Large Landau level splitting with tunable one-dimensional graphene superlattice probed by magneto capacitance measurements

The unique zero energy Landau Level of graphene has a particle-hole symmetry in the bulk, which is lifted at the boundary leading to a splitting into two chiral edge modes. It has long been theoretically predicted that the splitting of the zero-energy Landau level inside the {\it bulk} can lead to many interesting physics, such as quantum spin Hall effect, Dirac like singular points of the chiral edge modes, and others. However, so far the obtained splitting with high-magnetic field even on a hBN substrate are not amenable to experimental detection, and functionality. Guided by theoretical calculations, here we produce a large gap zero-energy Landau level splitting ($\sim$ 150 meV) with the usage of a one-dimensional (1D) superlattice potential. We have created tunable 1D superlattice in a hBN encapsulated graphene device using an array of metal gates with a period of $\sim$ 100 nm. The Landau level spectrum is visualized by measuring magneto capacitance spectroscopy. We monitor the splitting of the zeroth Landau level as a function of superlattice potential. The observed splitting energy is an order higher in magnitude compared to the previous studies of splitting due to the symmetry breaking in pristine graphene. The origin of such large Landau level spitting in 1D potential is explained with a degenerate perturbation theory. We find that owing to the periodic potential, the Landau level becomes dispersive, and acquires sharp peaks at the tunable band edges. Our study will pave the way to create the tunable 1D periodic structure for multi-functionalization and device application like graphene electronic circuits from appropriately engineered periodic patterns in near future.