Polarization screening and induced carrier density at the interface of LaAlO$_3$ overlayer on SrTiO$_3$ (001)

We investigate the role of lattice polarization in determination of induced carrier density at the $n$-type interface of LaAlO$_3$ overlayer on SrTiO$_3$ (001) by carrying out density-functional-theory calculations. When no oxygen vacancy or defect is present, the magnitude of polarization screening in the LaAlO$_3$ layers is found to be correlated with the carrier charge induced at the interface. For the interfaces with a few LaAlO$_3$ layers, the induced charge carrier is compensated by the electrostatic screening and consequently its density remains far less than 0.5 electrons per unit cell.