Three-Dimensional Coherence in Arrays of Parallel One-Dimensional Wigner Crystals

Abstract

Studies of Wigner crystals in semiconductor nanowires reveal significant electronic characteristics, especially in configurations where electron tunneling between adjacent wires occurs. This tunneling enables long-range coherence across nanowire arrays in both ground and excited states. We employ a Yukawa-like effective potential and the Kronig–Penney model along with matrix transfer methods to analyze coherence in N × N arrays, focusing on electronic distribution, resonant energies, and coherent superposition between adjacent wires. Our results demonstrate the formation of three-dimensional, noncontinuous charge distributions coherently connected by electronic tunneling. We discuss potential applications, methods for interacting with these distributions, and their experimental feasibility. These findings enable the formation of long-range coherent charge arrays, which can be externally tuned, paving the way for large-scale, high-density integration of coherent quantum systems.