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We demonstrate that the plasmon in one-dimensional Coulomb interactingelectron fluids can develop a finite-momentum maxon-roton-like nonmonotonicenergy-momentum dispersion. Such an unusual nonmonotonicity arises from thestrongly interacting $1/r$ Coulomb potential going beyond the conventional bandlinearization approximation used in the standard bosonization theories ofLuttinger liquids. We provide details for the nonmonotonic plasmon dispersionusing both bosonization and RPA theories. We also calculate the specific heatincluding the nonmonotonicity and discuss possibilities for observing thenonmonotonic plasmon dispersion in various physical systems includingsemiconductor quantum wires, carbon nanotubes, and the twisted bilayer grapheneat sub-degree twist angles, which naturally realize one-dimensional domain-wallstates.

Nonmonotonic plasmon dispersion in strongly interacting Coulomb Luttinger liquids