Absence of low temperature saturation of electron–electron scattering in a single mode quantum wire

Abstract

At helium temperatures electron–electron scattering determines the phase breaking and therefore limits the size of quantum interference devices. The electron–electron scattering times and scattering lengths are calculated numerically for ideal single mode quantum wires. The striking result of the present work is that there is no saturation of the electron–electron scattering time at low temperatures in an ideal single mode quantum wire without impurity scattering, in contrast to the two- and three-dimensional cases. Phase coherence lengths up to 10 mm are predicted for mK temperatures and up to 50 μm around 4 K. Conditions to observe such long coherence lengths are discussed.