A Non-Commutative Formula for the Isotropic Magneto-Electric Response

Abstract

A non-commutative formula for the isotropic magneto-electric response of disordered insulators under magnetic fields is derived using the methods of non-commutative geometry. Our result follows from an explicit evaluation of the Ito derivative with respect to the magnetic field of the non-commutative formula for the electric polarization reported in Ref. 1. The quantization, topological invariance and connection to a second Chern number of the magneto-electric response are discussed in the context of 3-dimensional, disordered, time-reversal or inversion symmetric topological insulators.

References in corpus (6)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Theory of orbital magnetoelectric response
• Manifestly gauge independent formulations of the Z2 invariants
• The noncommutative Kubo Formula: Applications to Transport in Disordered Topological Insulators with and without Magnetic Fields
• Topological quantization of ensemble averages