STRONGLY CORRELATED ELECTRONS IN GATED QUANTUM-WIRE STRUCTURES

Recent advances in semiconductor technology have renewed interest in i nteracting one-dimensional (1d) electron systems. By appropriately des igning gated quantum wires the rich physics of Luttinger liquids may i nvestigated. In this paper we discuss the properties of three differen t gated quantum wires: a long quantum wire with random disorder, a qua ntum wire in the presence of an external periodic potential, and a cou pled linear chain of quantum dots. First, we have investigated the den sity of states (DOS) near the Fermi energy of one-dimensional spin-pol arized quantum wires in the regime where the localization length is co mparable to or larger than the inter-particle distance. The Wigner lat tice gap of such a system can occur precisely at the Fermi energy, coi nciding with the Coulomb gap in position. The DOS near the Fermi energ y is found to be well described by a power law whose exponent decrease s with increasing disorder strength. We have then investigated the opt ical conductivity of disordered one-dimensional Wigner crystal in the presence of a periodic external potential. Our exact diagonalization c alculation shows that the optical conductivity develops two types of b roadened 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 ene rgy 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 th e dots. The chemical potential of the system, mu N = E(N) - E(N - 1), satisfies, (mu N + mu N-l+2-N)/2 approximate to V + 2t, (N, N-l, V, E( N) and t are the number of electrons, the number of dots, and the stre ngth of nearest neighbor electron-electron interactions, the total gro undstate energy and the hopping integral between two adjacent dots). T his property will be reflected in the spacing between the conductance peaks as the gate potential is varied.