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. The lower-energy symmetry-broken solutions of the 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 chains. 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, augmented by the quantum mechanically required parity restoration, go beyond the VAUHF solution, predicting the formation of entangled Wigner-molecule chains. The symmetry-restored VAUHF methodology enables investigations of multielectron 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.