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

Speaker
Dganit Meidan, Ben-Gurion university
Date
06/03/2014 - 15:30 - 14:30Add to Calendar 2014-03-06 14:30:00 2014-03-06 15:30:00 A scattering matrix formulation of the topological index of interacting fermions in one-dimensional superconductors TBDWe 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 {\it 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. Resnick Building 209, room 210 המחלקה לפיזיקה physics.dept@mail.biu.ac.il Asia/Jerusalem public
Place
Resnick Building 209, room 210
Abstract

TBDWe 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 {\it 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.

תאריך עדכון אחרון : 02/02/2014