Xiao-Liang Qi, Taylor L. Hughes, and Shou-Cheng Zhang. “Topological Field Theory of Time-Reversal Invariant Insulators.”

Physical Review B78, no. 19 (2008): 195424.

Xiao-Liang Qi, Taylor L. Hughes, and Shou-Cheng Zhang. “Topological Field Theory of Time-Reversal Invariant Insulators.”

Physical Review B78, no. 19 (2008): 195424.

As discussed in the paper on 3D topological insulators, using the topological band theory formalism developed by Fu and Kane, the distinction of topological versus trivial band insulators can be accomplished reliably. There are, however, some other exotic (field-theoretic) effects that band theory misses. The so-called topological magneto-electric (TME) effect, and its manifestation in the form of half quantum Hall effect and quantized Kerr rotation, has been predicted to occur on the time-reversal broken surface states of a 3D topological insulator. The above paper develops the necessary formalism, namely dimensional reduction in lattice models with specific symmetries, to obtain the low-energy effective field theory describing the electromagnetic response of surface states of a 3D topological insulator.

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