NMR profiling of quantum electron solids in high magnetic fields

Abstract

When the motion of electrons is restricted to a plane under a perpendicular magnetic field B, a variety of quantum phases emerge at low temperatures whose properties are dictated by the Coulomb interaction and its interplay with disorder. At very strong B, the sequence of fractional quantum Hall (FQH) liquid phases terminates in an insulating phase, which is widely believed to be due to the solidification of electrons into domains possessing Wigner crystal (WC) order. The existence of such WC domains is signaled by the emergence of microwave pinning-mode resonances, which reflect the mechanical properties characteristic of a solid. However, the most direct manifestation of the broken translational symmetry accompanying the solidification - the spatial modulation of particles' probability amplitude - has not been observed yet. Here, we demonstrate that nuclear magnetic resonance (NMR) provides a direct probe of the density topography of electron solids in the integer and fractional quantum Hall regimes. The data uncover quantum and thermal fluctuation of lattice electrons resolved on the nanometre scale. Our results pave the way to studies of other exotic phases with non-trivial spatial spin/charge order.

arXiv commentA revised version with additional data has been published in Nature Physics 10, 648 (2014)

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Cited by in corpus (44)

• Observation of Wigner crystal of electrons in a monolayer semiconductor
• Imaging the Wigner Crystal of Electrons in One Dimension
• Direct observation of a magnetic field-induced Wigner crystal
• Nuclear-spin-induced localization of the edge states in two-dimensional topological insulators
• Sharp Tunneling Resonance from the Vibrations of an Electronic Wigner Crystal
• Observation of Spontaneous Ferromagnetism in a Two-Dimensional Electron System
• Composite Fermions Waltz to the Tune of a Wigner Crystal
• Thermal and quantum melting phase diagrams for a magnetic-field-induced Wigner solid
• Anisotropic, two-dimensional, disordered Wigner solid
• Probing the Melting of a Two-dimensional Quantum Wigner Crystal via its Screening Efficiency
• Nuclear magnetic resonance and nuclear spin relaxation in AlAs quantum well probed by ESR
• Competing charge density waves probed by non-linear transport and noise in the second and third Landau levels
• Competition between fractional quantum Hall liquid and Wigner solid at small fillings: Role of layer thickness and Landau level mixing
• Microwave spectroscopic studies of the bilayer electron solid states at low Landau filling in a wide quantum well
• Electron Bubbles and the Structure of the Orbital Wavefunction
• Dynamic Response of Wigner Crystals
• A Highly Correlated Topological Bubble Phase of Composite Fermions
• Landauer-Büttiker approach for hyperfine mediated electronic transport in the integer quantum Hall regime
• Particle-Hole Symmetry and the Reentrant Integer Quantum Hall Wigner Solid
• Resistively-detected NMR lineshapes in a quasi-one dimensional electron system
• Disorder-induced stabilization of the quantum Hall ferromagnet
• Microwave spectroscopic observation of a Wigner solid within the 1/2 fractional quantum Hall effect
• Magnetotransport patterns of collective localization near $\nu =1$ in a high-mobility two-dimensional electron gas
• Signatures of correlated defects in an ultra-clean Wigner crystal in the extreme quantum limit
• Role of chiral quantum Hall edge states in nuclear spin polarization
• Stability of multielectron bubbles in high Landau levels
• Cyclotron Orbits of Composite Fermions in the Fractional Quantum Hall Regime
• RD-NMR spectra of the crystal states of the two-dimensional electron gas in a quantizing magnetic field
• Localized NMR Mediated by Electrical-Field-Induced Domain Wall Oscillation in Quantum-Hall-Ferromagnet Nanowire
• Wigner solid pinning modes tuned by fractional quantum Hall states of a nearby layer
• Dynamic nuclear polarization at high Landau levels in a quantum point contact
• Stabilization of a two-dimensional quantum electron solid in perpendicular magnetic fields
• Thermal Activation Signatures of the Anderson Insulator and the Wigner Solid forming near $\nu =1$
• Resistively detected NMR as a probe of the topological nature of conducting edge/surface states
• Critical Filling Factor for the Formation of a Quantum Wigner Crystal Screened by a Nearby Layer
• Developing fractional quantum Hall states at $\nu$ = $\frac{1}{7}$ and $\frac{2}{11}$ in the presence of significant Landau level mixing
• Density Dependence of the Phases of the $\nu =1$ Integer Quantum Hall Plateau in Low Disorder Electron Gases
• Pump-probe nuclear spin relaxation study of the quantum Hall ferromagnet at filling factor nu = 2
• Coexistence of two hole phases in high-quality $p$-GaAs/AlGaAs in the vicinity of Landau level filling factors $\nu$=1 and $\nu$=(1/3)
• Wigner solids of wide quantum wells near Landau filling $\nu =1$
• Importance of electron-phonon coupling near the electron-liquid to Wigner-crystal transition in two-dimensional atomically thin materials
• Inequivalence of the low-density insulating state and quantum Hall insulating states in a strongly correlated two-dimensional electron system
• Nuclear magnetic resonance line shapes of Wigner crystals in ${}^{13}$C-enriched graphene
• Quasi-two-dimensional spin helix and magnon-induced singularity in twisted bilayer graphene