Direct observation of a magnetic field-induced Wigner crystal

Abstract

Eugene Wigner predicted long ago that when the Coulomb interactions between electrons become much stronger than their kinetic energy, electrons crystallize into a closely packed lattice. A variety of two-dimensional systems have shown evidence for Wigner crystals; however, a spontaneously formed classical or quantum Wigner crystal (WC) has never been directly visualized. Neither the identification of the WC symmetry nor direct investigation of its melting has been accomplished. Here we use high-resolution scanning tunneling microscopy (STM) measurements to directly image a magnetic field-induced electron WC in Bernal-stacked bilayer graphene (BLG), and examine its structural properties as a function of electron density, magnetic field, and temperature. At high fields and the lowest temperature, we observe a triangular lattice electron WC in the lowest Landau Level (LLL) of BLG. The WC possesses the expected lattice constant and is robust in a range of filling factors between $\nu \sim$ 0.13 and $\nu \sim$ 0.38 except near fillings where it competes with fractional quantum Hall (FQH) states. Increasing the density or temperature results in the melting of the WC into a liquid phase that is isotropic but has a modulated structure characterized by the WC's Bragg wavevector. At low magnetic fields, the WC unexpectedly transitions into an anisotropic stripe phase, which has been commonly anticipated to form in higher LLs. Analysis of individual lattice sites reveals signatures that may be related to the quantum zero-point motion of electrons in the WC lattice.

19 pages, 4 figures

References in corpus (8)

• Visualizing Broken Symmetry and Topological Defects in a Quantum Hall Ferromagnet
• Melting of a 2D Quantum Electron Solid in High Magnetic Field
• Imaging tunable quantum Hall broken-symmetry orders in graphene
• Competing correlated states around the zero field Wigner crystallization transition of electrons in two-dimensions
• NMR profiling of quantum electron solids in high magnetic fields
• Observation of Spontaneous Ferromagnetism in a Two-Dimensional Electron System
• Thermal and quantum melting phase diagrams for a magnetic-field-induced Wigner solid
• Broken symmetries and excitation spectra of interacting electrons in partially filled Landau levels

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• Elementary Excitations, Melting Temperature, and Correlation Energy in Wigner Crystals