Graduate Course: Quantum Mechanical Models of Solids

Book and Reference List

John A. Venables and Malcolm Heggie,

School of Chemistry, Physics and Environmental Science,
University of Sussex, Brighton, UK.

This is one of several files containing lists of, and links to, web-based resources for use in connection with my graduate courses, book, web-based articles and talks. This file is a book and reference list for this Sussex-based course in the Autumn Terms 2004 and 2005. Latest version of this document 31st August 2005.

Book list for QMMS Course

The main books for the course are:
Electronic Structure of Materials by Adrian P. Sutton, a 1993/4 book published by Oxford (ISBN 0-19-851754-8, paperback).
Bonding and Structure of Molecules and Solids by David G. Pettifor, a 1995 book also published by Oxford (ISBN 0-19-851786-6, paperback).

You will find, perhaps not surprisingly, that some of the notes are related to corresponding passages in Introduction to Surface and Thin Film Processes by John A. Venables, published by Cambridge in August 2000 (ISBN 0-521-78500-6, paperback). This book has a web-based appendix which we may refer to; more detailed contents, comments and updates are also on the web.

You may wish also to have access to older standard texts, such as
Solid State Physics by Neil W. Ashcroft and N. David Mermin, a 1976 classic published by Saunders College, and/or
Introduction to Solid State Physics, by Charles Kittel, 6th edition (1986) or 7th edition (1996) published by John Wiley.

There are many other books in this area which you may wish to dip into, but this will depend on your individual background and interests. Some which are worth looking at include:
Solid State Physics: an introduction to the principles of materials science by Harald Ibach and Hans Lüth (Springer 1995);
Fundamentals of Semiconductors: Physics and Materials Properties by Peter Y. Yu and Manuel Cardona (Springer 1996);
Condensed Matter Physics by Michael P. Marder (John Wiley 2000);
Atomic and Electronic Structure of Solids by Efthimios Kaxiras (Cambridge 2003).

If you wish to obtain further insight into modern computing methods, you can try Computational Physics by J.M. Thijssen (Cambridge 1999), where you will find wide-ranging examples, as well as how to solve eigenvalue problems. Several of our computing examples are drawn from this book, but we are not assuming that you will need this level of detail for the course. You may also care to consult Essentials of Computational Chemistry by C.J. Cramer (Second Edition, John Wiley 2004) and/or Electronic Structure: basic theory and practical methods by R.M. Martin (Cambridge 2004). In the period of giving this course, references to review articles can now be replaced by references to books such as these two, and to Kaxiras' book cited above. But clearly not everyone is going to have access to these books, which in general go far beyond our course. However, on looking at the reference lists for these books and our course, one can see that there is a considerable level of agreement as to which developments have been, and remain, important. Thus the newer books can serve as further reading and reference manuals for practioners in this field.

If any faculty member or prospective student has further suggestions to make, please get in touch with one of us by email.

References and reading for QMMS Lecture 1

Here we want to check that we have a common language for discussion of the quantum mechanics of simple molecular systems. Aim to understand Sutton, chapters 1-2, p 9-37, following this lecture. Get out your undergraduate quantum mechanics books, and remember those parts you found useful. We need to be able to assume the easier mathematics of differential equations, operators and matrices.

You can find much of this stuff on the web as Background material for John's ASU Quantum Physics course. For example, the main book I use for this course is Quantum Physics, 2nd Edition by Stephen Gasiorowicz, a 1996 book published by John Wiley (ISBN 0-471-85737-8). There is now a 3rd Edition (2003, ISBN 0-471-05700-2), which has been used over the last two years. A list of corrections to the 2nd Edition,with suitable disclaimers, can be found here. The 3rd Edition has an associated web site that contains extra material.

An alternative book I use is Introductory Quantum Mechanics, 3rd Edition by Richard L. Liboff, a 1998 book published by Addison-Wesley (ISBN 0-201-87879). The 4th edition is now available, with one copy in the Sussex library.

For QMMS Lecture 2

In this second lecture we are checking that you have heard of the simpler concepts of electrons in solids, starting from the states of a one-dimensional (1D) box, and moving on to Bloch's theorem and the ideas of bands and band gaps. This is covered in many places, including Sutton, chapter 7, pages 132-151. The classic reference is Ashcroft and Mermin, chapters 2, 8 and 9, though this may not be the easiest place to start. All solid state physics books treat this topic in some detail. Explicit text references to Gasiorowicz and Liboff are given, books which John is using for his ASU Quantum Physics course. The book by Atkins and Friedman, Molecular Quantum Mechanics is at a suitable level for students with a chemistry background.

