title: Hierarchy of modes in an interacting one-dimensional system.
abstract: Studying interacting fermions in one dimension at high energy, we find a hierarchy in the spectral weights of the excitations theoretically, and we observe evidence for second-level excitations experimentally. Diagonalizing a model of fermions (without spin), we show that levels of the hierarchy are separated by powers of R^{2}/L^{2}, where R is a length scale related to interactions and L is the system length. The first-level (strongest) excitations form a mode with parabolic dispersion, like that of a renormalized single particle. The second-level excitations produce a singular power-law line shape to the first-level mode and multiple power laws at the spectral edge. We measure momentum-resolved tunneling of electrons (fermions with spin) from or to a wire formed within a GaAs heterostructure, which shows parabolic dispersion of the first-level mode and well-resolved spin-charge separation at low energy with appreciable interaction strength. We find structure resembling the second-level excitations, which dies away quite rapidly at high momentum.
authors.affiliation: School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom.
authors.forename: O
authors.initials: O
authors.lastname: Tsyplyatyev
authors.affiliation: School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom.
authors.forename: A J
authors.initials: AJ
authors.lastname: Schofield
authors.affiliation: Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom.
authors.forename: Y
authors.initials: Y
authors.lastname: Jin
authors.affiliation: Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom.
authors.forename: M
authors.initials: M
authors.lastname: Moreno
authors.affiliation: Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom.
authors.forename: W K
authors.initials: WK
authors.lastname: Tan
authors.affiliation: Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom.
authors.forename: C J B
authors.initials: CJ
authors.lastname: Ford
authors.affiliation: Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom.
authors.forename: J P
authors.initials: JP
authors.lastname: Griffiths
authors.affiliation: Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom.
authors.forename: I
authors.initials: I
authors.lastname: Farrer
authors.affiliation: Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom.
authors.forename: G A C
authors.initials: GA
authors.lastname: Jones
authors.affiliation: Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom.
authors.forename: D A
authors.initials: DA
authors.lastname: Ritchie