Strongly renormalized quasi-two-dimensional electron gas in a heterostructure with correlation effects

We present aspects of strong electron correlation in a model of a $BI∕M∕BI$ heterostructure where $BI$ is a band insulator and M can be tuned from a metal to a Mott insulator by varying the on-site repulsion. An effective one-dimensional Schr\"odinger equation for the low-energy part is derived in the framework of the Kotliar-Ruckenstein slave-boson mean-field theory and solved self-consistently for a wide range of the on-site interaction strength and of the width of the sandwiched material M. In the strongly interacting limit coherent quasiparticles responsible for metallic behavior are confined to a relatively narrow region near the interfaces where they form a quasi-two-dimensional electron gas. Due to the lack of spatial homogeneity these quasiparticles intrinsically obtain a nontrivial dependence on the transverse momentum which, for example, enters the low-energy behavior of the optical conductivity.