Imaging the zig-zag Wigner crystals in confinement-tunable quantum wires

Wigner crystal has so far only been evident in two-dimensional electron systems. For the more interacting one-dimensional (1D) systems, such a Wigner electron lattice has proven very challenging to probe experimentally, and the precise nature of it has remained elusive. Theory suggests that the 1D Wigner crystal will transit to a zig-zag phase when the confinement weakens. Here we utilize the magnetic focusing technique to probe the formation of a zig-zag Wigner lattice, in which the transverse distribution of electrons in a quantum wire reveals itself in the magnetic focusing spectrum. Trasition from a 1D Wigner to zig-zag phase, manifested in the evolution from a focusing peak singlet to doublet, is present when the wire confinement potential continuously weakens. The spin properties of the Wigner electron lattices can also be studied using our magnetic focusing technique. We show that a ferromagnetic phase can occur when the zig-zag Wigner crystal is formed.