Observation of replica dispersions in interacting 1D wires

At low excitation energies, a system of interacting one-dimensional (1D) electrons can be described theoretically as a Tomonaga-Luttinger liquid. However, it is only in the last few years that theoreticians have developed models of the behaviour at energies comparable to the Fermi energy, predicting `replicas' of the dispersion relation offset by multiples of the Fermi wave-vector. We measure momentum-resolved tunnelling of electrons between 1D wires formed within a GaAs heterostructure and a 2D electron gas used as a spectrometer and have previously found well-resolved spin-charge separation at low energy with appreciable interaction strength. Now we have detected structure resembling a replica, which dies away quite rapidly at high momentum, in line with the most recent theory. We have fabricated arrays of wires with lengths between 1 and 20$\mu$m, after developing a reliable technique to make thousands of `air-bridges' on each device. The replica seems strongest in the short wires, again as predicted by the theory. [Moreno \textit{et al., Nat. Commun.} {\bf 7}, 12784 (2016); Tsyplyatyev \textit{et al., Phys. Rev. Lett.} {\bf 114}, 19640 (2015); Tsyplyatyev \textit{et al., Phys. Rev. B}, {\bf 93}, 075147 (2016).]