Landau level diagram and the continuous rotational symmetry breaking in trilayer graphene

The sequence of the zeroth Landau levels (LLs) between filling factors $\nu$=-6 to 6 in ABA-stacked trilayer graphene (TLG) is unknown because it depends sensitively on the non-uniform charge distribution on the three layers of ABA-stacked TLG. Using the sensitivity of quantum Hall data on the electric field and magnetic field, in an ultraclean ABA-stacked TLG sample, we quantitatively estimate the non-uniformity of the electric field and determine the sequence of the zeroth LLs. We also observe anticrossings between some LLs differing by 3 in LL index, which result from the breaking of the continuous rotational to \textit{C}$_3$ symmetry by the trigonal warping.