Foundations of Solid State Physics E-Book

Siegmar Roth

• Herausgeber: Wiley-VCH Verlag GmbH & Co. KGaA
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 1039

Veröffentlichungsjahr: 2019

Beschreibung

An essential guide to solid state physics through the lens of dimensionality and symmetry

Foundations of Solid State Physics introduces the essential topics of solid state physics as taught globally with a focus on understanding the properties of solids from the viewpoint of dimensionality and symmetry. Written in a conversational manner and designed to be accessible, the book contains a minimal amount of mathematics. The authors?noted experts on the topic?offer an insightful review of the basic topics, such as the static and dynamic lattice in real space, the reciprocal lattice, electrons in solids, and transport in materials and devices.

The book also includes more advanced topics: the quasi-particle concept (phonons, solitons, polarons, excitons), strong electron-electron correlation, light-matter interactions, and spin systems. The authors' approach makes it possible to gain a clear understanding of conducting polymers, carbon nanotubes, nanowires, two-dimensional chalcogenides, perovskites and organic crystals in terms of their expressed dimension, topological connectedness, and quantum confinement. This important guide:

-Offers an understanding of a variety of technology-relevant solid-state materials in terms of their dimension, topology and quantum confinement
-Contains end-of-chapter problems with different degrees of difficulty to enhance understanding
-Treats all classical topics of solid state physics courses - plus the physics of low-dimensional systems

Written for students in physics, material sciences, and chemistry, lecturers, and other academics, Foundations of Solid State Physics explores the basic and advanced topics of solid state physics with a unique focus on dimensionality and symmetry.

Leseprobe

Foundations of Solid State Physics

Dimensionality and Symmetry

Siegmar Roth David Carroll

Copyright

Authors

Prof. Siegmar Roth

MPI für Festkörperforschung

Heisenbergstr. 1

70569 Stuttgart

Germany

Prof. Dr. David Carroll

Wake Forest University

Department of Physics

100 Olin Physical Laboratory

NC

United States

All books published by Wiley‐VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

Library of Congress Card No.:

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A catalogue record for this book is available from the British Library.

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The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at <http://dnb.d‐nb.de>.

© 2019 Wiley‐VCH Verlag GmbH & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany

All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.

Print ISBN: 978‐3‐527‐34504‐5

ePDF ISBN: 978‐3‐527‐81656‐9

ePub ISBN: 978‐3‐527‐81658‐3

oBook ISBN: 978‐3‐527‐81659‐0

Cover Design  Adam‐Design, Weinheim, Germany

Preface

There are a great many textbooks on solid‐state physics, condensed matter physics, or materials physics. Each has specific points, perspectives, or foci, that is, a purpose and an audience. There are, in fact, so many topics and principles that could be covered in the broad field of solid‐state physics, and it is surely impossible to be comprehensive for a single, accessible text. Thus, each school of thought must choose its own emphasis areas for its students from semiconductor physics to soft condensed matter, and that is what we have done here.

In Foundations of Solid State Physics, we have presented what is essential for us, the authors, in the field of emerging, exotic, novel materials. The reader will quickly notice our passion for molecular solids and carbon‐based systems and the phenomena associated with them. Conducting polymers, carbon nanotubes, nanowires/nanoparticles, two‐dimensional plates of dichalcogenides, perovskites, and organic crystals are systems understood largely through their dimensionality, topological connectedness, and quantum confinements. So studies of these materials expand our most fundamental solid‐state models, and they offer to us the basic challenge of connecting to deeper physical insights. In our writing, we have tried to embrace that invitation and challenge. We intend our text for the advanced undergraduate or beginning graduate student. But researchers with interests in the areas of dimensionality in solids, organic or molecular electronics, and molecular materials should also find our perspective enjoyable.

We have chosen an unusual presentation style for the text. It is conversational, and throughout the text there are italicized words and concepts. We intend these as focus points where we want the reader to go outside of the text to supplement their understanding of the concepts. So be ready when we return to these points again and again. There are also a number of graphical components and historical references intended to give discoveries, old and new, the context of their origins. Finally, we expand upon specific topical areas through the use of open‐ended exercises. Not surprisingly we have encouraged the reader to look through the references on which the exercises are based and therefore engage with the original authors of the work. We hope our readers find this engagement approach mentally stimulating, challenging, and fun. Think of the old adage from Ben Franklin: “Tell me and I may forget, teach me and I may remember, involve me and I learn.”

Some may prefer to skip through the mathematical details, problems, and references in a diagonal way to get to the physical models quickly. We believe that the text has been laid out in such a way as to accommodate this style of reading as well. However, as a textbook, the presentation is intended as a two‐semester detailed discussion of the world of solid‐state physics. Our core premise is that solid‐state physics is as fundamental in its nature as any field of physics, with unique models and explanations of reality. Understanding these models and explanations brings us ever closer to understanding the universe in its deepest complexities.

In preparing the text, two desks, one in Munich and one in Winston‐Salem, were filled with dozens of reference books. Of these we found that there was a subset we particularly enjoyed, and we used them (coupled with experiences in our labs, our own publications, and journal articles from outside our research groups) to form an outline of our presentation. Some of these texts are getting pretty old by now, and each expresses unique perspectives and passions for the field. But it is always useful to see how others frame things.

