Studying the broken symmetry states of Bernal-stacked bilayer graphene in a magnetic field by scanning tunneling microscope

Bernal-stacked bilayer graphene forms eight-fold degenerate lowest Landau levels with valley, spin and orbital degree of freedoms under a magnetic field. The Landau level degeneracy can be lifted by electron-electron interactions and leads to a rich set of symmetry-breaking ground states. We use a dilution refrigerator scanning tunneling microscope (STM) to study the ground states of a back-gated bilayer graphene sample under high magnetic field. With a combination of gate-dependent spectroscopy measurement and real-space imaging of the wavefunctions, we study the symmetry-breaking ground states of the lowest Landau level at each integer fillings. Our study reveals how the electron-electron interactions and external field tune the ground state of integer quantum Hall states in bilayer graphene. This research also paves the way for studying fractional quantum Hall states in bilayer graphene with STM.