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Kumar S, Pepper M. Interactions and non-magnetic fractional quantization in one-dimension. APPLIED PHYSICS LETTERS 2021; 119:110502. [PMID: 35382142 PMCID: PMC8970604 DOI: 10.1063/5.0061921] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2021] [Accepted: 08/27/2021] [Indexed: 06/14/2023]
Abstract
In this Perspective article, we present recent developments on interaction effects on the carrier transport properties of one-dimensional (1D) semiconductor quantum wires fabricated using the GaAs/AlGaAs system, particularly the emergence of the long predicted fractional quantization of conductance in the absence of a magnetic field. Over three decades ago, it was shown that transport through a 1D system leads to integer quantized conductance given by N·2e2/h, where N is the number of allowed energy levels (N = 1, 2, 3, …). Recent experiments have shown that a weaker confinement potential and low carrier concentration provide a testbed for electrons strongly interacting. The consequence leads to a reconfiguration of the electron distribution into a zigzag assembly which, unexpectedly, was found to exhibit quantization of conductance predominantly at 1/6, 2/5, 1/4, and 1/2 in units of e2/h. These fractional states may appear similar to the fractional states seen in the Fractional Quantum Hall Effect; however, the system does not possess a filling factor and they differ in the nature of their physical causes. The states may have promise for the emergent topological quantum computing schemes as they are controllable by gate voltages with a distinct identity.
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Affiliation(s)
- S. Kumar
- Author to whom correspondence should be addressed:
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Kumar S, Pepper M, Holmes SN, Montagu H, Gul Y, Ritchie DA, Farrer I. Zero-Magnetic Field Fractional Quantum States. PHYSICAL REVIEW LETTERS 2019; 122:086803. [PMID: 30932620 DOI: 10.1103/physrevlett.122.086803] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2018] [Indexed: 06/09/2023]
Abstract
Since the discovery of the fractional quantum Hall effect in 1982 there has been considerable theoretical discussion on the possibility of fractional quantization of conductance in the absence of Landau levels formed by a quantizing magnetic field. Although various situations have been theoretically envisaged, particularly lattice models in which band flattening resembles Landau levels, the predicted fractions have never been observed. In this Letter, we show that odd and even denominator fractions can be observed, and manipulated, in the absence of a quantizing magnetic field, when a low-density electron system in a GaAs based one-dimensional quantum wire is allowed to relax in the second dimension. It is suggested that such a relaxation results in formation of a zigzag array of electrons with ring paths which establish a cyclic current and a resultant lowering of energy. The behavior has been observed for both symmetric and asymmetric confinement but increasing the asymmetry of the confinement potential, to result in a flattening of confinement, enhances the appearance of new fractional states. We find that an in-plane magnetic field induces new even denominator fractions possibly indicative of electron pairing. The new quantum states described here have implications both for the physics of low dimensional electron systems and also for quantum technologies. This work will enable further development of structures which are designed to electrostatically manipulate the electrons for the formation of particular configurations. In turn, this could result in a designer tailoring of fractional states to amplify particular properties of importance in future quantum computation.
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Affiliation(s)
- S Kumar
- London Centre for Nanotechnology, 17-19 Gordon Street, London WC1H 0AH, United Kingdom
- Department of Electronic and Electrical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom
| | - M Pepper
- London Centre for Nanotechnology, 17-19 Gordon Street, London WC1H 0AH, United Kingdom
- Department of Electronic and Electrical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom
| | - S N Holmes
- Toshiba Research Europe Limited, Cambridge Research Laboratory, 208 Cambridge Science Park, Milton Road, Cambridge CB4 0GZ, United Kingdom
| | - H Montagu
- London Centre for Nanotechnology, 17-19 Gordon Street, London WC1H 0AH, United Kingdom
- Department of Electronic and Electrical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom
| | - Y Gul
- London Centre for Nanotechnology, 17-19 Gordon Street, London WC1H 0AH, United Kingdom
- Department of Electronic and Electrical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom
| | - D A Ritchie
- Cavendish Laboratory, J.J. Thomson Avenue, Cambridge CB3 OHE, United Kingdom
| | - I Farrer
- Cavendish Laboratory, J.J. Thomson Avenue, Cambridge CB3 OHE, United Kingdom
- Now at Department of Electronic and Electrical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, United Kingdom
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Zhu X, Louie SG. Variational quantum Monte Carlo study of two-dimensional Wigner crystals: Exchange, correlation, and magnetic-field effects. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:5863-5884. [PMID: 9981777 DOI: 10.1103/physrevb.52.5863] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Kivelson SA, Kallin C, Arovas DP, Schrieffer JR. Comment on "Ring exchange and the fractional quantum Hall effect". PHYSICAL REVIEW. B, CONDENSED MATTER 1988; 37:9085-9086. [PMID: 9944289 DOI: 10.1103/physrevb.37.9085] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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