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

一维（1D）系统的行为方式与高维系统明显不同，因为电子-电子相互作用现在不再被忽视。Tomonaga-Luttinger液体（TLL）模型是描述这类系统的理论。该模型预测了自旋电荷分离和零偏压下隧道电导的抑制等现象，并在实验中得到了验证。然而，它做了一些简化，例如假设无限长度的一维系统，只考虑低能激发。最近的理论工作集中在扩展TLL理论以包括高能量激励和有限长度系统。这导致了预测，在高阶激励下，除了简单的单粒子抛物色散外，还应该观察到具有更高动量的“复制”抛物线。我的工作重点是使用1D-2D隧道光谱方法对这些高阶激发进行实验检测和量化，以便绘制系统的色散图。此外，我们还对测量零偏压下隧穿的温度依赖性和其他有趣的特征以及观察一维导线中的不对称电流（即电荷分异）感兴趣。

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.