Tomonaga–Luttinger-liquid nature of edge excitations in integer quantum Hall edge channels

Abstract

In interacting one-dimensional (1D) systems, the quasi-particle picture in Fermi-liquid theory cannot successfully describe low-energy physics. Instead, electron dynamics in one dimension can be described as collective excitations, i.e., charge- and/or spin-density waves, which are elementary excitations in a Tomonaga-Luttinger (TL) liquid. Integer quantum Hall (QH) edge channels, which are chiral 1D electron states formed along the periphery of integer QH systems, provide a unique opportunity for studying TL-liquid physics. When edge channels lie parallel to each other, inter-channel interactions induce significant TL-liquid behaviors in coupled plasmons. One can prepare an arbitrary number of co- and/or counter-propagating channels of spin-up or -down electrons to form such a multiple edge-channel system. The plasmon dynamics can be experimentally investigated by using various functional devices such as charge injectors, detectors, and spin filters to select spin and bidirectional-momentum degrees of freedom. This article reviews electron dynamics in such QH TL liquids. We first introduce the chiral distributed-element circuit model for describing interactions in single and multiple integer-edge-channel systems. This simple model captures the TL-liquid nature of the 1D plasmon transport. We then review experimental studies on TL-liquid behaviors. These experiments show that plasmon velocity is significantly enhanced by the intra-channel interaction. In addition, they show that co-propagating channels with spin degrees of freedom exhibit TL-liquid behavior known as spin-charge separation, in which spin and charge excitations behave differently. This is demonstrated with a novel time- and spin-resolved charge detection technique. They also reveal that charge fractionalization occurs at the boundaries of counter-propagating channels with bidirectional-momentum degrees of freedom. A charge excitation even as small as an electron charge is fractionalized into smaller charges to form coupled plasmons in the interacting region. These experiments highlight the intriguing quantum many-body nature of QH TL liquids. Keywords: Tomonaga–Luttinger liquid, Quantum Hall edge channel