  Fan et al. [$\mathit{Annals}$ $\mathit{of}$ $\mathit{Statistics}$
$\textbf{47}$(6) (2019) 3009-3031] constructed a distributed principal
component analysis (PCA) algorithm to reduce the communication cost between
multiple servers significantly. However, their algorithm's guarantee is only
for sub-Gaussian data. Spurred by this deficiency, this paper enhances the
effectiveness of their distributed PCA algorithm by utilizing robust covariance
matrix estimators of Minsker [$\mathit{Annals}$ $\mathit{of}$
$\mathit{Statistics}$ $\textbf{46}$(6A) (2018) 2871-2903] and Ke et al.
[$\mathit{Statistical}$ $\mathit{Science}$ $\textbf{34}$(3) (2019) 454-471] to
tame heavy-tailed data. The theoretical results demonstrate that when the
sampling distribution is symmetric innovation with the bounded fourth moment or
asymmetric with the finite $6$-th moment, the statistical error rate of the
final estimator produced by the robust algorithm is similar to that of
sub-Gaussian tails. Extensive numerical trials support the theoretical analysis
and indicate that our algorithm is robust to heavy-tailed data and outliers.
