Akin to the charge density waves, the non-linear characteristics of a 1D WC depend critically on the homogeneity of the charge distribution sensitively affected by the disorder. Typical single-mode quantum wires of 10~nm width (to match the small electron wavelength) are challenging to achieve by electron beam lithography (EBL) because the wavelength is comparable to the EBL resolution. Moreover, narrow wires usually suffer from distortion not only due to system impurities (i.e. accumulated during the material synthesis) but also from the stress introduced during sample fabrication such as etching. As a result, 1D wires tend to be non-uniform or even “broken” (electrically instead of physically) into islands. Moreover, charge non-uniformity also arises in the 2D-1D transition region where screening is non-uniform. These effects break translational symmetry and alter essential properties, such as causing inhomogeneous LL, which tends to smear or violate the spin-charge separation.
Utilizing a novel type of undoped GaAs/AlGaAs heterostructures (grown by Loren Pfeiffer at Princeton University), we have realized ultra-dilute systems in which the average charge spacing (a=1/√πp) becomes enormous: up to≈500 nm or a Fermiwavelengthλ∼1μm(for charge density of 7×10^8 cm^{−2}). Consequently, a single mode 1D channel is achieved at up to 0.5 – 1 μm wire width. This enormous single-particle wavelength opens up plausible means for creating uniform 1D charges and implementing single-particle detection.
Inter-particle interaction measured by the Wigner-Seitz radius is effectively stronger in 1D systems due to reduced dimensionality. Lowering the charge concentration in the 1D channel is expected to drive a quantum phase transition from a gapless LL, where electrons are extended over the length of the wire, to eventually a gapped WC, where the electrons are spatially separated to minimize the Coulomb force. Our recent results show that, compared to the 2D behaviors, the 1D charge density and temperature dependence show a transition from a metallic phase to an insulator around a critical density of 1×105 cm-1.
