Chiral Luttinger Liquids at the Fractional Quantum Hall Edge
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00F0FF13310E463FA7727D78430EC88E |
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7.2 |
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118 |
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日期： |
2024-9-1 |
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Chiral Luttinger Liquids at the Fractional Quantum Hall Edge,A.MChang,Department of Physics,Purdue University, West Lafayette, IN 47907-1396,This article contains a comprehensive review of the chiral Tomonaga- Luttinger liquid.,Although the main emphasis is on the key experimental findings on electron-tunneling into,the chiral Tomonaga-Luttinger liquid, in which the tunneling is utilized to probe the powerlaw,tunneling density of states in this interacting 1-dimensional system at the edge of the,fractional quantum Hall fluid, this review also contains a basic description of the theoretical,aspectsThe inclusion of the theory section provides a suitable framework and language,for discussing the unique and novel features of the chiral Tomonaga-Luttinger liquidThe,key experimental results will be contrasted against the predictions of the standard theory,based on the effective, Chern-Simon field theories of the fractional Hall fluid edgePossible,ramifications of the differences between experiment and theory are highlightedIn addition,for completeness a brief survey of other 1-dimensional systems exhibiting the interaction,physics associated with the (non-chiral) Tomonaga-Luttinger liquid is also provided.,1,Contents,I INTRODUCTION 3,II THEORETICAL BACKGROUND 5,A Landau Fermi liquid6,1 Dynamics: The Boltzmann kinetic equation 10,B Many-body analysis11,1 Green's functions11,2 Lehman representation: spectral density, tunneling density of states 14,3 Intuitive Idea of a Quasi-Particle15,4 Two Particle Green's Function16,5 Dynamical equation of motion for the single particle Green function 17,6 Quasi-particle interaction20,C Breakdown of the Fermi liquid Picture in Id and the Tomonaga-Luttinger liquid 24,1 Bosonization 27,2 Power law behavior in the single particle Green's function29,3 g-ology 32,D Chiral Luttinger liquid36,1 Wen's hydro dynamic formulation 37,2 1-d effective field theory of the chiral Luttinger liquid.43,3 Role of Disorder46,4 Compressible fluid edges47,5 Scaling functions for electron tunneling49,6 Resonant tunneling56,7 Shot noise and fractional charge: quasi-particle tunneling.59,III EXPERIMENTS ON CHIRAL LUTTINGER LIQUIDS- TUNNELING INTO THE,FRACTIONAL QUANTUM HALL EDGE 59,A Historical Overview61,B Cleaved-edge overgrowth63,C Measurement techniques65,D Sample preparation 66,E Data presentation 67,1 Establishment of Chiral Luttinger Behavior in,Electron Tunneling into Fractional Quantum Hall Edges 67,2 An apparent g=l/2 chiral Luttinger liquid at the edge of,the レ=1/2 compressible composite Fermion liquid 73,3 A continuum of chiral Luttinger liquid behavior.77,4 Plateau behavior in the chiral Luttinger liquid exponent.79,5 Discussion: Is the chiral Luttinger liquid exponent universal? 83,6 Resonant tunneling into a biased fractional quantum Hall edge.87,7 Other Manifestations of Chiral Luttinger Liquid Characteristics in the Edge Properties,of Fractional Quantum Hall Fluids91,I V OTHER LUTTINGER LIQUID SYSTEMS 95,IINTRODUCTION,This article deals with electron transport in a new state of matter, specifically electron tunneling into,the chiral Luttinger liquid (CLL)The chiral Luttinger liquid, also known as the chiral Tomonaga-Luttinger,liquid (Wen, 1990a, 1990b, 1991a, 1991b, 1992, 1995; Kane et aL, 1994; Kane and Fisher, 1995; Fendley,et aL, 1995a, 1995b; Moon, 1993; Chang et aL, 1996, and 2001; Grayson et al1998)is a particularly,clean realization of a new class of strongly interacting 1-dimensional (1-d) metallic systems, distinguished,from conventional 3-dimensional (3-d) metals by the absence of a single-particle pole in the spectral density.,Instead, the usual pole is replaced by power law dependences in momentum and frequencyExperimentally,what this means is that in a transport measurement where electrons are injected into or removed from,the 1-d correlated metal across a tunneling barrier, a power law behavior is observed in either the tunnel,current or in the differential conductance as a function of energy, where this energy may be set by a bias,voltage or by temperatureFrom the perspective of measurements, the CLL is an extremely clean system.,Residing at the 1-dimensional edge of the 2-dimensional fractional quantum Hall fluid, the CLL is realized,in devices grown by the molecular beam epitaxy (MBE) growth technique, which offers extremely precise,atomic-scale controlThis control extends beyond the growth of the metallic electron system itself to include,the tunnel barrier as wellFurthermore, the nature of the CLL can be tuned by changing the magnetic field,and hence the filling factor of the fractional quantum Hall fluidThis tunability leads to a ri……
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