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Meidan D, Romito A, Brouwer PW. Scattering matrix formulation of the topological index of interacting fermions in one-dimensional superconductors. Phys Rev Lett. 2014;113(5):057003doi: 10.1103/PhysRevLett.113.057003.
Meidan, D., Romito, A., & Brouwer, P. W. (2014). Scattering matrix formulation of the topological index of interacting fermions in one-dimensional superconductors. Physical review letters, 113(5), 057003. https://doi.org/10.1103/PhysRevLett.113.057003
Meidan, Dganit, et al. "Scattering matrix formulation of the topological index of interacting fermions in one-dimensional superconductors." Physical review letters vol. 113,5 (2014): 057003. doi: https://doi.org/10.1103/PhysRevLett.113.057003
Meidan D, Romito A, Brouwer PW. Scattering matrix formulation of the topological index of interacting fermions in one-dimensional superconductors. Phys Rev Lett. 2014 Aug 01;113(5):057003. doi: 10.1103/PhysRevLett.113.057003. Epub 2014 Aug 01. PMID: 25126932.
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Phys Rev Lett. 2014 Aug 01;113(5):057003. doi: 10.1103/PhysRevLett.113.057003. Epub 2014 Aug 01.

Scattering matrix formulation of the topological index of interacting fermions in one-dimensional superconductors.

Physical review letters

Dganit Meidan, Alessandro Romito, Piet W Brouwer

Affiliations

  1. 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.
  2. Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany.

PMID: 25126932 DOI: 10.1103/PhysRevLett.113.057003

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.

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