Electronic Wigner-Molecule Polymeric Chains in Elongated Silicon Quantum Dots and Finite-Length Quantum Wires

Abstract

The spectral properties of electrons confined in a wire-like quasi-one-dimensional (1D) elongated quantum dot (EQD) coupler between silicon qubits, are investigated with a newly developed valley-augmented unrestricted Hartree-Fock (va-UHF) method, generalized to include the valley degree of freedom treated as an isospin, allowing calculations for a large number of electrons. The lower energy symmetry-broken solutions of the self-consistent generalized Pople-Nesbet equations exhibit, for a confinement that has been modeled after an experimentally fabricated one in silicon, formation of Wigner-molecular polymeric (longitudinal) chains, initiating through charge accumulation at the edges of the finite-length quasi-1D wire. An increasing number of parallel zig-zag chains form as the number of electrons loaded into the confinement is increased, with the formation of newly added chains determined by the strength of the transverse harmonic confinement. The broken-symmetry va-UHF solutions, subsequently augmented by the quantum-mechanically required parity-restoration, go beyond the va-UHF single-determinant solution, predicting formation of entangled Wigner-molecular chains whose charge distributions obliterate the zig-zag organization of the broken-symmetry solutions. The symmetry-restored va-UHF methodology enables systematic investigations of multi-electron complex nano-scale confined structures that could be targeted for future imaging microscopy experiments in silicon and other materials (e.g., 1D domain walls in TMD materials), and quantum information utilization.

10 pages, 10 color figures. Accepted for publication in Physical Review Applied. For related papers, see https://sites.gatech.edu/cyannouleas/

References in corpus (27)

• Silicon Quantum Electronics
• Semiconductor Spin Qubits
• Symmetry breaking and quantum correlations in finite systems: Studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods
• Generic properties of a quasi-one dimensional classical Wigner crystal
• Collective and independent-particle motion in two-electron artificial atoms
• Symmetry restoration in mean-field approaches
• Wigner crystal physics in quantum wires
• Observation and Spectroscopy of a Two-Electron Wigner Molecule in an Ultra-Clean Carbon Nanotube
• Excitation spectrum of two correlated electrons in a lateral quantum dot with negligible Zeeman splitting
• Quantum dots in high magnetic fields: Rotating-Wigner-molecule versus composite-fermion approach
• Wigner molecules in quantum dots: a quantum Monte Carlo study
• Strongly correlated wave functions for artificial atoms and molecules
• Coherent control and spectroscopy of a semiconductor quantum dot Wigner molecule
• Negative spin exchange in a multielectron quantum dot
• Imaging the zigzag Wigner crystal in confinement-tunable quantum wires
• Two ground-state modifications of quantum-dot beryllium
• Spin of a multielectron quantum dot and its interaction with a neighboring electron
• Single-shot readout of a driven hybrid qubit in a GaAs double quantum dot
• Unified microscopic approach to the interplay of pinned-Wigner-solid and liquid behavior of lowest-Landau-level states in the neighborhood of nu=1/3
• Jellybean quantum dots in silicon for qubit coupling and on-chip quantum chemistry
• Molecular formations and spectra due to electron correlations in three-electron hybrid double-well qubits
• Wigner molecules and hybrid qubits
• Quantum Wigner molecules in moiré materials
• Wigner-molecule supercrystal in transition-metal dichalcogenide moiré superlattices: Lessons from the bottom-up approach
• Valleytronic full configuration-interaction approach: An application to the excitation spectra of Si double-dot qubits
• Quantum dots based on parabolic quantum wells: importance of electronic correlations
• An elongated quantum dot as a distributed charge sensor

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