 
Summary: VOLUME 78, NUMBER 3 P H Y S I C A L R E V I E W L E T T E R S 20 JANUARY 1997
Piezoelectricity: Quantized Charge Transport Driven by Adiabatic Deformations
J. E. Avron,1,
* J. Berger,1
and Y. Last2
1
Department of Physics, Technion, 32000 Haifa, Israel
2
Division of Physics Mathematics and Astronomy, Caltech, Pasadena, California 91125
(Received 17 September 1996)
We study the (zero temperature) quantum piezoelectric response of Harperlike models with broken
inversion symmetry. The charge transport in these models is related to topological invariants (Chern
numbers). We show that there are arbitrarily small periodic modulations of the atomic positions that
lead to nonzero charge transport. [S00319007(96)021680]
PACS numbers: 72.10.Bg, 77.65.j
The Harper model is a tightbinding quantum Hamil
tonian describing the dynamics of noninteracting electrons
on a twodimensional lattice in the presence of magnetic
fields. It is known to have interesting Hall transport prop
erties. Here we study the electric response of Harperlike
