Berry phase has various applications in different fields. A theoretical study of Berry phase in spin system and topological insulator from the view point of quantum entanglement is searched for.
First of all I like to draw your attention to the fact that well before Berry rediscovered the so-called Berry phase S. Pancharatnam discovered what should be called "Pancharatnam-Berry phase" to be fair. For the original Pacharatnem work please read
S. Pancharatnam, Proc. Indian Academy of Sciences, vol. XLIV, 51 (1956).
A very good review is X. Xiao, M.C. Chang, Q. Niu, Rev. Mod. Phys. 82, 1959 (2010).
This article discusses several solid state physics application.
There is a very useful lecture note on
Berry phase effects on magnetism by P. Bruno:
My personal interest is Berry phase effect in orbital magnetism. This has been discussed in the Rev. Mod. Phys. article by Xiao on p. 1978. Also interesting is the anomalous Hall effect discussed on p. 1974 in the same Review. Bruno Patrik has also discussed many interesting magnetic phenomena. You can also read the popular article of Michael Berry "Application of the geometric phase" in Physics Today December 1990, p. 34
Thanks Prof. Chatterjee. I am searching problems for students specially like to work in condensed matter systems. Frustrated system and spintronics are seems to me interesting. Pancharatnam phase is also very familiar to me.
Patrik Bruno here at the ESRF does a lot of theoretical work on geometric phase. You can consult his works perhaps and read his lecture note.
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