Imaging the Zigzag Wigner Crystal in Confinement-Tunable Quantum Wires

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.

Figure 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 $1\mu \mathrm{m}$ and a length of $0.4\mu \mathrm{m}$, and a $0.6\mu \mathrm{m}$-long top gate separated by a 45 nm thick ${\mathrm{SiO}}_2$ insulator. The narrow quantum constriction on the right, which acts as both a charge collector and spin analyzer, is $0.4\mu \mathrm{m}$ wide and $0.2\mu \mathrm{m}$ 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 $L=1.9\mu \mathrm{m}$. (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 $-1\mathrm{V}$ (from top to bottom) in steps of 0.1 V while the top gate voltage is accordingly varied to fix the wire conductance at $100\mu \mathrm{S}$.

Figure 2

Gate controlled Wigner crystallization. (a),(b) The magnetic focusing spectra plotted as a function of magnetic field at various conductance values from 10 to $150\mu \mathrm{S}$ (from bottom to top) in steps of $10\mu \mathrm{S}$ when the split gate voltage is fixed at $V_{\mathrm{SG}}=-2\mathrm{V}$ (a) and at $V_{\mathrm{SG}}=-1.4\mathrm{V}$ (b). (c) A map of the characteristics of the magnetic focusing peaks as a function of conductance and split gate voltage settings. Data obtained from a different cooldown. Well-defined doublet (singlet) peaks are mapped in yellow (red) color while the peaks with ambiguous shapes are represented in orange.

Figure 3

Spin properties of the Wigner crystal. (a) The magnetic focusing peak doublet (top panel; the quantum wire emitter is fixed at $V_{\mathrm{SG}}=-1.1\mathrm{V}$ and $G=120\mu \mathrm{S}$) and singlet (bottom panel; the emitter is at $V_{\mathrm{SG}}=-3.1\mathrm{V}$ and $G=60\mu \mathrm{S}$) at various collector dc source-drain biases from 0 to 40 nA, where the collector conductance is fixed at $0.2\times 2e^2/h$. (b) The spin phase diagram mapped out using the ratio of the magnetic focusing peak when the QPC collector is tuned as a spin detector to that when it is tuned as a charge detector, plotted as a function of conductance and split gate voltage settings.

Figure 4

Temperature dependence of the zigzag Wigner crystallization and their spin properties. (a)–(c) Evolution of the magnetic focusing peak with increasing temperature for the focusing peak doublet (a), peaks without a well-defined shape (b), and the peak singlet (c). (d) The spin polarizations, which are estimated using the same method as in Fig. 3, as a function of temperature for the three focusing peaks shown in (a)–(c).