www.nature.com/npjcompumats




                  AUTHOR CORRECTION                                             OPEN

                  Author Correction: The elphbolt ab initio solver for the
                  coupled electron-phonon Boltzmann transport equations
                  Nakib H. Protik                 , Chunhua Li, Miguel Pruneda, David Broido      and Pablo Ordejón
                  npj Computational Materials (2022)8:58 ; https://doi.org/10.1038/s41524-022-00746-2




                  Correction to: npj Computational Materials https://doi.org/10.1038/                The correct expression for Eq. (7) is
                  s41524-022-00710-0, published online 07 February 2022                                              2 P
                                                                                                                         qffiffiffiffiffiffiffiffiffiffiffiffiffih     i
                                                                                                                                           y
                                                                                                      gFr;smn
                                                                                                       kq     ¼ i εe0 V        h
                                                                                                                          2mτ hωsq Uk Uk
                                                                                                                                         0
                                                                                                                            τ                     nm
                  The original version of this article contained typographical errors                  P      ðqþGÞZτ ξ τ;sq
                  in Equation (6) and Equation (7).                                                          ðqþGÞϵ1 ðqþGÞ      ´ exp½i ðq þ GÞ  rτ :
                                                                                                      G≠q

                  The correct expression for Eq. (6) is                                              which replaces the previous incorrect version:
                          qffiffiffiffiffiffiffiffiffiffiffiffiffi     P                                                                    2 P
                                                                                                                        qffiffiffiffiffiffiffiffiffiffiffiffiffi      P ðqþGÞZτ ξτ;sq
                   gsmn
                    kq ¼
                                h
                                
                            2mτ 
                                         1
                                 hωsq Ne Nph   exp ik  Re þ iq  Rph                                gFr;smn
                                                                                                      kq     ¼ i εe0 V        h       
                                                                                                                         2mτ hωsq Unk0 Umk   ðqþGÞϵ1 ðqþGÞ
1234567890():,;




                                                         Re Rph                                                           τ                        G≠q                                     (7)
                                  P           0    0 0         y                                                     ´ hnk0 j exp½i ðq þ GÞ  rτ jmki;
                             ´              gsRemRphn Unn0 k0 Um                Fr;smn
                                                                 0 mk us0 sq þ gkq     :
                                 s0 m0 n0

                                                                                                                        Open Access This article is licensed under a Creative Commons
                  which replaces the previous incorrect version:                                                        Attribution 4.0 International License, which permits use, sharing,
                          qffiffiffiffiffiffiffiffiffiffiffiffiffi     P                                                     adaptation, distribution and reproduction in any medium or format, as long as you give
                  gsmn
                   kq ¼
                                h
                                
                            2mτ 
                                         1
                                 hωsq Ne Nph   exp ik  Re þ iq  Rph                                appropriate credit to the original author(s) and the source, provide a link to the Creative
                                                         Re Rph                             (6)      Commons license, and indicate if changes were made. The images or other third party
                            ´ gsmn                   Fr;smn
                               Re Rph Unk0 Umk usq þ gkq     ;                                       material in this article are included in the article’s Creative Commons license, unless
                                                                                                     indicated otherwise in a credit line to the material. If material is not included in the
                                                                                                     article’s Creative Commons license and your intended use is not permitted by statutory
                                                                                                     regulation or exceeds the permitted use, you will need to obtain permission directly
                                                                                                     from the copyright holder. To view a copy of this license, visit http://creativecommons.
                                                                                                     org/licenses/by/4.0/.


                                                                                                     © The Author(s) 2022




                  Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciences