Ab initio calculation of the anomalous Hall conductivity by Wannier interpolation
By Xinjie Wang, Jonathan R. Yates, Ivo Souza, D. Vanderbilt. 2006
374 citations recorded by the source corpus.
The intrinsic anomalous Hall conductivity in ferromagnets depends on subtle spin-orbit-induced effects in the electronic structure, and recent ab initio studies found that it was necessary to sample the Brillouin zone at millions of $k$-points to converge the calculation. We present an efficient first-principles approach for computing this quantity. We start out by performing a conventional electronic-structure calculation including spin-orbit coupling on a uniform and relatively coarse $k$-point mesh. From the resulting Bloch states, maximally localized Wannier functions are constructed which reproduce the ab initio states up to the Fermi level. The Hamiltonian and position-operator matrix elements, needed to represent the energy bands and Berry curvatures, are then set up between the Wannier orbitals. This completes the first stage of the calculation, whereby the low-energy ab initio problem is transformed into an effective tight-binding form. The second stage only involves Fourier transforms and unitary transformations of the small matrices setup in the first stage. With these inexpensive operations, the quantities of interest are interpolated onto a dense $k$-point mesh and used to evaluate the anomalous Hall conductivity as a Brillouin zone integral. The present scheme, which also avoids the cumbersome summation over all unoccupied states in the Kubo formula, is applied to bcc Fe, giving excellent agreement with conventional, less efficient first-principles calculations. Remarkably, we find that about 99% of the effect can be recovered by keeping a set of terms depending only on the Hamiltonian matrix elements, not on matrix elements of the position operator.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/72e396c6691e432012daa8844e5a8c4599024167
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In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
Citations in the corpus
- Maximally-localized Wannier Functions: Theory and Applications (2011, methodology): “It is also possible to further modify the wannierization procedure so as to produce two separate subsets of spinor WFs: one with a predominantly spin-up character, and the other with a predominantly spin-down character (Wang et al., 2006).”
- Weyl Semimetal Phase in Noncentrosymmetric Transition-Metal Monophosphides (2014, methodology): “To determine precisely the location of each Weyl point, we divide the reduced BZ into a very dense k-point mesh and compute the Berry curvature or the “magnetic field in momentum space” [35,38] on that mesh, as shown in Fig.”
- Anomalous hall effect (2009, background): “Detailed first-principles calculations of the intrinsic contribution to the AHE conductivity have been performed for bcc Fe (Wang et al., 2006; Yao et al., 2004), fcc Ni, and hpc Co (Wang et al., 2007).”
- Wannier90 as a community code: new features and applications (2019, methodology): “This was done first for the inverse effective-mass tensor 59,60 and later for the Berry curvature, 32 and is at the heart of the Wannier-interpolation technique for calculating the intrinsic anomalous Hall conductivity (AHC).”
- Ab initio calculation of the shift photocurrent by Wannier interpolation (2018, methodology): “This is in contrast to previous Wannier-based schemes, where a parallel-transport gauge was assumed when calculating the interband matrix elements [25, 26].”