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Imaging the Zigzag Wigner Crystal in Confinement-Tunable Quantum Wires

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Imaging the Zigzag Wigner Crystal in Confinement-Tunable Quantum Wires View metadata, citation and similar papers at core.ac.uk brought to you by CORE PHYSICAL REVIEW LETTERS 121, 106801 (2018) provided by UCL Discovery Editors' Suggestion Featured in Physics Imaging the Zigzag Wigner Crystal in Confinement-Tunable Quantum Wires Sheng-Chin Ho,1 Heng-Jian Chang,1 Chia-Hua Chang,1 Shun-Tsung Lo,1 Graham Creeth,2 Sanjeev Kumar,2 Ian Farrer,3,4 † David Ritchie,3 Jonathan Griffiths,3 Geraint Jones,3 Michael Pepper,2,* and Tse-Ming Chen1, 1Department of Physics, National Cheng Kung University, Tainan 701, Taiwan 2Department of Electronic and Electrical Engineering, University College London, London WC1E 7JE, United Kingdom 3Cavendish Laboratory, J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom 4Department of Electronic and Electrical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, United Kingdom (Received 4 May 2018; revised manuscript received 3 July 2018; published 6 September 2018) The existence of Wigner crystallization, one of the most significant hallmarks of strong electron correlations, has to date only been definitively observed in two-dimensional systems. In one-dimensional (1D) quantum wires Wigner crystals correspond to regularly spaced electrons; however, weakening the confinement and allowing the electrons to relax in a second dimension is predicted to lead to the formation of a new ground state constituting a zigzag chain with nontrivial spin phases and properties. Here we report the observation of such zigzag Wigner crystals by use of on-chip charge and spin detectors employing electron focusing to image the charge density distribution and probe their spin properties. This experiment demonstrates both the structural and spin phase diagrams of the 1D Wigner crystallization. The existence of zigzag spin chains and phases which can be electrically controlled in semiconductor systems may open avenues for experimental studies of Wigner crystals and their technological applications in spintronics and quantum information. DOI: 10.1103/PhysRevLett.121.106801 Many exotic phases of matter arise when the interactions including a spontaneous spin polarization [8,13,14]. Such between electrons become significant, which is more likely spin chains are not merely of fundamental interest, but also to happen in low-dimensional systems due to the reduced have potential technological applications in spintronics and charge screening and low, controllable, carrier density. quantum information, e.g., serving as a quantum mediator One of the most intriguing examples is the Wigner crystal [15–17]. So far conductance measurements in quantum [1–4]—a crystalline phase where electrons are strongly wires in which the confinement has been relaxed have correlated and self-organize themselves in an ordered array shown that a liquidlike two-row structure can be observed to minimize the total potential energy. This situation can as can a conductance jump to 4e2=h that results from the arise when the Coulomb interaction dominates over the sum of the conductance of each individual row [18,19]. kinetic energy, and has been clearly observed in two Evidence of coupling between these two rows has also been dimensions (2D) for a nondegenerate electron gas on the reported showing an anticrossing of bonding and antibond- surface of liquid helium. In confined one-dimensional (1D) ing states [20,21]. However, conductance measurements systems, a trivial Wigner lattice is formed if carriers cannot observe the zigzag Wigner crystal as the dc maintain an identical distance between themselves which conductance remains at the quantized value of 2e2=h when will occur in the absence of disorder, and there have been measured with leads [22,23], because there is only one hints for its existence [5,6]. However, it has been shown excitation mode for the Wigner crystal as all electrons are both theoretically and experimentally that allowing a 1D tightly locked together. It is therefore highly desirable to electron system to relax in the second dimension would develop a technique which can directly image the formation enable observation of the effects of strong interactions of a zigzag Wigner crystal and assess its consequences. which can dominate over the spatial quantization. In order to image the formation of the zigzag Wigner Theory [7–12] suggests that for quantum wires with crystals, we create a system in which an on-chip detector is tunable confinement potential and carrier density, the located near a confinement-tunable quantum wire to probe strictly 1D Wigner crystal will first evolve into a zigzag the transverse charge distribution and the spin properties Wigner crystal wherein the relative motion of the two of the wire’s electrons as they are emitted. Figures 1(a) coupled chains is locked, and then evolve to form a two- and 1(b) illustrate our device structure and the principle of row liquidlike structure