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Efficient algorithm to compute the Berry conductivity

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http://dx.doi.org/10.1088/1367-2630/16/7/073016
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2014-07
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IOP Publishing
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We propose and construct a numerical algorithm to calculate the Berry conductivity in topological band insulators. The method is applicable to cold atom systems as well as solid state setups, both for the insulating case where the Fermi energy lies in the gap between two bulk bands as well as in the metallic regime. This method interpolates smoothly between both regimes. The algorithm is gauge-invariant by construction, efficient, and yields the Berry conductivity with known and controllable statistical error bars. We apply the algorithm to several paradigmatic models in the field of topological insulators, including Haldaneʼs model on the honeycomb lattice, the multi-band Hofstadter model, and the BHZ model, which describes the 2D spin Hall effect observed in CdTe/HgTe/CdTe quantum well heterostructures.
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© 2014 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. AD thanks the FRS-FNRS Belgium for financial support and N Goldman and P Gaspard for support and valuable discussions. We acknowledge support by the Spanish MICINN grants FIS2009-10061 and FIS2012-33152, the CAM research consortium QUITEMAD S2009-ESP- 1594, the European Commission PICC: FP7 2007-2013, Grant No. 249958, and the UCM-BS grant GICC-910758.
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https://hdl.handle.net/20.500.14352/34022
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