Energy levels of quantum wires determined from magnetophonon resonance experiments

We report the observation of magnetophonon resonances in quantum wires, fabricated by shallow etching on conventional high-mobility ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}-\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterojunctions. It is shown that magnetophonon resonance measurements can be used as an alternative transport tool for the characterization of the subband spectrum of quantum wires. The method proves to be particularly useful at low electron densities, when only a few subbands are occupied and the standard magnetic depopulation characterization technique can no longer be used. By variation of the electron density in the wires through illumination with a red light-emitting diode the one-dimensional (1D) subband spacing, as determined from magnetophonon resonance measurements, is found to increase with decreasing electron density and to be systematically higher than the subband spacing obtained from simultaneous magnetic depopulation measurements. We give an explanation of this observation, which indicates that the combination of both transport characterization methods provides information on the actual shape of the underlying confinement potential. In addition, also the effective mass of the 1D electrons can be determined from the magnetophonon data. We observe a slight increase of the effective mass with decreasing carrier density and a strikingly large enhancement of $m^{*}$ with stronger confinement, achieved by deeper etching. We discuss several possibilities that could lead to this strong mass enhancement.