Magnetoelectric Polarizability and Axion Electrodynamics in Crystalline Insulators

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Andrew M. Essin,¹ Joel E. Moore,^1,2 and David Vanderbilt³
¹Department of Physics, University of California, Berkeley, California 94720, USA
²Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
³Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA

Received 22 October 2008; published 10 April 2009

Theorbital motion of electrons in a three-dimensional solid can generatea pseudoscalar magnetoelectric coupling theta , a fact we derive forthe single-particle case using a recent theory of polarization inweakly inhomogeneous materials. This polarizability theta is the same parameterthat appears in the “axion electrodynamics” Lagrangian Delta [script L] _EM=( theta e²/2h)E·B, which isknown to describe the unusual magnetoelectric properties of the three-dimensionaltopological insulator ( theta =). We compute theta for a simple modelthat accesses the topological insulator and discuss its connection tothe surface Hall conductivity. The orbital magnetoelectric polarizability can begeneralized to the many-particle wave function and defines the 3Dtopological insulator, like the integer quantum Hall effect, in termsof a topological ground-state response function.

URL:	http://link.aps.org/doi/10.1103/PhysRevLett.102.146805
DOI:	10.1103/PhysRevLett.102.146805
PACS:	73.43.-f; 03.65.Vf; 73.20.At; 85.75.-d 73.43.-f Quantum Hall effects 03.65.Vf Phases: geometric; dynamic or topological (quantum theory) 73.20.At Surface states, band structure, electron density of states 85.75.-d Magnetoelectronics; spintronics YEAR: 2009