as the confinement weakens and/or operation. A narrow quantum constriction—also known as the carrier density increases. It has also been predicted that quantum point contact—is fabricated adjacent to the wire the spin-spin interactions in a zigzag Wigner crystal are in a GaAs=AlGaAs heterostructures (see Supplemental complicated and can result in a variety of spin phases Material [24]) and will be used as a charge detector and 0031-9007=18=121(10)=106801(5) 106801-1 © 2018 American Physical Society PHYSICAL REVIEW LETTERS 121, 106801 (2018) (a) (b)(i) (c) 30 V) µ ( V Top Gate B Split S SiO Gate 2 20 (ii) ) V) V µ ( µ ( V V 2DEG BD1 10 (iii) ) Vexc V V µ ( V Iexc B -80 -60 -40 D2 B (mT) FIG. 1. Imaging the zigzag Wigner crystallization. (a) Schematic of our device to image the formation of zigzag Wigner crystal. The device consists of a confinement-tunable quantum wire on the left, formed by a pair of split gates with a lithographically defined width of 1 μm and a length of 0.4 μm, and a 0.6 μm-long top gate separated by a 45 nm thick SiO2 insulator. The narrow quantum constriction on the right, which acts as both a charge collector and spin analyzer, is 0.4 μmwideand0.2 μm long. Note that the width of the quantum constriction in the two-dimensional electron gas is electrostatically defined by the gates, and the channel width becomes smaller the closer the channel gets to pinching off. The distance between the quantum wire and the collector is L ¼ 1.9 μm. (b) Illustration of the magnetic focusing peaks and their corresponding cyclotron motions. A single chain of electrons will give rise to a single peak as illustrated in (i) when focused into the detector, whereas electrons in a double chain are focused into the detector at two different magnetic fields, as illustrated in (ii) and (iii), giving rise to a peak doublet. (c) Magnetic focusing spectrum at various split gate voltages from −2.7 to −1 V (from top to bottom) in steps of 0.1 V while the top gate voltage is accordingly varied to fix the wire conductance at 100 μS. spin analyzer. This arrangement composes a magnetic G and correspondingly, the Fermi energy and carrier focusing geometry [26–31]. Electrons injected from the density, the same. A clear focusing peak singlet is observed confinement-tunable quantum wire undergo cyclotron when the quantum wire is strongly confined, indicating that motion in the presence of a transverse magnetic field, there is only one chain (row). The peak singlet evolves into and are focused towards the charge collector when the two peaks which progressively move away from the central cyclotron diameter is equal to the distance L between the point as the confinement is weakened (Supplemental injection point and the collector. This gives rise to voltage Material, Fig. 1 [24]), indicating a transition into two peaks across the collector (i.e., focusing peaks) at magnetic chains (rows). The spatial separation between the two fields chains can be calculated from the focusing peak separation. It is estimated to be around 200 nm using Eq. (1), which is B ¼ 2ℏkF=eL; ð1Þ of the same order of magnitude as the theoretical predic- tions [9]. We also note that the corresponding conductance 2 where ℏ is the reduced Planck constant, kF is the Fermi traces of the wire do not show a jump to 4e =h wave vector of the focusing electrons, and e is the (Supplemental Material, Fig. 2 [24]) as can occur for a elementary charge. Since L is inversely proportional to crossing [18,21], which implies that there could be an B, the lateral distribution of electrons can now be identified anticrossing as discussed [20,21] or the system is in the by the magnetic focusing spectrum. As depicted in zigzag configuration in which a single chain is distorted Fig. 1(b), a strictly 1D Wigner crystal (i.e., a line of into two locked chains within a single wave function [7,8]. electrons) will give rise to a single focusing peak—singlet, This technique allows investigation of the self- with no difference between this and a 1D Fermi liquid, arrangement of the electrons with increasing density at a whereas a double-chain structure (which can either be a fixed confinement. Figure 2(a) demonstrates that with zigzag Wigner crystal or a liquidlike two-row structure increasing G (which corresponds to increasing Fermi as noted above) with two peaks of charge being emitted energy and electron density) a peak singlet suddenly from different points of the emitter leads to a peak doublet. changes to a peak doublet at G ∼ 80 μS. The observed The difference in magnetic field between the two peaks will transition from one to two chains of electrons with give information on their spatial distribution in the emitter. increasing G is in agreement with previous theoretical Figure 1(c) shows a series of the magnetic focusing predictions that a strictly 1D phase will change to a zigzag V spectra as the split-gate voltage SG is incremented to Wigner crystal phase once the Coulomb repulsion domi- change the wire confinement, while the top gate is nates over the confinement potential.
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