Tunable band inversion in trilayer graphene

Displacement field control of elecronic bands in low-dimensional systems is a promising route toward engineering emergent quantum phases. Here, we report displacement-field-induced band inversion and modulation of the Berry phase of low-energy quasiparticles in high-mobility Bernal-stacked trilayer graphene (TLG). Using quantum oscillations, we track the evolution of the Fermi surface and topological properties of Dirac-like ``gully'' bands that emerge under a finite interlayer potential. We observe a striking sequence of transitions: at low displacement field $D$, the gullies are characterized by a Berry phase of $2\ensuremath{\pi}$ and large effective mass, indicating massive fermions. As $D$ increases, the Berry phase abruptly shifts to $\ensuremath{\pi}$ and the effective mass reaches a minimum, signaling the onset of massless Dirac behavior. At higher $D$, the Berry phase returns to $2\ensuremath{\pi}$, and the effective mass increases again, consistent with a band inversion. These findings demonstrate a rare, reversible topological phase transition---massive $\ensuremath{\rightarrow}$ massless $\ensuremath{\rightarrow}$ massive---driven entirely by an external displacement field. Despite robust theoretical predictions [Phys. Rev. B 87, 085424 (2013), Phys. Rev. B 87, 115422 (2013), and Phys. Rev. B 101, 245411 (2020)], this evolution of the band topology had escaped experimental detection. Our results establish TLG as a tunable platform for nanoscale control of band topology. They establish a means to tune between massive and Dirac-like dispersions dynamically providing a foundation for exploring field-switchable topological phenomena in layered two-dimensional systems.