  The tunneling current between independently contacted graphene sheets
separated by boron nitride insulator is calculated. Both dissipative tunneling
transitions, with momentum transfer due to disorder scattering, and
non-dissipative regime of tunneling, which appears due to intersection of
electron and hole branches of energy spectrum, are described. Dependencies of
tunneling current on concentrations in top and bottom graphene layers, which
are governed by the voltages applied through independent contacts and gates,
are considered for the back- and double-gated structures. The current-voltage
characteristics of the back-gated structure are in agreement with the recent
experiment [Science 335, 947 (2012)]. For the double-gated structures, the
resonant dissipative tunneling causes a ten times enhancement of response which
is important for transistor applications.
