Mapping a non-linear Luttinger Liquid using 1D-2D magnetotunelling spectroscopy

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One-dimensional (1D) systems behave in a significantly different way from their higher-dimensional counterparts as electron-electron interactions can now no longer be neglected. The Tomonaga-Luttinger Liquid (TLL) model is a theory that describes such systems. This model makes a number of predictions, such as spin-charge separation and suppression of tunnelling conductance at zero bias, both of which have been experimentally observed. It makes however some simplifications, such as assuming 1D systems of infinite length and only considering low-energy excitations.Recent theoretical work has focused on extending the TLL theory to include higher energy excitations and finite length systems. This led to the prediction that, at higher order excitations, 'replica' parabolas with higher momenta should be observed, in addition to the simple single-particle parabolic dispersion. My work focuses on the experimental detection and quantification of these higher order excitations using the method of 1D-2D tunnelling spectroscopy in order to map the dispersion of the system. In addition, we are also interested in measuring the temperature dependence of tunnelling at zero bias and at other interesting features as well as observing asymmetric current flow (i.e. charge fractionalisation) in 1D wires.