BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Eslam Khalaf (Harvard University) DTSTART:20201123T170000Z DTEND:20201123T180000Z DTSTAMP:20260423T024726Z UID:QM3/25 DESCRIPTION:Title: Loc alization at the edge of a topological insulator: Interplay of disorder-in duced-localization and topological protection\nby Eslam Khalaf (Harvar d University) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAb stract\nTransport in disordered one-dimensional wires is described by diff usion at short distances/times and by Anderson localization at long distan ces/times. I will investigate how this picture is altered in a disordered multi-channel wire where some of the channels are topologically protected. This scenario can be realized at the interface between two quantum Hall s ystems\, in a Weyl semimetal in a magnetic field or at the edge of a quant um spin Hall insulator. Technically\, the problem is described by a $0+1$- dimensional field theory in the form of a supersymmetric non-linear sigma model with a topological term. I will show how to solve this field theory exactly to obtain DC (static) transport quantities such as DC conductance and shot noise as well as dynamical responses such as diffusion probabilit y of return and correlations of local density of states. I will discuss se veral surprising findings of this exact solution. First\, I find that diso rder is much more effective in localizing the diffusive channels in the pr esence of topologically protected ones. This can be understood in terms of statistical level repulsion by mapping the problem to that of a random ma trix ensemble with zero eigenvalues. Second\, I find that localization cor rections dramatically alter the long time behavior of the return probabili ty in a system described by diffusion+drift equation at the classical leve l. Finally\, I find that in a disordered wire with topologically protected channels\, the wave functions display level attraction rather than level repulsion.\n LOCATION:https://researchseminars.org/talk/QM3/25/ END:VEVENT END:VCALENDAR