1.

Kittel

:

Introduction to Solid State Physics

, now in its eighth edition. This is the truth as it was revealed at UC Berkeley, wonderful for building a pedagogical understanding at the most fundamental level using elementary models. This book is simply hard to put down. Published by Wiley.

2.

Ashcroft and Mermin

:

Solid State Physics

first edition. While Kittel may be seen a bit as “Moses on his mountain,” this text is the truth as it is known in Ithaca. And it is frequently associated with things far more devilish. With more than 800 pages of electrical and optical properties in solids and one of the first texts to categorize the different models of electron behavior in a crystal, this text provides exquisite detail for every detail you might think of. It is a

must read

. Published by Brooks Cole.

3.

Ibach and Lüth

:

Solid‐State Physics: An Introduction to Principles of Materials Science

now in its fourth edition, a more modern compilation of solid‐state physics with plenty of experimental examples. This laboratory‐centered treatment is a favorite in many German universities. It certainly doesn't take long to see why. Published by Springer.

4.

Chaikin and Lubensky

:

Principles of Condensed Matter Physics

, a

tour de force

of thermodynamics in the solid state. These authors make the daring leap of dealing with novel systems in a fundamentally different way and help to define many aspects of modern solid‐state physics. From soft condensed systems to liquid crystals and to phase transitions, you will find the foundations here. Published by Cambridge University Press.

5.

Harrison

:

Solid State Theory

, the quantum chemistry of hybridization. The focus of this treatment is on how specific bonding characters arise in crystals. Special emphasis is given to the spatial mapping of bonds within the solid and how they become bands. It is especially important for people studying semiconductors or oxides. Published by Dover.

6.

Marder

:

Condensed Matter Physics second edition

, a graduate‐level introduction that has gained rapid acceptance. This text has focused on basic calculation approaches to a wide range of physical phenomena in solid‐state physics. Though relatively young, the text is already a classic. Published by Wiley.

Our text started as a fourth edition of the now well‐known One‐Dimensional Metals (ODM) by S. Roth in 1995 by VCH. Over the many years of teaching this material to undergraduates and graduate students at Wake Forest University, we have filled the margins of numerous copies of ODM with ideas, problems, and notes. All of these are penciled in during conversations with each other and with students. So it soon became apparent that ODM was set to evolve into more of a textbook presentation and so came the current text. It has remained important for us both, as authors, to retain the style, humor, and ease of access of that first text. This reflects who we are as scientists and as people. But it is also necessary to recognize the comments and thoughts of students at Wake Forest University and the Max‐Planck‐Institut für Festkörperforschung in Stuttgart, postdocs, and technical staff at both institutions, as well as our many colleagues that have read through sections of the text. For better or worse, their words and ideas are reflected in its pages as well.

It takes a long time to write a book even when there are two people doing it! This always means there is one group that should receive the most credit for its completion, and that group is our families. Thank you Richard, Jiangling, Lauren, and Melissa for supporting us in this endeavor. Without such families as you, textbooks would rarely be written at all.

Munich and Winston‐Salem 2019

Siegmar Roth and Dave Carroll

1Introduction*

“Dimensionality” and “atomic ordering in finite structures” seem like rather odd principles by which to organize thoughts on solid‐state physics. Indeed, this is not a historical approach to understanding solids at all. However, in learning solid state today, we must embrace the historical orthodoxy of crystal lattices, phonons, and band structure, as well as a whole zoo of emerging exotic materials that range from fullerenes to organic superconductors.

How do we understand two‐dimensional (2D) dichalcogenides, atomically layered permanent magnets, perovskites, topological insulators, conducting polymers, quantum dots, graphene, glassy carbon, etc.? And what of the low‐dimensional analogues of orthodox collective behavior: charge density waves, excitons, spin waves, and the like? We know these things “live” in/on such low‐dimensional structures. An interesting and instructive way to build a framework is to begin with the normative behavior of a special atom, carbon, and the dimensionality of the structures it makes. Why carbon? Because among the elements it is about the most robust at making compounds and structures. It is extremely flexible in how it chooses to arrange itself. Why dimension? Well, lower‐dimensional materials offer new approaches to technology, holding the key to everything from quantum computers to new medicines. But most importantly, it introduces the idea of “topology.”

Look, the traditional story goes like this. We begin our description of solids with an infinite mathematical construction (the lattice) given by specific point group symmetries. Onto the lattice points we attach some arbitrary set of atoms (generally picking something found in nature). We calculate specified properties based upon idealizations of how free the electron may be at each lattice point or how free the motion of the atom at the lattice point may be. We adiabatically add interactions between vibrations, carriers, etc. of the lattice to get more interesting phenomena.

Our story, though, is like a tale of die Brüder Grimm1: carbon is the central atom of the universe.2 It forms more compounds in more ways than any other atom. Thus, other atomic systems deviate from carbon by breaking its norms of symmetry. Beginning with large carbon molecules, we form nanometer structures. As we add, subtract, or substitute C atoms in the structure, we design materials with properties that can be examined through the dimensional change we have brought out. It isn't quite a chemical point of view, and it isn't quite solid‐state physics in its purest form. It is the type of conversation you hear in working research labs across the world: complementary and an enjoyable compromise between the perspectives.

