electro-chemical potential and local current patterns relate across quantum to classical regimes, revealing defect-induced resistivity dipoles and the transition from quantum to Ohmic behavior.

## Contribution

It introduces a comprehensive analysis of potential and current patterns using the Keldysh formalism, highlighting the emergence of Landauer resistivity dipoles due to defects.

## Key findings

- Potential and current patterns are similar near the quantum limit.
- Ohm's law applies only in the classical regime.
- Defects create Landauer resistivity dipoles with characteristic current patterns.

## Abstract

Using the non-equilibrium Keldysh formalism, we investigate the spatial relation between the electro-chemical potential measured in scanning tunneling spectroscopy, and local current patterns over the entire range from the quantum to the classical transport regime. These quantities show similar spatial patterns near the quantum limit, but are related by Ohm's law only in the classical regime. We demonstrate that defects induce a Landauer residual resistivity dipole in the electro-chemical potential with the concomitant spatial current pattern representing the field lines of the dipole.