The Luttinger liquid in superlattice structures: atomic gases, quantum dots and the classical Ising chain

Abstract

We study physical properties of a Luttinger liquid in a superlattice which is characterized by alternating two tunneling parameters. Employing the Bosonization approach, we describe the corresponding Hubbard model by the equivalent Tomonoga-Luttinger model. We analyze the spin-charge separation and transport property as the difference between the two tunneling parameter increases. We suggest that cold Fermi gases trapped in a bichromatic optical lattice and coupled quantum dots offer the opportunity to measure these effects in a convenient manner. We also study the classical Ising chain with two tunneling parameters. We found that the classical two-point correlator decreases as the difference between the two tunneling parameter increases.

Friedel oscillations and dynamical density of states of an inhomogeneous Luttinger liquid

“…Ishkhanyan et al [25] developed a Hubbard-Luttinger model to describe the motion of pi-conductivity electrons in one dimension in single walled carbon nano-tubes at low temperatures and compared the results with experimental data. Physical properties of a Luttinger liquid in a 1D superlattice like spin charge separation and transport properties are also studied by describing the corresponding Hubbard model in terms of the equivalent Tomonaga-Luttinger liquid model [26]. It is also well known that non-trivial interactions between electrons and impurities leads to the occurrence of Friedel oscillations in the charge density profile of Fermi liquids [27][28][29].…”