  Cryogenic field-effect transistors (FETs) offer great potential for a wide
range of applications, the most notable example being classical control
electronics for quantum information processors. In the latter context, on-chip
FETs with low power consumption are a crucial requirement. This, in turn,
requires operating voltages in the millivolt range, which are only achievable
in devices with ultra-steep subthreshold slopes. However, in conventional
cryogenic metal-oxide-semiconductor (MOS)FETs based on bulk material, the
experimentally achieved inverse subthreshold slopes saturate around a few
mV/dec due to disorder and charged defects at the MOS interface. FETs based on
two-dimensional materials offer a promising alternative. Here, we show that
FETs based on Bernal stacked bilayer graphene encapsulated in hexagonal boron
nitride and graphite gates exhibit inverse subthreshold slopes of down to 250
${\mu}$V/dec at 0.1 K, approaching the Boltzmann limit. This result indicates
an effective suppression of band tailing in van-der-Waals heterostructures
without bulk interfaces, leading to superior device performance at cryogenic
temperature.
