Controlling particle-hole symmetry of fractional quantum hall states in trilayer graphene

We present a detailed experimental study of the particle-hole symmetry (PHS) of the fractional quantum Hall (FQH) states about half filling in a multiband system. Specifically, we focus on the lowest Landau level of the monolayer-like band of Bernal stacked trilayer graphene (TLG). In pristine TLG, the excitation energy gaps, Land\'e g-factor, effective mass, and disorder broadening of the odd-denominator FQH states are identical to their hole-conjugate counterpart. This precise PH symmetry stems from the lattice mirror symmetry that precludes Landau-level mixing. Introducing a non-zero displacement field \(D\) disrupts this mirror symmetry, facilitating the hybridization between the monolayer-like and bilayer-like Landau levels. This inter-band coupling enhances the Landau level mixing factor $\eta$ and activates three-body interactions -- both of which explicitly break the PHS of FQHs. As a result, conventional FQHs are completely destabilized, offering a route to engineer symmetry breaking of FQHs in a controlled way. We establish that the PHS breaking in TLG is of extrinsic origin and is fundamentally distinct from the intrinsic, interaction-driven symmetry breaking observed in the lowest Landau levels of single-layer and bilayer graphene.