Imaging the Wigner Crystal of Electrons in One Dimension

Abstract

The quantum crystal of electrons, predicted more than eighty years ago by Eugene Wigner, is still one of the most elusive states of matter. Here, we present experiments that observe the one-dimensional Wigner crystal directly, by imaging its charge density in real-space. To measure this fragile state without perturbing it, we developed a new scanning probe platform that utilizes a pristine carbon nanotube as a scanning charge perturbation to image, with minimal invasiveness, the many-body electronic density within another nanotube. The obtained images, of few electrons confined in one-dimension, match those of strongly interacting crystals, with electrons ordered like pearls on a necklace. Comparison to theoretical modeling demonstrates the dominance of Coulomb interactions over kinetic energy and the weakness of exchange interactions. Our experiments provide direct evidence for this long-sought electronic state, and open the way for studying other fragile interacting states by imaging their many-body density in real-space.

References in corpus (8)

• Spin-orbit interaction and anomalous spin relaxation in carbon nanotube quantum dots
• Imaging the Wigner Crystal of Electrons in One Dimension
• Electron Attraction Mediated by Coulomb Repulsion
• Melting of a 2D Quantum Electron Solid in High Magnetic Field
• Microwave Resonance of 2D Wigner Crystal around integer Landau fillings
• NMR profiling of quantum electron solids in high magnetic fields
• Few-electron physics in a nanotube quantum dot with spin-orbit coupling
• Wigner crystal phases in confined carbon nanotubes

Cited by in corpus (59)

• Correlated Insulating States at Fractional Fillings of the WS2/WSe2 Moiré Lattice
• Signatures of bilayer Wigner crystals in a transition metal dichalcogenide heterostructure
• Observation of Wigner crystal of electrons in a monolayer semiconductor
• Imaging the Wigner Crystal of Electrons in One Dimension
• Probing quantum devices with radio-frequency reflectometry
• Direct observation of a magnetic field-induced Wigner crystal
• Spectroscopy of Wigner molecules on superfluid helium using a superconducting resonator
• Roadmap for Photonics with 2D Materials
• Observation of the spin-orbit gap in bilayer graphene by one-dimensional ballistic transport
• Coulomb and Riesz gases: The known and the unknown
• Coherent control and spectroscopy of a semiconductor quantum dot Wigner molecule
• Electronic Thermal Transport Measurement in Low-Dimensional Materials with Graphene Nonlocal Noise Thermometry
• Two-body Wigner molecularization in asymmetric quantum dot spin qubits
• Macroscopic Manifestation of Domain-wall Magnetism and Magnetoelectric Effect in a Néel-type Skyrmion Host
• Wigner solids of domain wall skyrmions
• Strong hole-photon coupling in planar Ge for probing charge degree and strongly-correlated states
• One-dimensional few-electron effective Wigner crystal in quantum and classical regimes
• Anomalous supercurrent and diode effect in locally perturbed topological Josephson junctions
• Accurate ground-state energies of Wigner crystals from a simple real-space approach
• Fabry-Pérot oscillations in correlated carbon nanotubes
• Electronic transport, metal-insulator transition, and Wigner crystallization in transition metal dichalcogenide monolayers
• Wigner Crystals in Two-Dimensional Transition-Metal Dichalcogenides: Spin Physics and Readout
• Floquet metal to insulator phase transitions in semiconductor nanowires
• Partition of Two Interacting Electrons by a Potential Barrier
• Topologically protected, correlated end spin formation in carbon nanotubes
• Electrostatic detection of Shubnikov-de-Haas oscillations in bilayer graphene by Coulomb resonances in gate-defined quantum dots
• Wigner crystallization of electrons in a one-dimensional lattice: a condensation in the space of states
• Nanoassembly technique of carbon nanotubes for hybrid circuit-QED
• Two dimensional quantum lattice models via mode optimized hybrid CPU-GPU density matrix renormalization group method
• Wigner molecules in phosphorene quantum dots
• Wigner localization in two and three dimensions: an \emph{ab initio} approach
• Wigner-molecularization-enabled dynamic nuclear field programming
• Band-Gap-Dependent Electronic Compressibility of Carbon Nanotubes in the Wigner Crystal Regime
• The carbon nanotube gatemon qubit
• Collective Dynamics and Defect Generation for Wigner Crystal Ratchets
• Drive Dependence of the Hall Angle for a Sliding Wigner Crystal in a Magnetic Field
• Evaporative cooling to a Rydberg crystal close to its ground state
• Modulation induced transport signatures in correlated electron waveguides
• Machine learning one-dimensional spinless trapped fermionic systems with neural-network quantum states
• Collective ground states in small lattices of coupled quantum dots
• Pauli crystals -- interplay of symmetries
• Nano-assembled open quantum dot nanotube devices
• Wire width and density dependence of the crossover in the peak of the static structure factor from $2k_{\text{F}}$ $\to$ $4k_{\text{F}}$ in one-dimensional paramagnetic electron gases
• Carbon Nanotube Millikelvin Transport and Nanomechanics
• Microscopic theory on magnetic-field-tuned sweet spot of exchange interactions in multielectron quantum-dot systems
• The Wigner localization of interacting electrons in a one-dimensional harmonic potential
• Resonator induced quantum phase transitions in a hybrid Josephson junction
• True decoherence-free-subspace derived from a semiconductor double quantum dot Heisenberg spin-trimer
• Crystallization of the transdimensional electron liquid
• Electric and Magnetic Field Nano-Sensing Using a New, Atomic-like Qubit in a Carbon Nanotube
• Sagnac Electron Interference as a Probe of Electronic Structure
• Few-body precursors of topological frustration
• Energy spectrum and structure of one-dimensional few-electron Wigner crystals with and without coupling to light in cavity
• Correlated insulating states in carbon nanotubes controlled by magnetic field
• Anomalous screening in narrow-gap carbon nanotubes
• Binding and spontaneous condensation of excitons in narrow-gap carbon nanotubes
• The exchange coupling of a Wigner dimer
• Artificial versus Natural Atoms: The uncanny capability of the many-body Schrödinger equation to produce emergent behavior
• Elementary Excitations, Melting Temperature, and Correlation Energy in Wigner Crystals