Luttinger liquid superlattices: Realization of gapless insulating phases

Abstract

We investigate Luttinger liquid superlattices, periodic structures composed of two kinds of one-dimensional systems of interacting electrons. We calculate several properties of the low-energy sector: the effective charge and spin velocities, the compressibility, various correlation functions, the Landauer conductance, and the Drude weight. The low-energy properties are subsumed into effective parameters, much like homogeneous onedimensional systems. A generic result is the weighted average nature of these parameters, in proportion to the spatial extent of the underlying subunits, pointing to the possibility of ''engineered'' structures. As a specific realization, we consider a one-dimensional Hubbard superlattice, which consists of a periodic arrangement of two long Hubbard chains with different coupling constants and different hopping amplitudes. This system exhibits a rich phase diagram with several phases, both metallic and insulating. We have found that gapless insulating phases are present over a wide range of parameters.

Multiperiodic magnetic structures in Hubbard superlattices

“…Another possible realization of our model would be to a ͑as yet hypothetical͒ superlattice made up of single-walled metallic carbon nanotubes, since these have been successfully described in terms of a Luttinger liquid; see, e.g., Ref. 16 for a partial list of references.…”

“…14 Further, by examining the Luttinger liquid version of the model, 15 one finds that these superlattices provide the means to realize gapless insulating phases. 16 Previous studies of the discrete version of the model 12-14 resorted to Lanczos diagonalization, which sets limits on the system sizes used; for instance, a 24-site lattice size could only be considered for the low-and high-density regimes ( ϭ1/6 and ϭ11/6). Nonetheless, one was still able to probe the period of exchange oscillations for these special densities through the analysis of the magnetic structure factor: the peak position displayed oscillatory behavior with the spacer thickness.…”

The effective charge velocity of spin-¹/2 superlattices

“…These systems are obtained when we consider the spatial variation of the coupling constants or an inhomogeneous magnetic field. The special case of spin superlattice (SS) composed of a repeated pattern of two long and different spin-1 2 XXZ chains, was considered by one of us in a previous work [10]. We found that the magnetization curve presents a nontrivial plateaus whose magnetization value depends on the relative size of sub-chains = L 2 /L 1 and is given by M s = 1/(1 + ).…”

“…Different Inhomogeneous spin chains has been studied in the last years [8][9][10]. These systems are obtained when we consider the spatial variation of the coupling constants or an inhomogeneous magnetic field.…”

Electronic excitations and correlations in quantum bars

“…In this respect, a 2D system of weakly coupled 1D quantum wires 2-4 looks promising. Indeed, a theoretical analysis of stable LL phases was recently presented for a system consisting of coupled parallel quantum wires [5][6][7] and for 3D stacks of sheets of such wires in parallel and crossed orientations 8 . In most of these cases, the interaction between the parallel quantum wires is assumed to be perfect along the wire 8 , whereas the interaction between the modes generated in different wires depends only on the inter-wire distance.…”