1.1 Dimensionality

The concept of dimensionality has been with us for a while, and it is an intellectually appealing concept. Speaking of a dimensionality other than three will surely attract some attention. Some years ago it was fashionable to admire physicists who apparently could “think in four dimensions” in striking contrast to Marcuse's One‐Dimensional Man (Figure 1.1) [1]. Physicists would then respond with the understatement: “We only think in two dimensions, one of which is always time. The other dimension is the quantity we are interested in, which changes with time. After all, we have to publish our results as two‐dimensional figures in journals. Why should we think of something we cannot publish?”

Figure 1.1 Marcuse's man. Simultaneously with Herbert Marcuse's book One‐Dimensional Man, which widely influenced the youth movement of the 1960s. W.A. Little's paper on “Possibility of Synthesizing an Organic Superconductor” was published, motivating many physicists and chemists to investigate low‐dimensional solids.

This fictitious dialogue implies more than just sophisticated plays on words. If physics is what physicists do, then in most parts of physics there is a profound difference between the dimension of time and other dimensions, and there is a logical basis for this difference [2]. In general, the quantity that changes with time and in which the physicist is interested is some intrinsic property of an object. The object in question is typically imbedded in a three‐dimensional (3D) space. Objects themselves, however, may be very flat such as flounders, saucers, or oil films with greater length and width than thickness. In materials such as graphene or MoS2, thickness can be negligibly small – atomic. Such objects can be regarded as (approximately) 2D. Now, if the intrinsic property that the physicist wishes to study is somehow constrained in behavior, in direct correlation to the dimension of the object, like a boat on the 2D surface of the sea is hopefully constrained to 2D motion, then we say the property is expressing the dimensionality of the object. In our everyday experience one‐dimensional (1D) and 2D objects and 1D and 2D constraints are more common than you might think. Indeed, low dimensionality should not be particularly spectacular to our expectations. For this reason too, it is reasonable to introduce non‐integer, or fractal, dimensions [3]. Not much imagination is necessary to assign a dimensionality between one and two to a network of roads and streets – more than a highway and less than a plane. It is a well‐known peculiarity that, for example, the coastline of Scotland has the fractal dimension of 1.33 and the stars in the universe that of 1.23.

Solid‐state physics treats solids both as objects and as the space in which objects of physics exist, e.g. various silicon single crystals can be compared with each other, or they can be considered as the space in which electrons or phonons move. The layers of a crystal, like the ab‐planes of graphite, can be regarded as 2D objects with interactions between them that extend into the third dimension. But these planes are also the 2D space in which electrons move rather freely. Similar considerations apply to the (quasi) 1D hydrocarbon chains of conducting polymers.

1.2 Approaching Dimensionality from Outside and from Inside

There are two approaches to low‐dimensional or quasi‐low‐dimensional systems in solid‐state physics: geometrical shaping as an external approach and increase of anisotropy as an internal approach. These are also sometimes termed top‐down and bottom‐up approaches, respectively. For the external approach, let us take a wire and draw it until it gets sufficiently thin to be 1D (Figure 1.2). How thin will it have to be to be truly 1D? This depends a little on exactly what property of the structure is desired to express low‐dimensional behavior. Certainly, thin compared to some microscopic parameter associated with that property. For example, for 1D electrical transport properties, the structure must have length scales such that the mean free path of an electron or the Fermi wavelength is affected by the physical confinement of the structure. We will discuss these concepts further a little later on in the text. But surely the meaning is clear: some fundamental aspect of an internal object responsible for the phenomenon of interest must be dramatically altered by its localization within the structure.

Figure 1.2 Wire puller. An “external approach” to one‐dimensionality. A man tries to draw a wire through a mandrel until it is thin enough to be regarded as one‐dimensional. Metallic wires can be made as thin as 1 μm in diameter like this, but this is still far away from being one‐dimensional. Lithographic processes using focused ion beams and focused electrons can produce some metal and semiconductor structures that are narrow enough to exhibit one‐dimensional properties (∼nanometers).

Technology today has made it possible to approach such sizes using methods of lithography as well as chemical assembly. Lithography is the top‐down approach to creating confining structures as it whittles away material until only very small structures remain. Chemical assembly is the “bottom‐up” approach, and it forms the structure through chemical reactions. The two approaches offer very different properties to the nanoscale structure created, both in terms of atomic ordering and control over object placement.

To achieve “one‐dimensionality” does the wire puller in Figure 1.2 have to draw the wire so extensively that it is finally to become a monatomic chain? Well, the Fermi wavelength, a fundamental property of the carrier electron responsible for conductivity, becomes relevant when discussing the eigenstates of all the electrons of the structure. If electrons are confined in a box, quantum mechanics tells us that the electrons can have only discrete values of kinetic energy. The energetic spacing of the eigenvalues depends on the dimensions of the box – the smaller the box the larger the spacing (Figure 1.3):

1.1