Analysis & Applied Math

Event Information Chirality induced Interface Currents in the Chalker Coddington Model
14:10 on Friday September 28, 2018
15:00 on Friday September 28, 2018
BA6183, Bahen Center, 40 St. George St.
Alain Joye

Grenoble

Chalker & Coddington provided in 1988 a simplified description of the quantum dynamics of electrons in a plane, submitted to an electric potential and a strong perpendicular magnetic field, in a model that now bears their names. The one time step electronic motion is given by a unitary operator on $l^2(Z^2)$ constructed in terms of scattering matrices attached to the sites of $Z^2$ that contain the main physical characteristics of the potential and magnetic field at these sites. The transport properties of the electrons are then encoded in the spectral properties of the unitary operator, which is our main concern. We consider the situation where the model presents asymptotically pure anti-clockwise rotation on the left and clockwise rotation on the right and we investigate the presence of induced currents at the interface between these two different localised phases. The existence of interface currents is shown by proving that the absolutely continuous spectrum of the Chalker Coddington unitary operator covers the whole unit circle. The result is independent of the details of the model within the interface and possesses some topological features. This is joint work with J.Asch and O.Bourget