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.

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Cited by in corpus (10)

• Field Induced Positional Shift of Bloch Electrons and its Dynamical Implications
• Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics
• Virtual Topological Insulators with Real Quantized Physics
• Topological phase transitions in (Bi${}_{1-x}$In${}_x{)}_2$Se${}_3$ and (Bi${}_{1-x}$Sb${}_x{)}_2$Se${}_3$
• The non-commutative n-th Chern number
• Notes on topological insulators
• Quantization of Topological Invariants under Symmetry-Breaking Disorder
• Bulk-Boundary Correspondence for Topological Insulators with Quantized Magneto-Electric Effect
• Synthetic magnetoelectric response of lattice bosonic insulators
• Coarse geometric approach to topological phases: Invariants from real-space representations