For QMMS Lecture 3

In the third lecture we are revising ideas about diffraction and the relation between real and reciprocal lattices. This is discussed in most crystallography books, but students who haven't immersed themselves in the topic often find it difficult. Sutton has a go at explaining the geometry in chapter 4, especially pages 74-80. He then discusses free electron and NFE theory in chapter 7. Pettifor's sections 5.3 and 5.4, pages 111-121, on the Kronig-Penney model and NFE bands are particularly clear. There are some simple ways of looking at the Fourier analysis involved, which we may put in the form of Web pages during the course.

Any time you want to start reading Sutton's chapter 3 is good from now on; this is a highly original approach to understanding the relationship between descriptions based on real and reciprocal lattices. Topics include the density of states, both total and local, the density matrix, band and bond energies, and finally the powerful moments theorem, all based on 1D chains of H-atoms and their boundary conditions. We are not going to take this 'head on' in lectures. Questions could, however, usefully influence what we teach later.

For QMMS Lecture 4

Here we first make contact with modern methods, based on the need for self-consistency of the potential which the (interacting) electrons see. The Hartree and Hartree-Fock (HF) methods are described in most books on Quantum Chemistry; Sutton restricts himself to the Hartree method and its relation to DFT in chapter 11, pages 204-214. Pettifor discusses HF briefly on pages 45-49 and 60-66. We will go through the ideas of jellium, and the derivation of DFT in the lecture. Both of these concepts are widely discussed, with many useful applications. There are a large number of references which one could follow up (if you want to find out why Walter Kohn received the 1998 Nobel prize for Chemistry), but be warned in advance that your life probably is too short to do this topic justice. For the first review article on the application of the jellium model to surfaces, see N.D. Lang Solid State Physics 28 (1973) 225-300. Just to get a feel for the amount of work done since then on clusters and solids, consult M.C. Payne et al. (1992) Rev. Mod. Phys. 64 1045-1097 and/or M. Brack (1993) Rev. Mod. Phys. 65 677-732.

If you wish to obtain further insight into modern computing methods, you can try Computational Physics by J.M. Thijssen (Cambridge 1999), where you will find wide-ranging examples, as well as how to solve eigenvalue problems. Several of our computing examples are drawn from this book, but we are not assuming that you will need this level of detail for the course. You may also care to consult Essentials of Computational Chemistry by C.J. Cramer (Second Edition, John Wiley 2004) and/or Electronic Structure: basic theory and practical methods by R.M. Martin (Cambridge 2004), and/or Atomic and Electronic Structure of Solids by Efthimios Kaxiras (Cambridge 2003). In the period of giving this course, references to review articles can now be replaced by references to books such as these. But clearly not everyone is going to have access to these books, which in general go far beyond our course.

For QMMS Lecture 5

For 5.1: Pettifor chapter 5.5 on pseudopotentials, p 121-131; Sutton chapter 8, pages 166-171, short summary only.
For 5.2: Pettifor chapter 5.7, p 131-135; more in chapter 6; Sutton chapter 9, pages 179-180, short summary of Finnis-Sinclair for d-electrons.
For 5.3: Pettifor chapter 7, especially 7.4, 7.5, p 180-198. Sutton chapter 9, p 172-189.

In addition, a survey of the literature on metals in relation to surfaces and thin films is given in John's book, primarily in chapter 6. The contents of this chapter and any updates are on the web.

Original literature references:
Alldredge, G.P. & L. Kleinman (1974) Phys. Rev. B 10 559-573.
Balasubramanian, K. (1988) J. Chem. Phys. 89 6310-6315.
Friedel, J. (1969) in The Physics of Metals (Ed. J.M. Ziman, Cambridge) 340-408.
Jacobsen, K.W., J.K. Nřrskov & M.J. Puska (1987) Phys. Rev. B 35 7423-7442.
Jacobsen, K.W. (1988) Comments on Cond. Matter Physics 14 129-161.
Moruzzi, V.L., J.F. Janak & A.R. Williams (1978) Calculated Electronic Properties of Metals (Pergamon).
Nřrskov, J.K., K.W. Jacobsen, P. Stolze & L.B. Hansen (1993) Surface Sci. 283 277-282.
Papaconstantopoulos, D.A. (1986) Handbook of the Band Structure of Elemental Solids (Plenum).
Skriver, H.L. & N.M. Rosengaard (1992) Phys. Rev. B 46 7157-7168.
Stolze, P. (1994) J. Phys. Condens. Matter 6 9495-9517; (1997) Simulations in Atomic Scale Materials Physics (Polyteknisk Verlag, Copenhagen).

