Screening of a Luttinger liquid wire by a scanning tunneling microscope tip: I. Spectral properties

TL;DR

This paper investigates how a scanning tunneling microscope tip influences the spectral properties of an interacting quantum wire, revealing significant deviations in local density of states due to electrostatic screening.

Contribution

It provides a non-perturbative analysis of the spectral properties of a Luttinger liquid wire under electrostatic screening by a STM tip using bosonization.

Findings

Screening by the tip significantly alters the spectral function.

Local density of states deviates strongly when the tip is close.

Deviations depend on Coulomb interaction and screening strength.

Abstract

The screening effect due to a scanning tunneling microscope tip which is placed in the vicinity of an interacting quantum wire is considered. With the help of a bosonization procedure, we are able to determine non perturbatively the Green's functions of the quantum wire in the presence of both electrostatic screening by the tip and Coulomb interactions in the wire. In our approach we justify that the working Hamiltonian of the whole system is quadratic when $K_c>1/2$ and can be solved by integration over the degrees of freedom of the tip. Once the Green's functions are known, we calculate the spectral properties. We show that the spectral function, as well as the tunnel density of states, is affected by the screening and that the local density of states strongly deviates from its unscreened value when the tip gets close to the wire. Moreover, we observe that the spatial extension of the deviation of the local density of states is related to both the Coulomb interactions parameter and the screening strength.