Low-temperature thermal relaxation of electrons in one-dimensional nanometer-size structures

We calculate the low-temperature power loss due to acoustic-phonon emission via the deformation-potential electron-lattice coupling by warm one-dimensionally confined electrons in GaAs quantum wires. The most spectacular feature of one-dimensional thermal relaxation, arising from the dominance of 2${\mathit{k}}_{\mathit{F}}$ scattering at very low temperatures, is an exponential temperature dependence of power loss at the lowest electron temperatures, in contrast to the well-known Bloch-Gru¨neisen algebraic temperature dependence in higher dimensions. We find that, in contrast to two- and three-dimensional systems, the temperature dependence of the power loss is rather strongly density dependent and remains qualitatively unaffected by electronic screening in one dimension. The magnitude of the one-dimensional power loss is comparable to that in two-dimensional heterostructures except at the lowest temperatures, where the one-dimensional power loss is exponentially suppressed.