Probing e-e interactions in a periodic array of GaAs quantum wires

We present the results of non-linear tunnelling spectroscopy between an array of independent quantum wires and an adjacent two-dimensional electron gas (2DEG) in a double-quantum-well structure. The two layers are separately contacted using a surface-gate scheme, and the wires are all very regular, with dimensions chosen carefully so that there is minimal modulation of the 2DEG by the gates defining the wires. We have mapped the dispersion spectrum of the 1D wires down to the depletion of the last 1D subband by measuring the conductance \emph{G} as a function of the in-plane magnetic field \emph{B}, the interlayer bias $V_{\rm dc}$ and the wire gate voltage. There is a strong suppression of tunnelling at zero bias, with temperature and dc-bias dependences consistent with power laws, as expected for a Tomonaga-Luttinger Liquid caused by electron-electron interactions in the wires. In addition, the current peaks fit the free-electron model quite well, but with just one 1D subband there is extra structure that may indicate interactions.