Rutgers University Department of
Physics and Astronomy
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)
Please send any comments on this page to
dhv@physics.rutgers.edu.