Abstract
One-dimensional metals, such as quantum wires or carbon nanotubes, can carry charge in arbitrary units, smaller or larger than a single electron charge. However, according to Luttinger theory, which describes the low-energy excitations of such systems, when a single electron is injected by tunneling into the middle of such a wire, it will tend to break up into separate charge pulses, moving in opposite directions, which carry definite fractions f and (1-f) of the electron charge, determined by a parameter g that measures the strength of charge interactions in the wire. (The injected electron will also produce a spin excitation, which will travel at a different velocity than the charge excitations.) Observing charge fractionalization physics in an experiment is a challenge in those (nonchiral) low-dimensional systems which are adiabatically coupled to Fermi liquid leads. We theoretically discuss a first important step towards the observation of charge fractionalization in quantum wires based on momentum-resolved tunneling and multi-terminal geometries, and explain the recent experimental results of Steinberg et al. [H. Steinberg, G. Barak, A. Yacoby, L.N. Pfeiffer, K.W. West, B.I. Halperin, K. Le Hur, Nature Physics 4 (2008) 116].
Highlights
Systems of low dimensions have provided special opportunities, challenges, and fascination for condensed matter physicists [1]
Luttinger liquid behavior has been observed through energy dependent local tunneling [6] and power-law tunneling lineshapes [7]. Another remarkable effect predicted by Luttinger liquid theory is charge fractionalization: the extra charge produced by an electron tunneling into the middle of a uniform Luttinger liquid will break up into pieces, moving in opposite directions, which will carry definite fractions f and (1 − f ) of the electron charge, determined by a parameter g that measures the strength of charge interactions in the wire
To elucidate the concept of charge fractionalization in a quantum wire embodied by a Luttinger theory, let us inject an extra electron with a welldefined momentum at one Fermi point
Summary
Systems of low dimensions have provided special opportunities, challenges, and fascination for condensed matter physicists [1]. Luttinger liquid behavior has been observed through energy dependent local tunneling [6] and power-law tunneling lineshapes [7] Another remarkable effect predicted by Luttinger liquid theory is charge fractionalization: the extra charge produced by an electron tunneling into the middle of a uniform Luttinger liquid will break up into pieces, moving in opposite directions, which will carry definite fractions f and (1 − f ) of the electron charge, determined by a parameter g (the Luttinger parameter) that measures the strength of charge interactions in the wire. While for fractional quantum Hall edge states, the counterpropagating modes are spatially separated, in quantum wires or carbon nanotubes, the nonchiral modes are confined to the same spatial channel, and cannot be contacted individually Their chemical potentials renormalize in a non-trivial manner when adiabatically coupled to metallic leads, making charge fractionalization phenomenoa difficult to observe. We introduce a novel universal ratio which allows to reveal the charge fractionalization mechanism in nonchiral Luttinger liquids
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