For QMMS Lecture 6

If you would like to know more about any topic discussed in this lecture, probably the most useful reference is Chapter 3 of Computational Physics by J.M. Thijssen (Cambridge 1999), where you will find examples, as well as some discussion on how to solve the eigenvalue problems. In addition, recap and review Sutton chapters 3-5, which will firm up the ideas which are dependent on long range order, as distinct from local, or short-range, order in clusters and solids. If you wish to concentrate on molecules and clusters, then Pettifor chapters 3 and 4 could also be studied. Pettifor's chapter 7 outlines the tight-binding method as it applies in 1, 2 and 3 dimensions. Here, however, we reserve a more detailed discussion to lectures 7 and 8.

For chemical and cluster developments beyond Hartree-Fock, you may also care to consult the recent Essentials of Computational Chemistry by C.J. Cramer (Second Edition, John Wiley 2004).

For QMMS Lectures 7 and 8

These two lectures open up a huge window on the solid state, both as descriptive science, and as an introduction to the science behind devices based on semiconductors- there is no way that we can do this topic justice in the space or time available. What we can do is to provide you with references to enable you to become familiar with both structures and band structures, and some acquaintance with an idea of the range of phenomena that we require Quantum Mechanics to explain. You will do well if you can grasp Sutton, chapter 6 (pages 112-131) on a first read. Pettifor devotes chapter 7.7 (pages 198-207) to semiconductors. This whole chapter is concerned with transition metals and the tight binding approximation; thus it is a good second read on the subject matter of lectures 5-8 inclusive.

Historically, the book by Harrison (1980) was very important, and much of this spirit is incorporated into the more recent book by Yu & Cardona (1996). This book has worked examples in chapter 2, especially sections 2.4-2.7 on the band structure of silicon, germanium, some III-V and II-VI compounds, which we will look at in the computation sessions. If your interest is centered on devices and/or low-dimensional structures, you may prefer to start from Kelly (1995) or Davies (1998), and only go to Yu and Cardona if you need more on the detailed computational methods. There is a review article (Goringe et al. 1997), a conference on tight binding methods (Turchi et al. 1998) and a review on Order-N methods by Gödecker (1999); some of these feature Edward Hernández's research papers (Edward helped to teach the 1999 course).

In addition, a survey of the literature on semiconductors in relation to surfaces and thin films is given in John's book, primarily in chapter 7. The contents of this chapter and any updates are on the web.

You may also care to consult the recent Electronic Structure: basic theory and practical methods by R.M. Martin (Cambridge 2004). In the period of giving this course, references to review articles can now be replaced by references to books such as this, and to Cramer's book cited for lecture 6. But clearly not everyone is going to have access to these books, which in general go far beyond our course. However, on looking at the reference lists for these books and our course, one can see that there is a considerable level of agreement as to which developments have been, and remain, important. Thus the newer books can serve as further reading and reference manuals for practioners in this field.

Textbook, review article and original literature references:
Car, R. & M. Parinello (1985) Phys. Rev. Lett. 55 2471-2474.
Cramer, C.J. (2004) Essentials of Computational Chemistry (Second Edition, John Wiley).
Davies, J.H. (1998) The Physics of Low-dimensional Semiconductors: an Introduction (Cambridge).
Gödecker, S. (1999) Rev. Mod. Phys. 71 1085-1123.
Goringe, C.M., D.R. Bowler & E. Hernández (1997) Rep. Prog. Phys. 60 1447-1512.
Harrison, W.A. (1980) Electronic Structures and the Properties of Solids (Freeman).
Jank, W. & J. Hafner (1990) Phys. Rev. B 41 1497-1515.
Kelly, M.J. (1995) Low-dimensional semiconductors (Oxford).
Lenosky, T.J., J.D. Kress, I. Kwon, A.F. Voter, B. Edwards, D.F. Richards, S. Yang & J.B. Adams (1997) Phys. Rev. B 55 1528-1544.
Martin, R.M. (2004) Electronic Structure: basic theory and practical methods (Cambridge).
Payne, M.C., M.P.Teter, D.C. Allan, T.A. Arias & J.D. Joannopoulos (1992) Rev. Mod. Phys. 64 1045-1097.
Qian, G.X. & D.J. Chadi (1987) J. Vac. Sci. Tech. A5 906-909; (1987) Phys. Rev. B35 1288-1293.
Remler, D.K. & P.A. Madden (1990) Molecular Physics 70 921-966.
Stich, I., R. Car & M. Parinello (1991) Phys. Rev. B 44 4262-4274.
Turchi, P.E.A., A. Gonis & L. Colombo (Eds.) (1998) Mater. Res. Soc. Symp. 491 1-542.
Wang, C.Z. & K.M. Ho (1996) Adv. Chem. Phys. 93 651-702.
Yu, P.Y. & M. Cardona (1996) Fundamentals of Semiconductors: Physics and Materials Properties (Springer), especially p43-90.


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