TOPMAGIC: Topological phase prediction from the magneto-electric effect
Research project selected under the 2016 call for proposals
Principal Investigator :
Arjan BERGER ()
LCPQ
Type of project : Disruptive Project
Date (start/end) : 2017 - 2019
(source: wikipedia): Schematic representation of the band structure of a topological insulator. The band gap of the bulk states is crossed by surface states which are topologically protected.
Abstract
The TOPMAGIC project aims to provide a theory and a numerical tool for the prediction of topological insulators from first principles. The phase of an insulator (ordinary or topological) can be determined from the orbital magnetic polarizability which is the response function related to the polarization induced by a magnetic field. Experimentally topological phases have already been determined in this way, but there is no first-principles theory available to predict these phases.
A phase of matter can be defined as the response of a system with respect to an external perturbation. For example, a metal has a non-zero conductivity in response to an applied external field at low temperature. The pertinent response quantity to distinguish an ordinary insulator from a topological insulator can be obtained using so-called axion electrodynamics in which the usual Maxwellian Lagrangian is supplemented by the scalar product of the electric and the magnetic field. The coefficient that corresponds to this additional term is called the axion angle and has only two values that are compatible with time-reversal symmetry; it is either zero, which corresponds to an ordinary insulator, or it is equal to π, which indicates a (strong) topological insulator. The axion angle can be linked to the magneto-electric polarizability which i s the response function of the magneto-electric effect in which an applied electric field generates a magnetic field or vice versa. In this project, we therefore propose to calculate directly the appropriate response function, i.e., the magneto-electric polarizability, from which the axion angle can be obtained.