  We present the first measurement of the correlation between the map of the
cosmic microwave background (CMB) lensing potential derived from the
\emph{Planck} nominal mission data and $z\gtrsim 1.5$ galaxies detected by the
\emph{Herschel}-ATLAS (H-ATLAS) survey covering about $600\,\hbox{deg}^2$, i.e.
about 1.4\% of the sky. We reject the hypothesis that there is no correlation
between CMB lensing and galaxy detection at a $20\,\sigma$ significance,
checking the result by performing a number of null tests. The significance of
the detection of the theoretically expected cross-correlation signal is found
to be $10\,\sigma$. The galaxy bias parameter, $b$, derived from a joint
analysis of the cross-power spectrum and of the auto-power spectrum of the
galaxy density contrast is found to be $b=2.80^{+0.12}_{-0.11}$, consistent
with earlier estimates for H-ATLAS galaxies at similar redshifts. On the other
hand, the amplitude of the cross-correlation is found to be a factor $1.62 \pm
0.16$ higher than expected from the standard model and also found by
cross-correlation analyses with other tracers of the large-scale structure. The
enhancement due to lensing magnification can account for only a fraction of the
excess cross-correlation signal. We suggest that part of it may be due to an
incomplete removal of the contamination of the CIB, that includes the H-ATLAS
sources we are cross-correlating with. In any case, the highly significant
detection reported here using a catalog covering only 1.4\% of the sky
demonstrates the potential of CMB lensing correlations with submillimeter
surveys.
