Kristen Kaasbjerg

Title: Single-molecule junctions - polarization effects and electronic
structure

A thesis submitted for the degree of Doctor of Philosophy on October, 2009.

Nano-Science Center
Niels Bohr Institute
The Graduate School
of Science
Faculty of Science
University of Copenhagen
Denmark

Supervisor: 
Karsten Flensberg
 

Abstract

Single-molecule junctions - polarization effects and electronic structure

This thesis addresses the electronic structure of single-molecule nanojunctions. Over the past decade the experimental field of single-molecule electronics has progressed tremendously. This has led to the realization of the single-molecule version of the field effect transistor. Due to a weak coupling between the molecule and the metal electrodes, these single-molecule transistor function similarly to single-electron transistors. The theoretical understanding of single-molecule junctions is, however, far from complete. Due to their small size, Coulomb interactions between the charge carriers on the molecule and polarization charges in the neighboring junction environment plays an important role for their fundamental properties.

A theoretical framework taking into account this effect is developed. It is based on an continuum electrostatic description of the junction combined with a quantum mechanical description of the molecule. The main result is an effective Hamiltonian for the molecule in which the junction is represented by its electrostatic potential. Hence, the solution to Poisson's equation for a given junction geometry is an important part of this approach. The framework is readily integrated into existing implementations of standard electronic structure methods.

In the present work a semi-empirical implementation of the approach has been applied to study polarization effects in a realistic single-molecule transistor. The Coulomb interaction between the molecule and the environment is demonstrated to alter the molecular electronic structure significantly. This is in agreement with experimental observations on single-molecule transistors. Furthermore, some general properties related to the electrostatic potential in single-molecule junctions are addressed.

Similar polarization effects can be expected to play a role for the electronic structure of metal-molecule interfaces where the molecule is chemically bonded to the surface. Theoretical descriptions of such interfaces are however complicated by the bonding between the surface and the molecule. A many-body description which treats the molecule and the surface on equal footing is one possible approach. The Green's function based GW method belongs to this type of methods. Recent theoretical first-principles studies of molecules on surfaces have demonstrated that GW gives a qualitative correct description of the molecular levels when physisorbed on metallic and dielectric surfaces. It is therefore important to know how well GW describes the electronic structure of isolated molecules. A benchmark study comparing GW with exact results for semi-empirical model descriptions of molecules is here given. It shows that GW gives a consistent and good description of molecular levels. In conjunction with the fact that surface polarization effects are included in GW, this makes the GW method well suited for the study of metal-molecule interfaces.