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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Anderson localization\, topology\, and interaction
- Ostrovsky\, P (Max Planck Institut fr Festkrper
forschung)
DTSTART;TZID=Europe/London:20120920T115000
DTEND;TZID=Europe/London:20120920T123000
UID:TALK39940AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/39940
DESCRIPTION:Field-theoretical approach to Anderson localizatio
n in 2D disordered fermionic systems of chiral sym
metry classes (BDI\, AIII\, CII) is developed. Imp
ortant representatives of these symmetry classes a
re random hopping models on bipartite lattices at
the band center. As was found by Gade and Wegner t
wo decades ago within the sigma-model formalism\,
quantum interference effects in these classes are
absent to all orders of perturbation theory. We de
monstrate that the quantum localization effects em
erge when the theory is treated nonperturbatively.
Specifically\, they are controlled by topological
vortexlike excitations of the sigma models by a m
echanism similar to the Berezinskii-Kosterlitz-Tho
uless transition. We derive renormalization-group
equations including these nonperturbative contribu
tions. Analyzing them\, we find that the 2D disord
ered systems of chiral classes undergo a metal-ins
ulator transition driven by topologically induced
Anderson localization. We also show that the topol
ogical terms on surfaces of 3D topological insulat
ors of chiral symmetry (in classes AIII and CII) o
verpower the vortex-induced localization.\n
\nSimilar vortex excitations also emerge in system
s with strong spin-orbit interaction (symplectic s
ymmetry class AII). Such systems may exhibit topol
ogical insulator state both in three and two dimen
sions. Interplay of nontrivial topology and Coulom
b repulsion induces a novel critical state on the
surface of a 3D topological insulator. Remarkably\
, this interaction-induced criticality\, character
ized by a universal value of conductivity\, emerge
s without any adjustable parameters. Interaction a
lso leads to a direct transition between trivial i
nsulator and topological insulator in 2D (quantum-
spin-Hall transition) via a similar critical state
. The nature of this latter critical state is clos
ely related to the effects of vortices within the
Finkelstein sigma model.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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