Local spectral weight of a Luttinger liquid: Effects from edges and impurities

We calculate the finite-temperature local spectral weight (LSW) of a Luttinger liquid with an open (hard-wall) boundary. Close to the boundary the LSW exhibits characteristic oscillations indicative of spin-charge separation. The line shape of the LSW is also found to have a Fano-like asymmetry, a feature originating from the interplay between electron-electron interaction and scattering off the boundary. Our results can be used to predict how edges and impurities influence scanning tunneling microscopy (STM) of one-dimensional electron systems at low temperatures and voltage bias. Applications to STM on single-walled carbon nanotubes are discussed.