# A scattering matrix formulation of the topological index of interacting fermions in one-dimensional superconductors

Meidan, Dganit and Romito, Alessandro and Brouwer, Piet W. (2014) A scattering matrix formulation of the topological index of interacting fermions in one-dimensional superconductors. Physical review letters, 113 (5). ISSN 0031-9007

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1312.6367v1 - Accepted Version

## 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 a closed geometry, Fidkowski and Kitaev have shown that such systems have a $\mathbb{Z}_8$ topological classification. We show that in the weak coupling limit, these systems retain a unitary scattering matrix at zero temperature, with a topological index given by the trace of the Andreev reflection matrix, $\mbox{tr}\, r_{\rm he}$. With interactions, $\mbox{tr}\, r_{\rm he}$ generically takes on the finite set of values $0$, $\pm 1$, $\pm 2$, $\pm 3$, and $\pm 4$. We show that the two topologically equivalent phases with $\mbox{tr}\, r_{\rm he} = \pm 4$ 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.

Item Type:
Journal Article
Journal or Publication Title:
Physical review letters
4 pages, 1 fig
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/3100
Subjects:
Departments:
ID Code:
85081
Deposited By:
Deposited On:
07 Mar 2017 10:28
Refereed?:
Yes
Published?:
Published