Tunable Fermi surface topology and Lifshitz transition in bilayer\n graphene

Bilayer graphene is a highly tunable material: not only can one tune the\nFermi energy using standard gates, as in single-layer graphene, but the band\nstructure can also be modified by external perturbations such as transverse\nelectric fields or strain. We review the theoretical basics of the band\nstructure of bilayer graphene and study the evolution of the band structure\nunder the influence of these two external parameters. We highlight their key\nrole concerning the ease to experimentally probe the presence of a Lifshitz\ntransition, which consists in a change of Fermi contour topology as a function\nof energy close to the edges of the conduction and valence bands. Using a\ndevice geometry that allows the application of exceptionally high displacement\nfields, we then illustrate in detail the way to probe the topology changes\nexperimentally using quantum Hall effect measurements in a gapped bilayer\ngraphene system.\n