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Research output: Contribution to Journal/Magazine › Journal article › peer-review

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In: Physical review letters, Vol. 113, No. 5, 057003, 01.08.2014.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Meidan, D, Romito, A & Brouwer, PW 2014, 'A scattering matrix formulation of the topological index of interacting fermions in one-dimensional superconductors', *Physical review letters*, vol. 113, no. 5, 057003. https://doi.org/10.1103/PhysRevLett.113.057003

Meidan, D., Romito, A., & Brouwer, P. W. (2014). A scattering matrix formulation of the topological index of interacting fermions in one-dimensional superconductors. *Physical review letters*, *113*(5), Article 057003. https://doi.org/10.1103/PhysRevLett.113.057003

Meidan D, Romito A, Brouwer PW. A scattering matrix formulation of the topological index of interacting fermions in one-dimensional superconductors. Physical review letters. 2014 Aug 1;113(5):057003. doi: 10.1103/PhysRevLett.113.057003

@article{ff7de233aad4471e945c78f5b46c352a,

title = "A 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 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.",

keywords = "cond-mat.mes-hall, cond-mat.str-el",

author = "Dganit Meidan and Alessandro Romito and Brouwer, {Piet W.}",

note = "4 pages, 1 fig",

year = "2014",

month = aug,

day = "1",

doi = "10.1103/PhysRevLett.113.057003",

language = "English",

volume = "113",

journal = "Physical review letters",

issn = "0031-9007",

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TY - JOUR

T1 - A scattering matrix formulation of the topological index of interacting fermions in one-dimensional superconductors

AU - Meidan, Dganit

AU - Romito, Alessandro

AU - Brouwer, Piet W.

N1 - 4 pages, 1 fig

PY - 2014/8/1

Y1 - 2014/8/1

N2 - 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.

AB - 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.

KW - cond-mat.mes-hall

KW - cond-mat.str-el

U2 - 10.1103/PhysRevLett.113.057003

DO - 10.1103/PhysRevLett.113.057003

M3 - Journal article

VL - 113

JO - Physical review letters

JF - Physical review letters

SN - 0031-9007

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M1 - 057003

ER -