  High carrier mobilities play a fundamental role for high-frequency
electronics, integrated optoelectronics as well as for sensor and spintronic
applications, where device performance is directly linked to the magnitude of
the carrier mobility. Van der Waals heterostructures formed by graphene and
hexagonal boron nitride (hBN) already outperform all known materials in terms
of room temperature mobility. Here, we show that the mobility of today's best
graphene/hBN devices can be surpassed by more than a factor of three by
heterostructures formed by tungsten diselenide (WSe$_2$), graphene and hBN,
which can have mobilities as high as 350,000 cm$^2$/(Vs) at room temperature,
and resistivities as low as 15 Ohm. The resistivity of these devices shows a
much weaker temperature dependence than the one of graphene on any other known
substrate. The origin of this behaviour points to modified acoustic phonon
bands in graphene and questions our understanding of electron-phonon scattering
in van der Waals heterostructures.
