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, e−e* (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.
Subscribe to Journal
Get full journal access for 1 year
only $15.58 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Tomonaga, S. Remarks on Bloch's method of sound waves applied to many-fermion problems. Prog. Theor. Phys. 5, 544–569 (1950).
Luttinger, J. M. An exactly soluble model of a many-fermion system. J. Math. Phys. 4, 1154–1162 (1963).
Tarucha, S., Honda, T. & Saku, T. Reduction of quantized conductance at low temperatures observed in 2 to 10 µm-long quantum wires. Solid State Commun. 94, 413–418 (1995).
Bockrath, M. et al. Luttinger-liquid behaviour in carbon nanotubes. Nature 397, 598–601 (1999).
Grayson, M., Tsui, D. C., Pfeiffer, L. N., West, K. W. & Chang, A. M. Continuum of chiral Luttinger liquids at the fractional quantum Hall edge. Phys. Rev. Lett. 80, 1062–1065 (1998).
Safi, I. & Schulz, H. J. Transport in an inhomogeneous interacting one-dimensional system. Phys. Rev. B 52, R17040–R17043 (1995).
Pham, K-V., Gabay, M. & Lederer, P. Fractional excitations in the Luttinger liquid. Phys. Rev. B 61, 16397–16422 (2000).
Imura, K-I., Pham, K-V., Lederer, P. & Piéchon, F. Conductance of one-dimensional quantum wires. Phys. Rev. B 66, 035313 (2002).
Kamata, H., Ota, T., Muraki, K. & Fujisawa, T. Voltage-controlled group velocity of edge magnetoplasmon in the quantum Hall regime. Phys. Rev. B 81, 085329 (2010).
Berg, E., Oreg, Y., Kim, E-A. & von Oppen, F. Fractional charges on an integer quantum Hall edge. Phys. Rev. Lett. 102, 236402 (2009).
Venkatachalam, V., Hart, S., Pfeiffer, L., West, K. & Yacoby, A. Local thermometry of neutral modes on the quantum Hall edge. Nature Phys. 8, 676–681 (2012).
Van Wees, B. J. et al. Quantized conductance of point contacts in a two-dimensional electron gas. Phys. Rev. Lett. 60, 848–850 (1988).
Kane, C. L. & Fisher, M. P. A. Transport in a one-channel Luttinger liquid. Phys. Rev. Lett. 68, 1220–1223 (1992).
Chang, A. M. Chiral Luttinger liquids at the fractional quantum Hall edge. Rev. Mod. Phys. 75, 1449–1505 (2003).
Steinberg, H. et al. Charge fractionalization in quantum wires. Nature Phys. 4, 116–119 (2008).
Ashoori, R. C., Stormer, H. L., Pfeiffer, L. N., Baldwin, K. W. & West, K. Edge magnetoplasmons in the time domain. Phys. Rev. B 45, 3894–3897 (1992).
Fetter, A. L. Edge magnetoplasmons in a bounded two-dimensional electron fluid. Phys. Rev B 32, 7676–7684 (1985).
Volkov, V. A. & Mikhailov, S. A. Edge magnetoplasmons: low frequency weakly damped excitations in inhomogeneous two-dimensional electron systems. Sov. Phys. JETP 67, 1639–1653 (1988).
Talyanskii, V. I. et al. Spectroscopy of a two-dimensional electron gas in the quantum-Hall-effect regime by use of low-frequency edge magnetoplasmons. Phys. Rev. B 46, 12427–12432 (1992).
Hashisaka, M. et al. Distributed-element circuit model of edge magnetoplasmon transport. Phys. Rev. B 88, 235409 (2013).
Chklovskii, D. B., Shklovskii, B. I. & Glazman, L. I. Electrostatics of edge channels. Phys. Rev. B 46, 4026–4034 (1992).
Kumada, N., Kamata, H. & Fujisawa, T. Edge magnetoplasmon transport in gated and ungated quantum Hall systems. Phys. Rev. B 84, 045314 (2011).
Lee, H. C. & Yang, S.-R. E. Spin-charge separation in quantum Hall edge liquids. Phys. Rev. B 56, R15529–R15532 (1997).
Bocquillon, E. et al. Separation of neutral and charge modes in one-dimensional chiral edge channels. Nature Commun. 4, 1839 (2013).
Roulleau, P. et al. Direct measurement of the coherence length of edge states in the integer quantum Hall regime. Phys. Rev. Lett. 100, 126802 (2008).
Gabelli, J. et al. Relaxation time of a chiral quantum R–L circuit. Phys. Rev. Lett. 98, 166806 (2007).
Larkin, I. A. & Davies, J. H. Edge of the two-dimensional electron gas in a gated heterostructure. Phys. Rev. B 52, R5535–R5538 (1995).
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.
The authors declare no competing financial interests.
About this article
Cite this article
Kamata, H., Kumada, N., Hashisaka, M. et al. Fractionalized wave packets from an artificial Tomonaga–Luttinger liquid. Nature Nanotech 9, 177–181 (2014). https://doi.org/10.1038/nnano.2013.312
Physical Review B (2020)
Physical Review Letters (2020)
EPJ Web of Conferences (2020)
Applied Physics Express (2019)
Physical Review B (2019)