Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 46, Issue 8, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/46/8/085205
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Funding
- US NSF [DMS-1066045, DMR-1056168]
- Direct For Mathematical & Physical Scien
- Division Of Materials Research [1056168] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1066045] Funding Source: National Science Foundation
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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 Schulz-Baldes and Teufel (2012 arXiv:1201.4812v1). The quantization, topological invariance and connection to a second Chern number of the magneto-electric response are discussed in the context of three-dimensional, disordered, time-reversal or inversion symmetric topological insulators.
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