Theoretical Description of Scanning Tunneling Potentiometry

TL;DR

This paper develops a quantum transport-based theoretical framework for scanning tunneling potentiometry, enabling better interpretation of experimental measurements on macroscopic samples.

Contribution

It provides a new theoretical description of STP measurement based on the density matrix and quantum transport, connecting to previous results and highlighting future directions.

Findings

Derived expressions for measured voltages under specific assumptions

Connected theoretical results to previous experimental interpretations

Discussed the importance of local density matrix formulation

Abstract

A theoretical description of scanning tunneling potentoimetry (STP) measurement is presented to address the increasing need for a basis to interpret experiments on macrscopic samples. Based on a heuristic understanding of STP provided to facilitate theoretical understanding, the total tunneling current related to the density matrix of the sample is derived within the general framework of quantum transport. The measured potentiometric voltage is determined implicitly as the voltage necessary to null the tunneling current. Explicit expressions of measured voltages are presented under certain assumptions, and limiting cases are discussed to connect to previous results. The need to go forward and formulate the theory in terms of a local density matrix is also discussed.