  Using a data set of electron-positron collisions corresponding to an
integrated luminosity of ${\rm 2.93~fb^{-1}}$ taken with the BESIII detector at
a center-of-mass energy of 3.773 GeV, a search for the baryon ($B$) and lepton
($L$) number violating decays $D^{\pm}\to n(\bar{n})e^{\pm}$ is performed. No
signal is observed and the upper limits on the branching fractions at the
$90\%$ confidence level are set to be $1.43\times10^{-5}$ for the decays
$D^{+(-)}\to \bar{n}(n)e^{+(-)}$ with $\Delta|B-L|=0$, and $2.91\times10^{-5}$
for the decays $D^{+(-)}\to n(\bar{n})e^{+(-)}$ with $\Delta|B-L|=2$ , where
$\Delta|B-L|$ denotes the change in the difference between baryon and lepton
numbers.
