Rutgers University Department of
Physics and Astronomy
PHYSICS 603
BERRY PHASES IN SOLID STATE PHYSICS
BOOKS AND
REVIEW ARTICLES
This page is under construction! The references
given below need to be updated.
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)
Please send any comments on this page to
dhv@physics.rutgers.edu.