Localization in a quantum spin hall system

The localization problem of electronic states in a two-dimensional quantum spin Hall system (that is, a symplectic ensemble with topological term) is studied by the transfer matrix method. The phase diagram in the plane of energy and disorder strength is exposed, and demonstrates “ levitation†and “pair annihilation†of the domains of extended states analogous to that of the integer quantum Hall system. The critical exponent Î for the divergence of the localization length is estimated as Î â‰-1.6, which is distinct from both exponents pertaining to the conventional symplectic and the unitary quantum Hall systems. Our analysis strongly suggests a different universality class related to the topology of the pertinent system.