Condensed Matter in a Nutshell by Gerald D. Mahan

By Gerald D. Mahan

Condensed topic in a Nutshell is the main concise, obtainable, and self-contained creation to this interesting and state of the art sector of recent physics. This best textbook covers all of the normal themes, together with crystal buildings, strength bands, phonons, optical homes, ferroelectricity, superconductivity, and magnetism. It comprises in-depth discussions of delivery concept, nanoscience, and semiconductors, and in addition positive factors the most recent experimental advances during this fast-developing box, akin to high-temperature superconductivity, the quantum corridor influence, graphene, nanotubes, localization, Hubbard versions, density sensible thought, phonon focusing, and Kapitza resistance. wealthy intimately and whole of examples and difficulties, this textbook is the full source for a two-semester graduate path in condensed subject and fabric physics.

  • Covers average themes like crystal constructions, power bands, and phonons
  • Features the newest advances like high-temperature superconductivity and more
  • Full of instructive examples and difficult problems
  • Solutions guide (available in basic terms to teachers)

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95) Now evaluate the eigenvalue for nonzero k. 96) The term with V' 2 just gives the atomic eigenvalue. 99) The term V is called the k · p interaction. The term E' (k) is the free electron kinetic energy. Take eqn. 97), multiply by exp(-ik · r) ; (r) from the left, and integrate over all volume. 100) (k·p)u(k, r) The interaction V has odd parity and ; has even parity. The integral is zero unless a term in u (k, r) has odd parity. Write k · p = kxPx + kYpY + k p The integral is nonzero in the term kxPx only for the term in u (k, r) that has odd parity with respect to x.

Similarly, the term kYpY is nonzero only for the term in u (k, r) that has odd parity with respect to y. 102) 'f'µ The symbol P cv,µ ' (µ = x, y, z), is the matrix element of momentum between the conduction and valence bands. It has the same value for all three choices of µ, so call it P cv · Next take eqn.

2. o 1 ¡¡ a Nea rly free electron energy bands in one dimension. '-, ...... --· 1 2rr a 38 1 Chapter 3 points, such as the edge of the BZ, and at k = O. Where bands cross there are energy gaps dueto nonzero values of uª . The resulting energy bands are a periodic structure. It is sufficient to show these energy bands in the first BZ. Each different band is labeled E" (k), where k is in the BZ. Where two free electron bands cross, it is often accurate to approximate the energy bands in this local region by the dispersion of the two bands that cross.

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