Mode softening in the far-infrared excitation of quantum-wire arrays

We have studied the far-infrared response of GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum-wire arrays of 200- and 300-nm periods, realized by biasing a periodic surface-grating gate structure below the two-dimensional electron-gas conduction threshold. We find that in our samples, which have substantially smaller periods than those in previous work, the resonance is observed at a frequency ${\mathrm{\omega }}_{\mathit{r}}$ much smaller than that of the depolarization-shifted subband resonance and that the 200-nm-period wires have a smaller ${\mathrm{\omega }}_{\mathit{r}}$ than the 300-nm-period wires of the same carrier densities. The experiment demonstrates mode softening in coupled quantum wires. We also present a theoretical model, based on the generalized Kohn theorem, to take into account the mode softening. Our model can quantitatively describe the observed mode softening and explain the experimental results.