Seminar
The noncommutative topology of dirty superconductors: the "case study" of the Spin Hall effect (joint work with H. SchulzBaldes)

Hold Date 
20130425 16:00～20130425 17:30 


Place 
Seminar Room 6, Faculty of Mathematics building, Ito Campus 


Object person 



Speaker 
G. De Nittis (FriedrichAlexander Universität ErlangenNürnberg, FAU) 

Abstract
The BCS theory of superconductors leads to simple lattice models, known as BdG Hamiltonians. The properties of these secondquantize Hamiltonians can be investigate just looking at their firstquantized counterparts which turn out to be matrixvalued lattice models. The physics of these operators is made more interesting by the presence of discrete symmetries known as particlehole (PH). According to the parity of the PHsymmetry and to the presence of additional symmetries (spinrotation, timereversal, etc.), the (firstquantized) BdG Hamiltonians are classified in classes which are parametrized by topological invariants.
Albeit the physics of these models is well understood in the pure periodic case, a systematic study in the presence of disorder seems to be still missing. One of the main features of the physics of the BdG Hamiltonians is the presence of topological protected states which allow quantized bulkcurrents (spin, thermal, etc) et related edgecurrents. Such topological quantities have to persist also in the presence of (at least weak) disorder. The aim of this talk is to present first results in this direction.
As explained by Bellissard et coworkers during the 80's90's, the natural setting to combine differential topology and randomness is the noncommutative geometry. In this talk I will present the noncommutative (differential) topology associated to dirty BdG Hamiltonians. The PHsymmetry adds to the usual algebraic structure and provides a natural notion of "Reality" (à la Atiyah) which enters in the definitions of the relevant geometric objects. These general results will be tested on the case study of the Ctype BdG Hamiltonians in order to provide a noncommutative explanation of the spin quantum Hall effect both in the bulk and on the edge.