Density wave ground state and fractional fermions in LaAlO3/SrTiO3 heterostructure.

We show that the non-homogeneous charged layer distribution of the LaAlO 3 /SrT iO 3 heterostructure undergoing interface reconstruction is the density wave ground state of the well known anharmonic lattice model described by the {lambda}{phi} 4 continuum model. The two dimensional planar structure of the charged surfaces with alternating polarity leads to an effective one dimensional model, with fermions coupled to the planar distortions acting as long wavelength optical phonons in one dimension. The Hamiltonian with the desired anharmonicity for describing the non-homogeneous density wave type distortion is the same one that describes the fermion number fractionalization in polyacetylene. The general solution of this theory is the Jacobi elliptic sine function sn(x;k), which in the limiting case of lattice distortion being localized gives the kink/anti-kink solution.