Interaction effects in a one-dimensional quantum wire

One of the most fascinating areas of research in mesoscopic physics is the transport properties of one-dimensional (1D) quantum wires. A quasi-1D quantum wire is realised by electrostatically squeezing a high mobility two-dimensional-electron-gas using patterned gates fabricated on a GaAs/AlGaAs heterostructure. In a 1D quantum wire the conductance takes quantised values, with each 1D sub-band contributing a spin degenerate conductance of 2e2/h and total conductance is N2e2/h, where N=1,2,3,4…; here the 1D electrons have freedom to change momentum in one dimension only with a progressive filling of the sub-bands. However when electron-electron interaction is considered, a number of 1D states are predicted, including a ferromagnetic state and various spin phases, which has aroused a considerable interest in the research of interacting fermions in quantum wires. One of the predictions is the observation of Wigner crystallization in low density 1D system. 

In this talk, recent experimental results of a low-density quasi-1D device fabricated using GaAs/AlGaAs heterostructure, having split-gates, top-gate combination to control the carrier density and confinement potential will be presented. At a particular confinement configuration, and electron density, the ground state of a 1D quantum wire splits into two rows of electrons which results in first conductance plateau at 4e2/h than the usual 2e2/h, which is a signature of Wigner crystallization. Non-linear transport measurement revealed that in addition to the usual 0.25(2e2/h) due to the lifting of momentum degeneracy, an additional structure at 0.5(2e2/h) is visible which indicates addition of two 0.25(2e2/h) structures contributed by each rows. Analysis of the level movement with confinement potential indicates that row formation proceeds by an interchange of the single electron ground and first excited states, this can result in an anticrossing and a hybridization of the levels. In the presence of in-plane magnetic field, the 1D subbands take a complex form due to Zeeman splitting in addition to the Coulomb interactions. The most remarkable observation was the interaction combined with weak confinement results in the first excited state becoming the ground state as the two rows are formed, and the ground state moves up and crosses the higher levels. This unexpected manifestation of the electron interaction encourages us to explore gate geometries to engineer the double rows to realize integrated quantum devices.