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Register a new userImaging the zigzag Wigner crystal in confinement-tunable quantum wires
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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.
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A system of confined charged electrons interacting via the long-range Coulomb force can form a Wigner crystal due to their mutual repulsion. This happens when the potential energy of the system dominates over its kinetic energy, i.e., at low temperatures for a classical system and at low densities for a quantum one. At $T=0$, the system is governed by quantum mechanics, and hence, the spatial density peaks associated with crystalline charge localization are sharpened for a lower average density. Conversely, in the classical limit of high temperatures, the crystalline spatial density peaks are suppressed (recovered) at a lower (higher) average density. In this paper, we study those two limits separately using an exact diagonalization of small one-dimensional (1D) systems containing few ($<10$) electrons and propose an approximate method to connect them into a unified effective phase diagram for Wigner few-electron crystallization. The result is a qualitative quantum-classical crossover phase diagram of an effective 1D Wigner crystal. We show that the spatial density peaks associated with the quasi-crystallization should be experimentally observable in a few-electron 1D system. We find that the effective crystalline structure slowly disappears with both the crossover average density and crossover temperature for crystallization decreasing with increasing particle number, consistent with the absence of any true long-range 1D order. In fact, one peculiar aspect of the effective finite-size nature of 1D Wigner crystallization we find is that even a short-range interaction would lead to a finite-size 1D crystal, except that the crystalline order vanishes much faster with increasing system size in the short-range interacting system compared with the long-range interacting one.
Ballistic quantum wires are exposed to longitudinal profiles of perpendicular magnetic fields composed of a spike (magnetic barrier) and a homogeneous part. An asymmetric magnetoconductance peak as a function of the homogeneous magnetic field is found, comprising quantized conductance steps in the interval where the homogeneous magnetic field and the magnetic barrier have identical polarities, and a characteristic shoulder with several resonances in the interval of opposite polarities. The observations are interpreted in terms of inhomogeneous diamagnetic shifts of the quantum wire modes leading to magnetic confinement.
The electronic excitations at the edges of a Hall bar not much wider than a few magnetic lengths are studied theoretically at filling $ u = 2$. Both mean-field theory and Luttinger liquid theory techniques are employed for the case of a null Zeeman energy splitting. The first calculation yields a stable spin-density wave state along the bar, while the second one predicts dominant Wigner-crystal correlations along the edges of the bar. We propose an antiferromagnetic Wigner-crystal groundstate for the edge electrons that reconciles the two results. A net Zeeman splitting is found to produce canting of the antiferromagnetic order.
The Wigner crystal on liquid He accompanies with periodic corrugation of the He surface; dimples. The dynamics of the crystal is coupled with the motion and the deformation of the dimples. Nonlinear phenomena found in AC Corbino conductivity are attributed to the collective sliding of the electrons out of the dimples. In order to inspect the dynamical transition to the sliding state, we have developed a novel experimental method using a so-called t^2 pulse, whose leading and trailing edges change in proportion to the square of time; V = at^2. Since the force exerting upon the crystal is proportional to the time derivative of the input voltage, dV/dt, the t^2-pulsed method is expected to realize a continuous sweep of the driving force, resulting in the real-time observation of the sliding transition. The observed response shows clearly the sliding, revealing that the external force to the crystal determines the sliding transition.
When the Coulomb repulsion between electrons dominates over their kinetic energy, electrons in two dimensional systems were predicted to spontaneously break continuous translation symmetry and form a quantum crystal. Efforts to observe this elusive state of matter, termed a Wigner crystal (WC), in two dimensional extended systems have primarily focused on electrons confined to a single Landau level at high magnetic fields, but have not provided a conclusive experimental signature of the emerging charge order. Here, we use optical spectroscopy to demonstrate that electrons in a pristine monolayer semiconductor with density $ lesssim 3 cdot 10^{11}$ cm$^{-2}$ form a WC. The interactions between resonantly injected excitons and electrons arranged in a periodic lattice modify the exciton band structure so that it exhibits a new umklapp resonance, heralding the presence of charge order. Remarkably, the combination of a relatively high electron mass and reduced dielectric screening allows us to observe an electronic WC state even in the absence of magnetic field. The tentative phase diagram obtained from our Hartree-Fock calculations provides an explanation of the striking experimental signatures obtained up to $B = 16$ T. Our findings demonstrate that charge-tunable transition metal dichalcogenide (TMD) monolayers enable the investigation of previously uncharted territory for many-body physics where interaction energy dominates over kinetic energy, even in the absence of a moire potential or external fields.
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