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

Authors
  • Meidan, Dganit
  • Romito, Alessandro
  • Brouwer, Piet W
Type
Published Article
Journal
Physical Review Letters
Publisher
American Physical Society
Publication Date
Aug 01, 2014
Volume
113
Issue
5
Pages
57003–57003
Identifiers
PMID: 25126932
Source
Medline
License
Unknown

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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