Wigner-molecule supercrystal in transition-metal dichalcogenide moiré superlattices: Lessons from the bottom-up approach

Abstract

The few-body problem for $N=4$ fermionic charge carriers in a double-well moiré quantum dot (MQD), representing the first step in a bottom-up strategy to investigate formation of molecular supercrystals in transition metal dichalcogenide (TMD) moiré superlattices with integral fillings, $\nu >1$, is solved exactly by employing large-scale exact-diagonalization via full configuration interaction (FCI) computations. A comparative analysis with the mean-field solutions of the often used spin-and-space unrestricted Hartree Fock (sS-UHF) demonstrates the limitations of the UHF method (by itself) to provide a proper description of the influence of the interdot Coulomb interaction. In particular, it is explicitly shown for $\nu =2$ that the exact charge densities (CDs) within each MQD retain the ring-like shape characteristic (for a wide range of relevant parameters) of a fully isolated MQD, as was found for sliding Wigner molecules (WMs). This deeply quantum-mechanical behavior contrasts sharply with the UHF CDs that portray solely orientationally pinned and well localized dumbbell dimers. An improved CD, which agrees with the FCI-calculated one, derived from the restoration of the sS-UHF broken parity symmetries is further introduced, suggesting a beyond-mean-field methodological roadmap for correcting the sS-UHF results. It is conjectured that the conclusions for the $\nu =2$ moiré TMD superlattice case extend to all cases with integral fillings that are associated with sliding WMs in isolated MQDs. The case of $\nu =3$, associated with a pinned WM in isolated MQDs, is an exception.

arXiv comment9-page Letter with 5 color figures. For related papers, see https://sites.gatech.edu/cyannouleas/

References in corpus (46)

• Spins in few-electron quantum dots
• Silicon Quantum Electronics
• Semiconductor Spin Qubits
• Hubbard model physics in transition metal dichalcogenide moiré bands
• Wigner Crystallization in mesoscopic 2D electron systems
• Crossover from Fermi liquid to Wigner molecule behavior in quantum dots
• Symmetry breaking and quantum correlations in finite systems: Studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods
• $\Gamma$-Valley Transition-Metal-Dichalcogenide Moirè Bands
• Full configuration interaction approach to the few-electron problem in artificial atoms
• Moiré quantum chemistry: charge transfer in transition metal dichalcogenide superlattices
• Quantum textures of the many-body wavefunctions in magic-angle graphene
• Collective and independent-particle motion in two-electron artificial atoms
• Symmetry restoration in mean-field approaches
• 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
• A molecular state of correlated electrons in a quantum dot
• Wigner molecules in quantum dots: a quantum Monte Carlo study
• Incipient Wigner Localization in Circular Quantum Dots
• Formation and control of electron molecules in artificial atoms: Impurity and magnetic-field effects
• Strong electron-electron interactions in Si/SiGe quantum dots
• Strongly correlated wave functions for artificial atoms and molecules
• Structural properties of electrons in quantum dots in high magnetic fields: Crystalline character of cusp states and excitation spectra
• Coherent control and spectroscopy of a semiconductor quantum dot Wigner molecule
• Gate-Controlled Quantum Dots Based on Two-Dimensional Materials
• Three-electron anisotropic quantum dots in variable magnetic fields: exact results for excitation spectra, spin structures, and entanglement
• Two ground-state modifications of quantum-dot beryllium
• Unified description of floppy and rigid rotating Wigner molecules formed in quantum dots
• Crystalline character of high-magnetic-field cusp states in quantum dots
• Single-shot readout of a driven hybrid qubit in a GaAs double quantum dot
• Rapidly rotating boson molecules with long or short range repulsion: an exact diagonalization study
• Two-body Wigner molecularization in asymmetric quantum dot spin qubits
• Double-well ultracold-fermions computational microscopy: Wave-function anatomy of attractive-pairing and Wigner-molecule entanglement and natural orbitals
• Bosonic molecules in rotating traps
• Edge states in graphene quantum dots: Fractional quantum Hall effect analogies and differences at zero magnetic field
• From a few to many electrons in quantum dots under strong magnetic fields: Properties of rotating electron molecules with multiple rings
• Artificial quantum-dot Helium molecules: Electronic spectra, spin structures, and Heisenberg clusters
• Electron and boson clusters in confined geometries: symmetry breaking in quantum dots and harmonic traps
• Molecular formations and spectra due to electron correlations in three-electron hybrid double-well qubits
• Spin-dependent Rotating Wigner Molecules in Quantum dots
• Wigner molecules and hybrid qubits
• Quantum Wigner molecules in moiré materials
• Valleytronic full configuration-interaction approach: An application to the excitation spectra of Si double-dot qubits
• Interference, spectral momentum correlations, entanglement, and Bell inequality for a trapped interacting ultracold atomic dimer: Analogies with biphoton interferometry
• Wigner-molecularization-enabled dynamic nuclear field programming
• Exact closed-form analytic wave functions in two dimensions: Contact-interacting fermionic spinful ultracold atoms in a rapidly rotating trap

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• Electronic Wigner-Molecule Polymeric Chains in Elongated Silicon Quantum Dots and Finite-Length Quantum Wires
• Crystal-field effects in the formation of Wigner-molecule supercrystals in moiré TMD superlattices
• Determinant- and Derivative-Free Quantum Monte Carlo Within the Stochastic Representation of Wavefunctions
• Wave-function microscopy: Derivation and anatomy of exact algebraic spinful wave functions and full Wigner-molecular spectra of a few highly correlated rapidly rotating ultracold fermionic atoms
• Spin-orbital magnetism in moiré Wigner molecules
• Artificial versus Natural Atoms: The uncanny capability of the many-body Schrödinger equation to produce emergent behavior