  Wigner crystals (WC) are electronic phases peculiar to low-density systems,
particularly in the uniform electron gas. Since its introduction in the early
twentieth century, this model has remained essential to many aspects of
electronic structure theory and condensed-matter physics. Although the
(lowest-energy) ground-state WC (GSWC) has been thoroughly studied, the
properties of excited-state WCs (ESWCs) are basically unknown. To bridge this
gap, we present a well-defined procedure to obtain an entire family of ESWCs in
a one-dimensional electron gas using a symmetry-broken mean-field approach.
While the GSWC is a commensurate crystal (i.e.~the number of density maxima
equals the number of electrons), these ESWCs are incommensurate crystals
exhibiting more or less maxima. Interestingly, they are lower in energy than
the (uniform) Fermi fluid state. For some of these ESWCs we have found
asymmetrical band gaps, which would lead to anisotropic conductivity. These
properties are associated to unusual characteristics in their electronic
structure.
