Quantum phase transition in a resonant level coupled to interacting leads


A Luttinger liquid is an interacting one-dimensional electronic system, quite distinct from the ‘conventional’ Fermi liquids formed by interacting electrons in two and three dimensions1. Some of the most striking properties of Luttinger liquids are revealed in the process of electron tunnelling. For example, as a function of the applied bias voltage or temperature, the tunnelling current exhibits a non-trivial power-law suppression2,3. (There is no such suppression in a conventional Fermi liquid.) Here, using a carbon nanotube connected to resistive leads, we create a system that emulates tunnelling in a Luttinger liquid, by controlling the interaction of the tunnelling electron with its environment. We further replace a single tunnelling barrier with a double-barrier, resonant-level structure and investigate resonant tunnelling between Luttinger liquids. At low temperatures, we observe perfect transparency of the resonant level embedded in the interacting environment, and the width of the resonance tends to zero. We argue that this behaviour results from many-body physics of interacting electrons, and signals the presence of a quantum phase transition4,5. Given that many parameters, including the interaction strength, can be precisely controlled in our samples, this is an attractive model system for studying quantum critical phenomena in general, with wide-reaching implications for understanding quantum phase transitions in more complex systems, such as cold atoms6 and strongly correlated bulk materials7.

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Figure 1: Emulating Luttinger liquid with resistive environment.
Figure 2: Resonant lineshape: symmetric and asymmetric cases.
Figure 3: Resonant peak parameters at different degrees of asymmetry.
Figure 4: Phase diagram and the quantum critical point.


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We appreciate discussions with I. Affleck, D. V. Averin, A. M. Chang, C. H. Chung, S. Florens, M. Goldstein, L. I. Glazman, K. Ingersent, K. Le Hur, M. Lavagna, A. H. MacDonald, Yu. V. Nazarov, D. G. Polyakov and M. Vojta. We thank J. Liu for providing the nanotube growth facilities and W. Zhou for helping to optimize the nanotube synthesis. The work was supported by US DOE awards DE-SC0002765, DE-SC0005237 and DE-FG02-02ER15354.

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H.T.M., I.V.B. and G.F. designed the experiment. H.T.M. fabricated the samples. H.T.M., I.V.B., Y.V.B., A.S. and G.F. conducted the experiment. H.T.M. and G.F. analysed the data. H.T.M, D.E.L., H.Z., H.U.B. and G.F. interpreted the data. D.E.L., H.Z. and H.U.B. developed the theory.

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Correspondence to Gleb Finkelstein.

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Mebrahtu, H., Borzenets, I., Liu, D. et al. Quantum phase transition in a resonant level coupled to interacting leads. Nature 488, 61–64 (2012). https://doi.org/10.1038/nature11265

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