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@Article{Jin_JPhysCondensMatterInstPhysJ_2021_v33_p325503,
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author = {Gan Jin and Daye Zheng and Lixin He},
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title = {{Calculation of Berry curvature using non-orthogonal atomic orbitals}},
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journal = {J. Phys., Condens. Matter: Inst. Phys. J.},
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year = 2021,
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volume = 33,
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number = 32,
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pages = 325503,
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doi = {10.1088/1361-648X/ac05e5},
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abstract = {We present a derivation of the full formula to calculate the Berry
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curvature on non-orthogonal numerical atomic orbital (NAO) bases.
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Because usually, the number of NAOs is larger than that of the Wannier
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bases, we use a orbital contraction method to reduce the basis sizes,
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which can greatly improve the calculation efficiency without
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significantly reducing the calculation accuracy. We benchmark the
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formula by calculating the Berry curvature of ferroelectric BaTiO3and
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bcc Fe, as well as the anomalous Hall conductivity for Fe. The results
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are in excellent agreement with the finite-difference and previous
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results in the literature. We find that there are corrections terms to
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the Kubo formula of the Berry curvature. For the full NAO base, the
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differences between the two methods are negligibly small, but for the
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reduced bases sets, the correction terms become larger, which may not
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be neglected in some cases. The formula developed in this work can
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readily be applied to the non-orthogonal generalized Wannier
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functions.},
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}
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@Article{Chen_PhysRevB_2009_v80_p165121,
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author = {Mohan Chen and Wei Fang and G.-Z. Sun and G.-C. Guo and Lixin He},
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title = {{Method to construct transferable minimal basis sets forab

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