Correction to: Nature https://doi.org/10.1038/s41586-019-1809-8 Published online 18 December 2019

In this Article, in the ‘Calculation of system free energy’ section of the Methods, there were omissions in equation (7). The equation should read:

“Or, if K11 < K33,

$${F}_{{\rm{f}}}={\rm{\pi }}{K}_{11}\left[2+\frac{k}{\sqrt{k-1}}{\tan }^{-1}\sqrt{k-1}-\frac{k}{\sqrt{k-1}}{\tan }^{-1}\left(\frac{\sqrt{k-1}}{\sigma }\right)-\frac{{K}_{24}}{{K}_{11}}\right]\,L+\gamma 2{\rm{\pi }}rL$$

Or, if K11 > K33,\({F}_{{\rm{f}}}={\rm{\pi }}{K}_{11}\left[2+\frac{k}{\sqrt{1-k}}{\tanh }^{-1}\sqrt{1-k}-\frac{k}{\sqrt{1-k}}{\tanh }^{-1}\left(\frac{\sqrt{1-k}}{\sigma }\right)-\frac{{K}_{24}}{{K}_{11}}\right]\,L+\gamma 2{\rm{\pi }}rL\) (7)”

instead of:

“Or, if K11 < K33,

$${F}_{{\rm{f}}}={\rm{\pi }}{K}_{11}\left[2+\frac{k}{\sqrt{k-1}}{\tan }^{-1}\sqrt{k-1}-\frac{k}{\sqrt{k-1}}{\tan }^{-1}\left(\frac{\sqrt{k-1}}{\sigma }\right)-\frac{{K}_{24}}{{K}_{11}}\right]\,$$

Or, if K11 > K33:

\({F}_{{\rm{f}}}={\rm{\pi }}{K}_{11}\left[2+\frac{k}{\sqrt{1-k}}{\tanh }^{-1}\sqrt{1-k}-\frac{k}{\sqrt{1-k}}{\tanh }^{-1}\left(\frac{\sqrt{1-k}}{\sigma }\right)-\frac{{K}_{24}}{{K}_{11}}\right]\,\) (7)”

All calculations and conclusions presented in the Article were carried out using the correct equations and are unaffected by these changes. The original Article has been corrected online.