Filling-enforced quantum oscillation phase shift anomaly in few-layer graphene

Quantum oscillations provide a striking visualization of the Fermi surface of metals: Fermi surface size, shape, and Berry phase naturally manifest in quantum oscillation frequency, field-direction dependence, and phase shift respectively. We report on unconventional magneto-transport of ABA-trilayer graphene, a multiband system comprising a (non-trivial) gapped monolayer graphene (MLG)-like band, nested within a large (trivial) bilayer graphene (BLG)-like band. Detailed field and density maps reveal BLG-like Shubnikov-de Hass (SdH) oscillations shifted by an anomalous non-trivial phase that sharply departs from that expected from the constant and trivial (2π) Berry phase of the BLG-like Fermi surface. The anomalous phase shift switches sharply from π to – π as density is tuned from below the MLG-like gap to above it. This originates from a strong filling-enforced constraint between the BLG-like and MLG-like Fermi surfaces, enabling the quantum oscillations of one Fermi surface to inherit the phase shifts of the other co-existing Fermi surface. We expect filling-enforced phases in quantum oscillations to arise generically in multi-Fermi-surface metals, and provide a detailed window to map the rich pattern of carrier filling in multi-band topological materials.