Fractionalized wave packets from an artificial Tomonaga–Luttinger liquid


The model of interacting fermion systems in one dimension known as a Tomonaga–Luttinger liquid (TLL)1,2 provides a simple and exactly solvable theoretical framework that predicts various intriguing physical properties. Evidence of a TLL has been observed as power-law behaviour in electronic transport on various types of one-dimensional conductor3,4,5. However, these measurements, which rely on d.c. transport involving electron tunneling processes, cannot identify the long-awaited hallmark of charge fractionalization, in which an injection of elementary charge e from a non-interacting lead is divided into the non-trivial effective charge e* and the remainder, ee* (refs 6, 7, 8). Here, we report time-resolved transport measurements9 on an artificial TLL composed of coupled integer quantum Hall edge channels10, in which we successfully identify single charge fractionalization processes. A wave packet of charge q incident from a non-interacting region breaks up into several fractionalized charge wave packets at the edges of the artificial TLL, from which transport eigenmodes can be evaluated directly. These results are informative for elucidating the nature of TLLs and low-energy excitations in the edge channels11.

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Figure 1: Experimental set-up for the time-resolved measurement of charge fractionalization.
Figure 2: Observed charge wave packets injected and extracted from the TLL regions.
Figure 3: Gate voltage and filling factor dependence of the TLL parameters.
Figure 4: Microscopic model of Coulomb interaction with electrostatic capacitances.


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The authors thank K-I. Imura and M. Nakamura for discussions and M. Ueki for experimental support. This work was partially supported by Grants-in-Aid for Scientific Research (21000004, 11J09248) and the Global Center of Excellence Program from the MEXT of Japan through the ‘Nanoscience and Quantum Physics’ Project of the Tokyo Institute of Technology.

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H.K. performed the experiments, analysed the data and wrote the manuscript. T.F. supervised the research. K.M. grew the wafer. All authors discussed the results and commented on the manuscript.

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Correspondence to H. Kamata or T. Fujisawa.

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The authors declare no competing financial interests.

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Kamata, H., Kumada, N., Hashisaka, M. et al. Fractionalized wave packets from an artificial Tomonaga–Luttinger liquid. Nature Nanotech 9, 177–181 (2014).

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