Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2002-01-25
Phys. Rev. B 66, 085118 (2002)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
Corrected a typo. To be published in Phys. Rev. B
Scientific paper
10.1103/PhysRevB.66.085118
We consider Bloch electrons in the presence of the uniform electromagnetic field in two- and three-dimensions. It is renowned that the quantized Hall effect occurs in such systems. We suppose a weak and homogeneous electric field represented by the time-dependent vector potential which is changing adiabatically. The adiabatic process can be closed in the parameter space and a Berry phase is generated. In the system, one can define the macroscopic electric polarization whose time derivative is equivalent to the quantized Hall current and its conductivity is written by the Chern number. Then, the polarization is induced perpendicular to the electric field. We show that the induced polarization per a cycle in the parameter space is quantized and closely related to the Berry phase as well as the Chern number. The process is adiabatic and the system always remains the ground state, then, the polarization is quite different from the usual dielectric polarization and has some similarity to the spontaneous polarization in the crystalline dielectrics which is also written by the Berry phase. We also point out the relation between our results and the adiabatic pumping.
Goryo Jun
Kohmoto Mahito
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