In partial fulfillment of the requirements for the degree of 

Doctor of Philosophy in Physics 

School of Physics Thesis Dissertation Defense

Arnon Goldberg  

Dr. Uzi Landman, School of Physics, Georgia Institute of Technology (Advisor)

The Many Faces of Electrons in a 1D Tight Spot: From Linear and Zigzag Wigner Molecules to Luttinger Liquids, with Dimerization in between

Date: Friday, September 26, 2026

Time:  3:00 p.m.

Location: Howey N201/202

Thesis Committee: 

Dr. Itamar Kimchi, School of Physics, Georgia Institute of Technology
Dr. Michael Pustilnik, School of Physics, Georgia Institute of Technology
Dr. Bokwon Yoon, School of Physics, Georgia Institute of Technology
Prof. Emeritus, Roger Wartell, School of Biology, Georgia Institute of Technology

Abstract:

In this thesis, we explore the organization and spectral properties of interacting electrons confined in silicon elongated quantum dots (EQDs), a wirelike architecture proposed for coherent spin-transfer between quantum dots. To enable these investigations, we developed two novel numerical methods: valley-augmented unrestricted Hartree-Fock (VAUHF), and spin- and space-adapted configuration interaction (SSACI). The VAUHF method entails solving the valley-generalized Pople-Nesbet equations, treating the valley degree of freedom in silicon as an isospin. These solutions exhibit symmetry-broken Wigner-molecule polymeric chains, with electrons arranged in linear and zigzag configurations along the length of the EQD confinement. Weakening the transverse confinement or increasing the number of confined electrons leads to the predicted formation of additional zigzag chains in the EQD. Restoring the parity-inversion symmetry of the VAUHF wavefunctions generates entangled Wigner-molecule chains. The SSACI method goes beyond the symmetry-restored VAUHF approximation, generating solutions that respect the Hamiltonian symmetries by representing the wavefunction as a superposition of nonorthogonal Slater determinants, obtained by applying symmetry transformations (e.g., parity-inversions and spin-permutations) to multiple solutions of the Pople-Nesbet equations. In the crossover between the strong (Wigner-molecule) and weak (Luttinger liquid) interelectron repulsion regimes, the (near-exact) SSACI wavefunctions exhibit the predicted formation of a dimerized spin-singlet ground state in both linear and zigzag chains. Analyses of charge distributions, local entropies and spin-resolved conditional probability distributions reveal the emergent formation of singlet-like entangled pairs (dimers) between neighboring electrons, with the chain modulating between paired and unpaired electrons. Increased spin-multiplicity of the SSACI solution obliterates the dimer signatures. The newly developed hierarchical computational methodology—starting from VAUHF solutions, followed by symmetry restoration, and culminating with SSACI computations—enables explorations offering fundamental insight into the quantum state of electrons in semiconductor EQDs, with future investigations including studies of organization, spectra and transport in multi-dot systems, 1D domain walls in transition-metal dichalcogenides, Moiré quantum dots and superatom materials.