  Evidence for the singly Cabibbo suppressed decay $\Lambda_c^+\to p\pi^0$ is
reported for the first time with a statistical significance of $3.7\sigma$
based on 6.0 $\mathrm{fb}^{-1}$ of $e^+e^-$ collision data collected at
center-of-mass energies between 4.600 and 4.843 GeV with the BESIII detector at
the BEPCII collider. The absolute branching fraction of $\Lambda_c^+\to p\pi^0$
is measured to be $(1.56^{+0.72}_{-0.58}\pm0.20)\times 10^{-4}$. Combining with
the branching fraction of $\Lambda_c^+\to n\pi^+$, $(6.6\pm1.3)\times10^{-4}$,
the ratio of the branching fractions of $\Lambda_c^+\to n\pi^+$ and
$\Lambda_c^+\to p\pi^0$ is calculated to be $3.2^{+2.2}_{-1.2}$. As an
important input for the theoretical models describing the decay mechanisms of
charmed baryons, our result indicates that the non-factorizable contributions
play an essential role and their interference with the factorizable
contributions should not be significant. In addition, the absolute branching
fraction of $\Lambda_c^+\to p\eta$ is measured to be $(1.63\pm0.31_{\rm
stat}\pm0.11_{\rm syst}) \times10^{-3}$.
