Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2007-11-12
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
Scientific paper
We develop a general theory of electric polarization induced by inhomogeneity in crystals. We show that contributions to polarization can be classified in powers of the gradient of the order parameter. The zeroth order contribution reduces to the well-known result obtained by King-Smith and Vanderbilt for uniform systems. The first order contribution, when expressed in a two-point formula, takes the Chern-Simons 3-form of the vector potentials derived from the Bloch wave functions. Using the relation between polarization and charge density, we demonstrate our formula by studying charge fractionalization in a two-dimensional dimer model recently proposed.
Clougherty Dennis P.
Niu Qian
Shi Junren
Xiao Di
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