  Fermi surface topology plays an important role in determining the electronic
properties of metals. In bulk metals, the Fermi energy is not easily tunable at
the energy scale needed for reaching conditions for the Lifshitz transition - a
singular point in the band structure where the connectivity of the Fermi
surface changes. Bilayer graphene is a unique system where both Fermi energy
and the low-energy electron dispersion can be tuned using the interplay between
trigonal warping and a band gap opened by a transverse electric field. Here, we
drive the Lifshitz transition to experimentally controllable carrier densities
by applying large transverse electric fields through a h-BN-encapsulated
bilayer graphene structure, and detect it by measuring the degeneracies of
Landau levels. These degeneracies are revealed by filling factor -3 and -6
quantum Hall effect states of holes at low magnetic fields reflecting the
existence of three maxima on the top of the valence band dispersion. At high
magnetic fields all integer quantum Hall states are observed, indicating that
deeper in the valence band the constant energy contours are singly-connected.
The fact that we observe ferromagnetic quantum Hall states at odd-integer
filling factors testifies to the high quality of our sample, and this enables
us to identify several phase transitions between correlated quantum Hall states
at intermediate magnetic fields, in agreement with the calculated evolution of
the Landau level spectrum.
