High performance Wannier interpolation of Berry curvature and related quantities with WannierBerri code
Source abstract
Abstract
Abstract Wannier interpolation is a powerful tool for performing Brillouin zone integrals over dense grids of k points, which are essential to evaluate such quantities as the intrinsic anomalous Hall conductivity or Boltzmann transport coefficients. However, more complex physical problems and materials create harder numerical challenges, and computations with the existing codes become very expensive, which often prevents reaching the desired accuracy. In this article, I present a series of methods that boost the speed of Wannier interpolation by several orders of magnitude. They include a combination of fast and slow Fourier transforms, explicit use of symmetries, and recursive adaptive grid refinement among others. The proposed methodology has been implemented in the python code WannierBerri, which also aims to serve as a convenient platform for the future development of interpolation schemes for other phenomena.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Black Holes and Theoretical Physics · Theoretical and Computational Physics · Algebraic structures and combinatorial models
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (59)
Show source-provided references
1. Wannier, G. H. The structure of electronic excitation levels in insulating crystals. Phys. Rev. 52, 191–197 (1937).10.1103/PhysRev.52.191 ↗
2. Marzari, N., Mostofi, A. A., Yates, J. R., Souza, I. & Vanderbilt, D. Maximally localized Wannier functions: theory and applications. Rev. Mod. Phys. 84, 1419–1475 (2012).10.1103/RevModPhys.84.1419 ↗
3. Vanderbilt, D. & King-Smith, R. D. Electric polarization as a bulk quantity and its relation to surface charge. Phys. Rev. B 48, 4442–4455 (1993).10.1103/PhysRevB.48.4442 ↗
4. King-Smith, R. D. & Vanderbilt, D. Theory of polarization of crystalline solids. Phys. Rev. B 47, 1651–1654 (1993).10.1103/PhysRevB.47.1651 ↗
5. Resta, R. Macroscopic polarization in crystalline dielectrics: the geometric phase approach. Rev. Mod. Phys. 66, 899–915 (1994).10.1103/RevModPhys.66.899 ↗
6. Thonhauser, T., Ceresoli, D., Vanderbilt, D. & Resta, R. Orbital magnetization in periodic insulators. Phys. Rev. Lett. 95, 137205 (2005).10.1103/PhysRevLett.95.137205 ↗
7. Ceresoli, D., Thonhauser, T., Vanderbilt, D. & Resta, R. Orbital magnetization in crystalline solids: multi-band insulators, chern insulators, and metals. Phys. Rev. B 74, 024408 (2006).10.1103/PhysRevB.74.024408 ↗
8. Xiao, D., Chang, M.-C. & Niu, Q. Berry phase effects on electronic properties. Rev. Mod. Phys. 82, 1959–2007 (2010).10.1103/RevModPhys.82.1959 ↗
9. Soluyanov, A. A. & Vanderbilt, D. Computing topological invariants without inversion symmetry. Phys. Rev. B 83, 235401 (2011).10.1103/PhysRevB.83.235401 ↗
10. Bradlyn, B. et al. Topological quantum chemistry. Nature 547, 298–305 (2017).10.1038/nature23268 ↗
11. Wu, Q., Zhang, S., Song, H.-F., Troyer, M. & Soluyanov, A. A. WannierTools: An open source software package for novel topological materials. Comput. Phys. Commun. 224, 405–416 (2018).10.1016/j.cpc.2017.09.033 ↗
12. Bouhon, A., Black-Schaffer, A. M. & Slager, R.-J. Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time-reversal symmetry. Phys. Rev. B 100, 195135 (2019).10.1103/PhysRevB.100.195135 ↗
13. Varnava, N., Souza, I. & Vanderbilt, D. Axion coupling in the hybrid Wannier representation. Phys. Rev. B 101, 155130 (2020).10.1103/PhysRevB.101.155130 ↗
14. Souza, I., Marzari, N. & Vanderbilt, D. Maximally localized Wannier functions for entangled energy bands. Phys. Rev. B 65, 035109 (2001).10.1103/PhysRevB.65.035109 ↗
15. Slater, J. C. & Koster, G. F. Simplified LCAO method for the periodic potential problem. Phys. Rev. 94, 1498–1524 (1954).10.1103/PhysRev.94.1498 ↗
16. Gosálbez-Martínez, D., Souza, I. & Vanderbilt, D. Chiral degeneracies and Fermi-surface Chern numbers in bcc Fe. Phys. Rev. B 92, 085138 (2015).10.1103/PhysRevB.92.085138 ↗
17. Wang, X., Yates, J. R., Souza, I. & Vanderbilt, D. Ab initio calculation of the anomalous Hall conductivity by Wannier interpolation. Phys. Rev. B 74, 195118 (2006).10.1103/PhysRevB.74.195118 ↗
18. Lopez, M. G., Vanderbilt, D., Thonhauser, T. & Souza, I. Wannier-based calculation of the orbital magnetization in crystals. Phys. Rev. B 85, 014435 (2012).10.1103/PhysRevB.85.014435 ↗
19. Pizzi, G., Volja, D., Kozinsky, B., Fornari, M. & Marzari, N. BoltzWann: a code for the evaluation of thermoelectric and electronic transport properties with a maximallylocalized Wannier functions basis. Comput. Phys. Commun. 185, 422–429 (2014).10.1016/j.cpc.2013.09.015 ↗
20. Yates, J. R., Wang, X., Vanderbilt, D. & Souza, I. Spectral and Fermi surface properties from Wannier interpolation. Phys. Rev. B 75, 195121 (2007).10.1103/PhysRevB.75.195121 ↗
21. Ibanez-Azpiroz, J., Tsirkin, S. S. & Souza, I. Ab initio calculation of the shift photocurrent by Wannier interpolation. Phys. Rev. B 97, 245143 (2018).10.1103/PhysRevB.97.245143 ↗
22. Giustino, F., Cohen, M. L. & Louie, S. G. Electron-phonon interaction using Wannier functions. Phys. Rev. B 76, 165108 (2007).10.1103/PhysRevB.76.165108 ↗
23. Poncé, S., Margine, E., Verdi, C. & Giustino, F. EPW: electron-phonon coupling, transport and superconducting properties using maximally localized Wannier functions. Comput. Phys. Commun. 209, 116–133 (2016).10.1016/j.cpc.2016.07.028 ↗
24. Tsirkin, S. S., Puente, P. A. & Souza, I. Gyrotropic effects in trigonal tellurium studied from first principles. Phys. Rev. B 97, 035158 (2018).10.1103/PhysRevB.97.035158 ↗
25. Qiao, J., Zhou, J., Yuan, Z. & Zhao, W. Calculation of intrinsic spin Hall conductivity by Wannier interpolation. Phys. Rev. B 98, 214402 (2018).10.1103/PhysRevB.98.214402 ↗
26. Ryoo, J. H., Park, C.-H. & Souza, I. Computation of intrinsic spin Hall conductivities from first principles using maximally localized Wannier functions. Phys. Rev. B 99, 235113 (2019).10.1103/PhysRevB.99.235113 ↗
27. Marzari, N. & Vanderbilt, D. Maximally localized generalized Wannier functions for composite energy bands. Phys. Rev. B 56, 12847 (1997).10.1103/PhysRevB.56.12847 ↗
28. Mostofi, A. A. et al. wannier90: a tool for obtaining maximally-localised Wannier functions. Comput. Phys. Commun. 178, 685–699 (2008).10.1016/j.cpc.2007.11.016 ↗
29. Mostofi, A. A. et al. An updated version of wannier90: a tool for obtaining maximally localised Wannier functions. Comput. Phys. Commun. 185, 2309–2310 (2014).10.1016/j.cpc.2014.05.003 ↗
30. Pizzi, G. et al. Wannier90 as a community code: new features and applications. Matter 32, 165902 (2020).
31. Mustafa, J. I., Coh, S., Cohen, M. L. & Louie, S. G. Automated construction of maximally localized Wannier functions for bands with nontrivial topology. Phys. Rev. B 94, 125151 (2016).10.1103/PhysRevB.94.125151 ↗
32. Damle, A., Lin, L. & Ying, L. Compressed representation of Kohn-Sham orbitals via selected columns of the density matrix. J. Chem. Theory Comput. 11, 1463–1469 (2015).10.1021/ct500985f ↗
33. Damle, A. & Lin, L. Disentanglement via entanglement: a unified method for Wannier localization. Multiscale model. Sim 16, 1392–1410 (2018).
34. Vitale, V. et al. Automated high-throughput Wannierisation. npj Comput. Mater. 6, 66 (2020).10.1038/s41524-020-0312-y ↗
35. Zhang, Z. et al. High-throughput screening and automated processing toward novel topological insulators. J. Phys. Chem. Lett. 9, 6224–6231 (2018).10.1021/acs.jpclett.8b02800 ↗
36. Garrity, K. F. & Choudhary, K. Database of Wannier Tight-binding Hamiltonians using high-throughput density functional theory. http://arxiv.org/abs/2007.01205 [cond-mat.mtrl-sci] (2020).10.1038/s41597-021-00885-z ↗
37. Garrity, K.F., Choudhary, K. JARVIS-WannierTB : database Wannier Tight-binding hamiltonian derived properties of 3D and 2D materials, online https://jarvis.nist.gov/jarviswtb/. Accessed 06/02/2021.
