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.\u00a0 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 \u00a0the two topologically equivalent phases with $\\mbox{tr}\\, r_{\\rm he} = \\pm 4$ \u00a0support \u00a0emergent {\\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 \u00a0connect the topological index to transport properties, thereby highlighting the experimental signatures of interacting topological phases in one dimension.<\/p>\n","protected":false},"excerpt":{"rendered":"
Dganit Meidan 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.\u00a0 We show that in the weak coupling limit, these systems retain a unitary …<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[1],"tags":[],"class_list":{"0":"post-43","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-uncategorized","7":"entry"},"yoast_head":"\n