Screening of a Luttinger liquid wire by a scanning tunneling microscope tip: II. Transport properties

TL;DR

This paper investigates how electrostatic coupling between an STM tip and a Luttinger liquid wire affects tunneling current and noise, revealing screening effects that modify transport properties without changing the Fano factor.

Contribution

It introduces a non-perturbative Green's function approach to analyze electrostatic screening effects on transport in a Luttinger liquid wire with an STM tip.

Findings

Screening reduces tunneling current significantly.

Zero-frequency noise is altered but Fano factor remains constant.

Screening impacts finite-frequency noise asymmetry and conductance.

Abstract

We study the effect of an electrostatic coupling between a scanning tunneling microscope tip and a Luttinger liquid wire on the tunneling current and noise between the two. Solving the Dyson equations non perturbatively for a local interaction potential, we derive the Green's functions associated to the wire and to the tip. Interestingly, the electrostatic coupling leads to the existence of new correlators, which we call mixed Green's functions, which are correlators between the bosonic fields of the wire and the tip. Next, we calculate the transport properties up to second order with the amplitude of the tunnel transfer: the tunnel current is strongly reduced by the presence of screening. The zero-frequency noise is modified in a similar way, but the Fano factor remains unchanged. We also consider the effect of the screening on the asymmetry of the finite-frequency non-symmetrized noise and on the conductance.