  LaAlO$_{3}$/SrTiO$_{3}$ heterostructure with polar and non-polar constituents
has been shown to exhibit interface metallic conductivity due to fractional
charge transfer to the interface. The interface reconstruction by electron
redistribution along (001) orientation, in which half of an electron is
transferred per two dimensional unit cell to the adjacent planes, resulting in
a net transfer of half of the charge, to both the interface and top most atomic
planes, has been ascribed to a polar discontinuity at the interface in the
Polar Catastrophe model. This avoids the divergence of electrostatic potential,
as the number of layers are increased, producing an oscillatory electric field
and finite potential. Akin to the description of charge fractionalization in
quasi one-dimensional polyacetylene by the field theoretic Jackiw-Rebbi model
with fermions interacting with topologically non-trivial background field, we
show an analogous connection between polar catastrophe model and Bell-Rajaraman
model, where the charge fractionalization occurs in the soliton free sector as
an end effect.
