Transport phenomena in quantum wells and wires in presence of disorder and interactions

Abstract

Present-day electronics employ circuits of smaller and smaller dimensions, and today the length scales are so small that the laws of physics which rule micro-cosmos, quantum mechanics, become directly important. This thesis reports on theoretical work on electron

transport in different nanostructures. We have studied semiconductor quantum wells, layered materials where each layer can be only a few atomic layers thick, and transport in thin atomic wires. The layered materials have been studied semi-classically by means the so-called

Bolzmann equation and Monte-Carlo techniques. The works on layered

materials focused on effects of resonant scattering mechanisms on the

electron transport and the feasibility to use semiconductor super-

lattices for generating terahertz (THz)radiation. The quantum wires

were modeled by 1D Hubbard chains connected to semi-infinite leads and

were treated fully quantum-mechanically via the time-dependent density-

functional theory (TDDFT). Our TDDFT treatment appears to be able to

capture complex features due to competition between correlation and

disorder. The merits of the coherent-potential approximation are also

analyzed for contacted chains.

In total, four papers are included in the thesis.

In paper I, Monte Carlo simulations of transport in various two-

dimensional semiconductor hetero-structures, in particular in cases

where accurately calculated scattering probabilities are needed.

In paper II, we present result for electron transport in į-doped

Si/SiGe quantum wells at different temperatures and field strengths.

In paper III, we develop a Monte-Carlo technique to handle electron

transport between quantum-well layers when an electric field is applied

along the growth direction. We use this method to study scattering-

assisted transport under strong fields in the Wannier-Stark regime.

In paper IV, finally, the static and dynamical behavior of 1D Hubbard

chains are investigated. The focus is on how the interplay of

interactions and disorder affects the localization of fermions in

Hubbard chains contacted to semi-infinite leads.

Abstract (Swedish)

Popular Abstract in Undetermined

All of our present information technology culture with computers, internet, smart-phones, Bluetooth links, 3D-Tv, iPad tablets, programmable washing/cooking machines, car engines, navigation computers, etc. (the list goes on and on) is based on small electrical circuits. The smaller these circuits can be made, the faster and the better microelectronics can perform.

There is much more round the corner: nano-chip technology could soon dim the

boundary between living and non-living entities, and perhaps even between us and

what is just outside our body: the external world. Some of our capabilities could

be improved or fully regained from deficit situations (think of people recovering

neural abilities, improving their eyesight, using cyber-prostethics, having real-time monitoring of non-perfect vital functions, etc.)

It is fair to say that some of these developments could impel us to deal with

novel bio-ethical conflicts (voices of concern exist already), but science has forced us before to face dilemmas of this sort. Past experience over the last few millennia shows that each time humanity has made a great discovery (e.g. the fire, the wheel, the printing press, the steam engine, the electricity, penicillin, the transistor, internet) the subsequent technological evolution has always proceeded in one

direction: forward.

Regaining a more down-to-earth perspective, present-day electrical circuits

have reached such small dimensions that the laws of physics which govern the

microscopic world, called quantum mechanics, are becoming center-stage. Even

within the status-quo of technological development (we refer to it as "nanoelec-

tronics"), it is becoming increasingly important to have a basic understanding

of how small systems with a finite number of atoms and electrons behave when

subjected to perturbing agents, for example by electric current passing through

them.

The knowledge we have of such systems relies, first and foremost, on elaborate

and careful experiments. However, experimental data can be difficult to interpret,

because even such small systems are in-fact many-particle systems. The analysis

can be (and usually is) further complicated by the fact that samples are "disor-

dered", i.e. we have incomplete knowledge and control of the kind of atoms and

their positions in the sample.

In principle, theoretical research can contribute significantly to this endeavor,

by answering a number of important questions. In practice, often a major obstacle

is the lack of accurate theoretical information on how interactions among particles

and disorder affect the results.

This thesis is about research work in this direction, namely theoretical investi-

gations of the electric current in different nano-structures. We have analyzed quan-

tum wells (layered slices of semiconductors), and quantum wires (one-dimensional

conducting aggregates of atoms). Both are man-made artificial structures where,

as their name suggests, quantum effect play an important role in the current trans-mission. These systems have great potential for technological breakthroughs. We

have employed rather different theoretical techniques, aimed to look directly into

the behavior of the current in the steady-state (where the current does not change

in time), or to follow how the current changes in time to reach such steady state.

We have used the Boltzmann’s equation, a method with a long and eminent ser-

vice record in physics, but also a rather new approach (called "density functional

theory"), which uses the total electron density as a basic but only variable and

therefore requires significantly less computing power than traditional methods.

In the end, the actual common denominator to the different parts of our thesis

work is the presence of disorder in our systems. Disorder is ubiquitous in nature:

in fact, in many instances, the notion of order corresponds more to our need for

simple conceptualizations of reality, than to reality itself (that is, in most cases,

in nature, order exists only in an approximate way). Nanoscale systems are no

exception and, in fact, the effects of disorder are expected to be strong in these

small systems.

From the outside, and especially to the eye of the professional physicist, these

considerations can seem a rather tenuous link to thread together somewhat differ-

ent subjects, systems and methodologies in the same thesis. For us, who worked

on these topics for several years, this thesis is a confirmation that, as life itself,

scientific research is often made of pieces whose mutual connection is not imme-

diately apparent, and that, in the end, there is beauty in all different parts of

Physics.

• author: Vettchinkina, Valeria
• supervisor: Claudio Verdozzi
• opponent: Professor Sanvito, Stefano, Department of Physics Trinity College, Dublin
• organization: Mathematical Physics
• publishing date: 2012
• type: Thesis
• publication status: published
• subject: Condensed Matter Physics
• keywords: time-dependent density-functional theory, disorder, electron correlation, Lowdimensional semiconducting systems, transport phenomena, Fysicumarkivet F:2012:Vettchinkina
• pages: 144 pages
• defense location: Lecture hall F, Sölvegatan 14A
• defense date: 2012-05-29 13:30:00
• ISBN: 978-91-7473-328-0
• language: English
• LU publication?: yes
• id: 5797b65c-b215-4773-a4eb-89b6c4919468 (old id 2520291)
• date added to LUP: 2016-04-04 11:07:31
• date last changed: 2018-11-21 21:02:49