Strongly correlated electrons in gated quantum wire structures

Recent advances in semiconductor technology have renewed interest in interacting one-dimensional (Id) electron systems. By appropriately designing gated quantum wires the rich physics of Luttinger liquids may investigated. In this paper we discuss the properties of three different gated quantum wires: a long quantum wire with random disorder, a quantum wire in the presence of an external periodic potential, and a coupled linear chain of quantum dots. First, we have investigated the density of states (DOS) near the Fermi energy of one-dimensional spin-polarized quantum wires in the regime where the localization length is comparable to or larger than the inter-particle distance. The Wigner lattice gap of such a system can occur precisely at the Fermi energy, coinciding with the Coulomb gap in position. The DOS near the Fermi energy is found to be well described by a power law whose exponent decreases with increasing disorder strength. We have then investigated the optical conductivity of disordered one-dimensional Wigner crystal in the presence of a periodic external potential. Our exact diagonalization calculation shows that the optical conductivity develops two types of broadened peaks. The lower energy peak is due to a wide distribution of local pinning frequencies while the higher energy peak is due to the creation of pairs of solitons. We have also investigated the total energy of a linearly coupled finite chain of spin-polarized quantum dots when the number of electrons is equal to or less than the number of the dots. The chemical potential of the system, μN = E(N) - E(N - 1), satisfies, (μN + μN_l+2-N)/2 ≈ V + 2t, (N, N_l, V, E(N) and t are the number of electrons, the number of dots, and the strength of nearest neighbor electron-electron interactions, the total groundstate energy and the hopping integral between two adjacent dots). This property will be reflected in the spacing between the conductance peaks as the gate potential is varied.