Akin to the charge density waves, the non-linear characteristics of a 1D WC depend critically on the homogeneity of the charge distribution and the disorder. Typical single-mode quantum wires of 10~nm width (to match the small electron wavelength) are difficult 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 arises also in the 2D-1D transition region where screening is non-uniform. These effects break translational symmetry and alter important properties such as causing inhomogeneous LL which tend 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 both creating uniform 1D charges and for implementing single particle detection.