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Foundations of Solid State Physics

Dimensionality and Symmetry

Siegmar Roth
David Carroll

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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 There are also a number of graphical components and historical references intended to give discoveries, old and new, the context of their origins.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.

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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. 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. 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. 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. 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. 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. 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