PHYSICS 682
BERRY PHASES IN SOLID STATE PHYSICS
BOOKS AND REVIEW ARTICLES

General solid state physics texts

• Kittel, Introduction to Solid-State Physics.
• Ashcroft and Mermin, Solid State Physics (1976).
• Madelung, Introduction to Solid-State Theory (1978).
• Kaxiras, Atomic and Electronic Structure of Solids (2003).
• Marder, Condensed Matter Physics (2000).
  Atypically, this text has a discussion of anomalous velocity in Ch. 16.

Books with some coverage of course material

• Shankar, Principles of Quantum Mechanics, 2nd Edition (1994).
  Chapter 21, starting on p. 592, has a nice discussion of the Berry phase and the adiabatic separation of slow and fast variables.
• Martin, Electronic Structure (2004; paperback 2008).
  Especially Ch. 21 (Wannier functions) and Ch. 22 (Polarization, Localization, and Berry's Phase)
• Bernevig, Topological Insulators and Topological Superconductors (2013).
  Somewhat faster and more field-theoretic treatment of some of the same material.
• Nakahara, Geometry, Topology, and Physics (2003).
  A serious book on differential geometry, topology, manifolds, topological invariants, etc.

Review articles

• M.V. Berry, "The quantum phase, five years after", in "Geometric Phases in Physics," Shapere and Wilczek, Eds., World Scientific, 1989. (link)
• R. Resta, "Macroscopic polarization in crystalline dielectrics: The geometric phase approach," Rev. Mod. Phys. 66, 899 (1994). (local copy)
• R. Resta, "Manifestations of Berry's phase in molecules and in condensed matter," J. Phys.: Condens. Matter 12, R107 (2000). (local copy)
• I.B. Bersuker, "Modern aspects of the Jahn-Teller effect theory and applications to molecular problems," Chem. Rev. 101, 1067 (2001). (local copy)
• R. Resta and D. Vanderbilt, "Theory of Polarization: A Modern Approach," in Physics of Ferroelectrics: a Modern Perspective, ed. by K.M. Rabe, C.H. Ahn, and J.-M. Triscone (Springer-Verlag, 2007, Berlin), pp. 31-68. (local copy)
• D. Vanderbilt and R. Resta, "Quantum electrostatics of insulators: Polarization, Wannier functions, and electric fields," in Conceptual foundations of materials properties: A standard model for calculation of ground- and excited-state properties, S.G. Louie and M.L. Cohen, eds. (Elsevier, The Netherlands, 2006), pp. 139-163. (local copy)
• D.Xiao, M.-C. Chang, and Q. Niu, "Berry phase effects on electronic properties," Rev. Mod. Phys. 82, 1959 (2010). (local copy)
• R. Resta, "Electrical polarization and orbital magnetization: the modern theories," J. Phys.: Condens. Matter 22, 123201 (2010). (local copy)
• M. Z. Hasan and C. L. Kane, "Colloquium: Topological insulators," Rev. Mod. Phys. 82, 3045, 2010. (local copy)
• N. Marzari, A.A. Mostofi, J.R. Yates, I. Souza, and D. Vanderbilt, "Maximally localized Wannier functions: Theory and applications," Rev. Mod. Phys. 84, 1419 (2012). (local copy)

Topological insulators

• L. Fu and C.L. Kane, "Time reversal polarization and a Z2 adiabatic spin pump," PRB 74, 195312 (2006). (local copy)
• L. Fu and C.L. Kane, "Topological insulators with inversion symmetry," PRB 76, 045302 (2007). (local copy)
• L. Fu, C.L. Kane, and E.J. Mele, "Topological Insulators in Three Dimensions," PRL 98, 106803 (2007). (local copy)
• J.E. Moore and L. Balents, "Topological invariants of time-reversal-invariant band structures," PRB 75, 121306 (2007). (local copy)
• X.L. Qi, T.L. Hughes, and S.-C. Zhang, "Topological field theory of time-reversal invariant insulators," PRB 78, 195424 (2008). (local copy)
• M. Z. Hasan and C. L. Kane, "Colloquium: Topological insulators," Rev. Mod. Phys. 82, 3045, 2010. (local copy)