Electronic Wigner-molecule polymeric chains in elongated silicon quantum dots and finite-length quantum wires

The spectral properties of electrons confined in a wirelike quasi-one-dimensional (1D) elongated quantum dot coupler between silicon qubits are investigated with a valley-augmented unrestricted Hartree-Fock (VAUHF) 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, the formation of Wigner-molecule polymeric (longitudinal) chains, which are initiated through charge accumulation at the edges of the finite-length quasi-1D wire. An increasing number of parallel zigzag 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 VAUHF solutions, subsequently augmented by the quantum mechanically required parity restoration, go beyond the VAUHF single-determinant solution, predicting the formation of entangled Wigner-molecule chains, the charge distributions of which obliterate the zigzag organization of the broken-symmetry solutions. The symmetry-restored VAUHF methodology enables systematic investigations of multielectron-complex nanoscale confined structures that could be targeted for future imaging-microscopy experiments in silicon and other materials (e.g., 1D domain walls in transition-metal dichalcogenide materials) and quantum information utilization.