  This paper presents a search for massive charged long-lived particles
produced in pp collisions at $\sqrt{s}=$ 13 TeV at the LHC using the ATLAS
experiment. The dataset used corresponds to an integrated luminosity of 3.2
fb$^{-1}$. Many extensions of the Standard Model predict the existence of
massive charged long-lived particles, such as $R$-hadrons. These massive
particles are expected to be produced with a velocity significantly below the
speed of light, and therefore to have a specific ionization higher than any
Standard Model particle of unit charge at high momenta. The Pixel subsystem of
the ATLAS detector is used to measure the ionization energy loss of
reconstructed charged particles and to search for such highly ionizing
particles. The search presented here has much greater sensitivity than a
similar search performed using the ATLAS detector in the $\sqrt{s}=$ 8 TeV
dataset, thanks to the increase in expected signal cross-section due to the
higher center-of-mass energy of collisions, to an upgraded detector with a new
silicon layer close to the interaction point, and to analysis improvements. No
significant deviation from Standard Model background expectations is observed,
and lifetime-dependent upper limits on $R$-hadron production cross-sections and
masses are set. Gluino $R$-hadrons with lifetimes above 0.4 ns and decaying to
$q\bar{q}$ plus a 100 GeV neutralino are excluded at the 95% confidence level,
with lower mass limit ranging between 740 GeV and 1590 GeV. In the case of
stable $R$-hadrons the lower mass limit at the 95% confidence level is 1570
GeV.
