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Power laws in physics have until now always been associated with a scale invariance originating from the absence of a length scale. Recently, an emergent invariance even in the presence of a length scale has been predicted by the newly-developed nonlinear-Luttinger-liquid theory for a one-dimensional (1D) quantum fluid at finite energy and momentum, at which the particle’s wavelength provides the length scale. We present experimental evidence for this new type of power law in the spectral function of interacting electrons in a quantum wire using a transport-spectroscopy technique. The observed momentum dependence of the power law in the high-energy region matches the theoretical predictions, supporting not only the 1D theory of interacting particles beyond the linear regime but also the existence of a new type of universality that emerges at finite energy and momentum., Power laws are usually associated with a scale invariance due to the absence of a length scale. Here, Jin et al. report experimental evidence of a new type of power law in a GaAs/AlGaAs double quantum-well heterostructure, suggesting existence of a new type of universality that emerges at finite energy and momentum.

We present a single-exposure fabrication technique for a very large array of microscopic air-bridges using a tri-layer resist process with electron-beam lithography. The technique is capable of forming air-bridges with strong metal-metal or metal-substrate connections. This was demonstrated by its application in an electron tunnelling device consisting of 400 identical surface gates for defining quantum wires, where the air-bridges are used as suspended connections for the surface gates. This technique enables us to create a large array of uniform one-dimensional channels that are open at both ends. In this article, we outline the details of the fabrication process, together with a study and the solution of the challenges present in the development of the technique, which includes the use of water-IPA (isopropyl alcohol) developer, calibration of resist thickness and numerical simulation of the development., 6 pages, 5 figures; This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing