Editing Wannier function (section)

==Wannier interpolation==
Wannier functions are often used to interpolate bandstructures calculated ''ab initio'' on a coarse grid of '''k'''-points to any arbitrary '''k'''-point. This is particularly useful for evaluation of Brillouin-zone integrals on dense grids and searching of Weyl points, and also taking derivatives in the '''k'''-space. This approach is similar in spirit to the [[Tight binding#Connection to Wannier functions|tight binding]] approximation, but in contrast allows for an exact description of bands in a certain energy range. Wannier interpolation schemes have been derived for spectral properties,<ref name="Yates Wang Vanderbilt Souza p. ">{{cite journal | last1=Yates | first1=Jonathan R. | last2=Wang | first2=Xinjie | last3=Vanderbilt | first3=David | last4=Souza | first4=Ivo | title=Spectral and Fermi surface properties from Wannier interpolation | journal=Physical Review B | publisher=American Physical Society (APS) | volume=75 | issue=19 | date=2007-05-21 | page=195121 | issn=1098-0121 | doi=10.1103/physrevb.75.195121 | arxiv=cond-mat/0702554| bibcode=2007PhRvB..75s5121Y | s2cid=31224663 }}</ref>
[[Hall effect#Anomalous Hall effect|anomalous Hall conductivity]],<ref name="Wang Yates Souza Vanderbilt p. ">{{cite journal | last1=Wang | first1=Xinjie | last2=Yates | first2=Jonathan R. | last3=Souza | first3=Ivo | last4=Vanderbilt | first4=David | title=Ab initiocalculation of the anomalous Hall conductivity by Wannier interpolation | journal=Physical Review B | volume=74 | issue=19 | date=2006-11-21 | page=195118 |arxiv=cond-mat/0608257| issn=1098-0121 | doi=10.1103/physrevb.74.195118 | bibcode=2006PhRvB..74s5118W | s2cid=30427871 }}</ref>
[[orbital magnetization]],<ref name="Lopez Vanderbilt Thonhauser Souza p. ">{{cite journal | last1=Lopez | first1=M. G. | last2=Vanderbilt | first2=David | last3=Thonhauser | first3=T. | last4=Souza | first4=Ivo | title=Wannier-based calculation of the orbital magnetization in crystals | journal=Physical Review B | volume=85 | issue=1 | date=2012-01-31 | page=014435 | issn=1098-0121 | doi=10.1103/physrevb.85.014435 | arxiv=1112.1938 | bibcode=2012PhRvB..85a4435L | s2cid=44056938 }}</ref>
thermoelectric and electronic transport properties,<ref name="Computer Physics Communications 2014 pp. 422–429">{{cite journal | title=BoltzWann: A code for the evaluation of thermoelectric and electronic transport properties with a maximally-localized Wannier functions basis | journal=Computer Physics Communications | volume=185 | issue=1 | date=2014-01-01 | issn=0010-4655 | doi=10.1016/j.cpc.2013.09.015 | pages=422–429 |arxiv=1305.1587 | url=https://www.sciencedirect.com/science/article/pii/S0010465513003160 | access-date=2020-07-13| last1=Pizzi | first1=Giovanni | last2=Volja | first2=Dmitri | last3=Kozinsky | first3=Boris | last4=Fornari | first4=Marco | last5=Marzari | first5=Nicola | bibcode=2014CoPhC.185..422P | s2cid=6140858 }}</ref>
[[Magneto-optic effect|gyrotropic effects]],<ref name="Tsirkin Puente Souza p. ">{{cite journal | last1=Tsirkin | first1=Stepan S. | last2=Puente | first2=Pablo Aguado | last3=Souza | first3=Ivo | title=Gyrotropic effects in trigonal tellurium studied from first principles | journal=Physical Review B | volume=97 | issue=3 | date=2018-01-29 | page=035158 | issn=2469-9950 | doi=10.1103/physrevb.97.035158 | arxiv=1710.03204| bibcode=2018PhRvB..97c5158T | s2cid=55517213 }}</ref>
[[Anomalous photovoltaic effect|shift current]],<ref name="Ibañez-Azpiroz Tsirkin Souza p. ">{{cite journal | last1=Ibañez-Azpiroz | first1=Julen | last2=Tsirkin | first2=Stepan S. | last3=Souza | first3=Ivo | title=Ab initio calculation of the shift photocurrent by Wannier interpolation | journal=Physical Review B | volume=97 | issue=24 | date=2018-06-26 | page=245143 | issn=2469-9950 | doi=10.1103/physrevb.97.245143 |arxiv=1804.04030| bibcode=2018PhRvB..97x5143I | s2cid=67751414 }}</ref>
[[Spin Hall effect|spin Hall conductivity]]
<ref name="Qiao Zhou Yuan Zhao p. ">{{cite journal | last1=Qiao | first1=Junfeng | last2=Zhou | first2=Jiaqi | last3=Yuan | first3=Zhe | last4=Zhao | first4=Weisheng | title=Calculation of intrinsic spin Hall conductivity by Wannier interpolation | journal=Physical Review B | volume=98 | issue=21 | date=2018-12-03 | page=214402 |arxiv=1810.07637| issn=2469-9950 | doi=10.1103/physrevb.98.214402 | bibcode=2018PhRvB..98u4402Q | s2cid=119223848 }}</ref>
<ref name="Ryoo Park Souza p. ">{{cite journal | last1=Ryoo | first1=Ji Hoon | last2=Park | first2=Cheol-Hwan | last3=Souza | first3=Ivo | title=Computation of intrinsic spin Hall conductivities from first principles using maximally localized Wannier functions | journal=Physical Review B | volume=99 | issue=23 | date=2019-06-07 | page=235113 | arxiv=1906.07139| issn=2469-9950 | doi=10.1103/physrevb.99.235113 | bibcode=2019PhRvB..99w5113R | s2cid=189928182 }}</ref> 
and other effects.