  High mobility is a crucial requirement for a large variety of electronic
device applications. The state-of-the-art for high quality graphene devices is
based on heterostructures made with graphene encapsulated in $>80\,$nm-thick
flakes of hexagonal boron nitride (hBN). Unfortunately, scaling up multilayer
hBN while precisely controlling the number of layers remains an elusive
challenge, resulting in a rough material unable to enhance the mobility of
graphene. This leads to the pursuit of alternative, scalable materials, which
can be simultaneously used as substrate and encapsulant for graphene. Tungsten
disulfide (WS$_2$) is a transition metal dichalcogenide, which was successfully
grown in large ($\sim$mm-size) multi-layers by chemical vapour deposition.
However, the resistance \textit{vs} gate voltage characteristics when gating
graphene through WS$_2$ exhibit largely hysteretic shifts of the charge
neutrality point (CNP) in the order of $\Delta n\sim$2.6$\cdot$10$^{11}$
cm$^{-2}$, hindering the use of WS$_2$ as a reliable encapsulant. The
hysteresis originates due to the charge traps from sulfur vacancies present in
WS$_2$. In this work, we report for the first time the use of WS$_2$ as a
substrate and the overcoming of hysteresis issues by chemically treating WS$_2$
with a super-acid, which passivates these vacancies and strips the surface from
contaminants. The hysteresis is significantly reduced below the noise level by
at least a factor five (to $\Delta n<$5$\cdot$10$^{10}$ cm$^{-2}$) and,
simultaneously, the room-temperature mobility of WS$_2$-encapsulated graphene
is as high as $\sim$6.2$\cdot$10$^{4}$ cm$^{-2}$V$^{-1}$s$^{-1}$ at a carrier
density $n$ $\sim$1$\cdot$ 10$^{12}$ cm$^{-2}$. Our results promote WS$_2$ to a
valid alternative to hBN as encapsulant for high-performance graphene devices.
