Correction to: Communications Physics https://doi.org/10.1038/s42005-021-00742-w, published online 11 November 2021.

Some of the notations and equations of this article contained errors. The list of corrections is as follows:

  1. 1)

    In the caption of Fig. 2, the symbols ‘ρ’ and ‘μ’ were erroneously typeset in regular font, and have now been italicised as ‘ρ’ and ‘μ

  2. 2)

    Eq. 2 originally read as

    $${\mu }_{imp}=\frac{e}{{m}^{\ast }}\frac{{\tau }_{I}E}{E}$$

    and has now been corrected to

    $${\mu }_{imp}=\frac{e}{{m}^{\ast }}\frac{\langle {\tau }_{I}E\rangle }{\langle E\rangle }$$
  3. 3)

    In the subsection of the Methods titled “Calculations of electron–phonon interactions and electron mobility”, just above equation (3) the sentence starting with ‘The thermal average A, where A….’ has been replaced by ‘The thermal average \(\langle A\rangle\), where A…”

  4. 4)

    Eq. 3 was originally written as

    $$A=\int _{0}^\infty dEA(E)g(E)f(E,{E}_{f})$$

    And has been replaced by

    $$\langle A\rangle =\int _{0}^{\infty }dE\,A(E)\,g(E)\,f(E,{E}_{f})$$
  5. 5)

    Eq. 5 was

    $$n=\int _{0}^{\infty }dEg(E)f(E,{E}_{f})$$

    And has now been corrected to

    $$\,n=\int_{0}^{\infty }dE\,g(E)\,f(E,{E}_{f})$$

In addition to the above, the following mistakes came to the authors attention and have also been corrected.

  1. i)

    In the subsection “Successful n-type doping with Nd” within the “Results and discussion” section, in the second paragraph the sentence “For this reason, although not directly, the observed behavior is a strong evidence of 100% activation in our samples” has been replaced by “For this reason, although not directly, the observed behavior is strong evidence of 100% activation in our samples”.

  2. ii)

    In the subsection “Calculations of electron–phonon interactions and electron mobility”, within the “Methods”, in the 2nd paragraph, in the first line ‘mimp’ has been replaced with ‘μimp’. In the same subsection, in 4th paragraph, fourth line from the top: – ‘es’ has been replaced by ‘εs’.

  3. iii)

    The original figure 5

Correction Fig. 1: original figure 5

Has been replaced with

Correction Fig. 2: new figure 5

Where the reference data to ‘Wei et. al. LaxSr1-xSnO3’ (filled blue squares) has now been included in the figure data and key. This is cited as Ref. 6 in the corresponding figure caption, the text of which was already present in the caption as originally published.

The above have now been corrected in both the HTML and PDF version of the article.