Charge transport in a Hubbard-Holstein junction: Preliminary results from a DFT approach.

Abstract

Many-body systems are extremely complicated to describe due to mutual interactions between the constituent particles. This is for example the case of systems with electron-electron (e-e) and electron-phonon (e-ph) interactions.
Here, we consider e-e and e-ph interactions within the Hubbard-Holstein model,
a very popular template to describe electron-phonon systems. Specifically, we perform an explorative investigation of the nonequilibrium (transport) properties of a Hubbard-Holstein single impurity coupled to two finite but large noninteracting 1D chains. Such situation is addressed using Density Functional Theory (DFT), where the one-particle density of a many-body interacting system is determined in terms of a non interacting many-particle image system.
In more detail, we calculate the electronic density by solving the so-called Kohn-Sham equations, while the central ingredient of the DFT approach, the exchange-correlation potential, is obtained from a reference system using an adiabatic and local density approximation. At the same time, the phonon displacement is evaluated within the Ehrenfest approximation. This two-component (electron+phonon)
Kohn-Sham system is time evolved via numerical methods.
The conduction properties of the junction are studied as a function of electron-electron and electron-phonon interactions, and of the applied bias. It is found that interactions strongly affect the conductance, mostly in the transient regime, but have relatively small influence on the steady state current.
Finally, the current calculated using DFT is also compared to a treatment based on the Ehrenfest approximation.
It is found that the latter is a good approximation to the DFT result for large frequencies but not for smaller ones.

Popular Abstract

Electricity is a vital resource of our everyday life. It is safe to say that without it the world would not look the way it does today and that our society depends on it. Unfortunately, a great part of the electric power created in power plants is lost during transport and distribution. A solution to this problem could be by utilizing superconductors. A superconductor is a material that transports electricity with little to no loss. Superconductors are a topic of current research since they currently only perform at low temperatures. The invention of a room temperature superconductor has the potential to spring many new technologies.
The conduction in a microscopic solid material is challenging to study since molecules, which are clusters of atoms, tend to vibrate. We can think of the molecules in a molecular solid as boxes that are aligned in a straight line. Each box is connected to the closest one by a spring. We can then imagine a small toy car that is placed on top of them and can only move from one box to the next.
Its movement causes motion to the boxes. If a box is moved from its initial position, because of the car, it will stretch the spring by which it is attached to the adjacent ones. When released it will create an oscillation in the line since every box is connected.
The movement of the toy car is then in turn affected by the movement of the boxes. Then imagine multiple cars moving on the boxes together in a cluster. Each car affects the movement of the others since they can touch each other.
These interactions become problematic for a large number of cars. In our analogy the molecules, which are connected by a force, are represented by the boxes connected by the springs. The vibration of the molecules is represented by the movement of the boxes and the electrons are represented by the toy cars that, just like in the analogy, are affected by each others movement and that of the molecules.
In this thesis a simulation of a molecular junction with electrons flowing across it is performed. The atoms composing the molecule are allowed to vibrate. In an oversimplified version of this problem we can imagine the molecular junction as to be attached to a spring in the vertical direction as shown in figure. The interaction between electrons is accounted for by introducing an effective interaction amongst them. The aim of this thesis is to analyze how the simultaneous effect of the electronic interactions and the molecular vibration affect the current of electrons that flows through a molecular junction.

• author: Ceccarelli, Eric
• supervisor: Claudio Verdozzi; Emil Boström
• organization: Mathematical Physics; Department of Physics
• course: FYSK02 20191
• year: 2019
• type: M2 - Bachelor Degree
• subject: Physics and Astronomy
• keywords: Density functional theory, DFT, Hubbard-Holstein, Hubbard-Holstein model, HH, Quantum transport
• language: English
• id: 8979313
• date added to LUP: 2019-06-17 08:14:40
• date last changed: 2019-06-17 08:14:40