38. Cooley, J. W. & Tukey, J. W. An algorithm for the machine computation of the complex Fourier series. Math. Comput. 19, 297–301 (1965).10.1090/S0025-5718-1965-0178586-1 ↗
39. Heideman, M., Johnson, D. & Burrus, C. Gauss and the history of the fast Fourier transform. IEEE ASSP Mag. 1, 14–21 (1984).10.1109/MASSP.1984.1162257 ↗
40. Duhamel, P. & Vetterli, M. Fast fourier transforms: a tutorial review and a state of the art. Signal Process. 19, 259–299 (1990).10.1016/0165-1684(90)90158-U ↗
41. Van Loan, C. Computational Frameworks for the Fast Fourier Transform (Society for Industrial and Applied Mathematics, 1992).10.1137/1.9781611970999 ↗
42. Yao, Y. et al. First principles calculation of anomalous Hall conductivity in ferromagnetic bcc Fe. Phys. Rev. Lett. 92, 037204 (2004).10.1103/PhysRevLett.92.037204 ↗
43. Sakuma, R. Symmetry-adapted Wannier functions in the maximal localization procedure. Phys. Rev. B 87, 235109 (2013).10.1103/PhysRevB.87.235109 ↗
44. Sodemann, I. & Fu, L. Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials. Phys. Rev. Lett. 115, 216806 (2015).10.1103/PhysRevLett.115.216806 ↗
45. Zhong, S., Moore, J. E. & Souza, I. Gyrotropic magnetic effect and the magnetic moment on the Fermi surface. Phys. Rev. Lett. 116, 077201 (2016).10.1103/PhysRevLett.116.077201 ↗
46. Kawamura, M. FermiSurfer: Fermi-surface viewer providing multiple representation schemes. Comput. Phys. Commun. 239, 197–203 (2019).10.1016/j.cpc.2019.01.017 ↗
47. Destraz, D. et al. Magnetism and anomalous transport in the Weyl semimetal PrAlGe: possible route to axial gauge fields. npj Quantum Mater. 5, 5 (2020).10.1038/s41535-019-0207-7 ↗
48. Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous Hall effect. Rev. Mod. Phys. 82, 1539–1592 (2010).10.1103/RevModPhys.82.1539 ↗
49. Xiao, D., Yao, Y., Fang, Z. & Niu, Q. Berry-phase effect in anomalous thermoelectric transport. Phys. Rev. Lett. 97, 026603 (2006).10.1103/PhysRevLett.97.026603 ↗
50. Giannozzi, P. et al. Quantum ESPRESSO toward the exascale. J. Chem. Phys. 152, 154105 (2020).10.1063/5.0005082 ↗
51. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).10.1103/PhysRevLett.77.3865 ↗
52. van Setten, M. et al. The PseudoDojo: training and grading a 85 element optimized norm-conserving pseudopotential table. Comput. Phys. Commun. 226, 39–54 (2018).10.1016/j.cpc.2018.01.012 ↗
53. Hamann, D. R. Optimized norm-conserving Vanderbilt pseudopotentials. Phys. Rev. B 88, 085117 (2013).10.1103/PhysRevB.88.085117 ↗
54. Oliphant, T. E. A Guide to NumPy (Trelgol Publishing, 2006).
55. Virtanen, P. et al. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat. Methods 17, 261–272 (2020).10.1038/s41592-019-0686-2 ↗
56. Frigo, M. & Johnson, S. G. The design and implementation of FFTW3. In Fawwaz T. Ulaby (ed) Proceedings of the IEEE 93. Special issue on "Program Generation, Optimization, and Platform Adaptation", 216–231 (IEEE, 2005).10.1109/JPROC.2004.840301 ↗
57. Kresse, G., et al. Vienna Ab initio Simulation Package (VASP) code. online https://www.vasp.at/. Accessed 06/12/2021.
58. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).10.1103/PhysRevB.50.17953 ↗
59. Hunter, J. D. Matplotlib: a 2D graphics environment. Comput. Sci. Eng. 9, 90–95 (2007).10.1109/MCSE.2007.55 ↗