Inter-subband Landau level couplings induced by in-plane magnetic fields in trilayer graphene

We observed broken-symmetry quantum Hall effects and level crossings between spin- and valley- resolved Landau levels (LLs) in Bernal stacked trilayer graphene. When the magnetic field was tilted with respect to sample normal from \(0^{\circ}\) to \(66^\circ\), the LL crossings formed at intersections of zeroth and second LLs from monolayer-graphene-like and bilayer-graphene-like subbands, respectively, exhibited a sequence of transitions. The results indicate the LLs from different subbands are coupled by in-plane magnetic fields (\(B_{\parallel}\)), which was explained by developing the tight-binding model Hamiltonian of trilayer graphene under \(B_{\parallel}\).