title: Scattering matrix formulation of the topological index of interacting fermions in one-dimensional superconductors.
abstract: We construct a scattering matrix formulation for the topological classification of one-dimensional superconductors with effective time-reversal symmetry in the presence of interactions. For an isolated system, Fidkowski and Kitaev have shown that such systems have a Z_{8} topological classification. We here show that these systems have a unitary scattering matrix at zero temperature when weakly coupled to a normal-metal lead, with a topological index given by the trace of the Andreev-reflection matrix, trr_{he}. With interactions, trr_{he} generically takes on the finite set of values 0, ±1, ±2, ±3, and ±4. We show that the two topologically equivalent phases with trr_{he}=±4 support emergent many-body end states, which we identify to be a topologically protected Kondo-like resonance. The path in phase space that connects these equivalent phases crosses a non-Fermi-liquid fixed point where a multiple-channel Kondo effect develops. Our results connect the topological index to transport properties, thereby highlighting the experimental signatures of interacting topological phases in one dimension.
authors.affiliation: Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel and Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany.
authors.forename: Dganit
authors.initials: D
authors.lastname: Meidan
authors.affiliation: Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany.
authors.forename: Alessandro
authors.initials: A
authors.lastname: Romito
authors.affiliation: Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany.
authors.forename: Piet W
authors.initials: PW
authors.lastname: Brouwer