Symmetry breaking and fractionalization beyond the zero Landau level of graphene

• Applicant: Professor Dr. Inti Sodemann Villadiego
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 518372354

In the presence of perpendicular magnetic fields graphene displays a fascinatingly rich set of states in the quantum Hall regime, featuring an intricate interplay of symmetry breaking, topology and fractionalization of its valley and spin degrees of freedom. Despite our substantial progress in understanding these states many puzzles and un-explored directions remain. For example, in the zero Landau level recent STM experiments have revealed valence bond solid and charge density wave states under the conditions where earlier experiments reported evidence for anti-ferromagnets. Experiments in higher Landau levels have displayed many other puzzles, such as the presence of bubble states in the second Landau level but with no concomitant evidence of stripes states. And, amazingly, also evidence of even denominator fractional quantum Hall states near partial half-filling of the third Landau level. The precise nature of these states and their valley/spin order remains to be understood. Because of its exposed character graphene offers to us an unprecedented opportunity to directly image these states with local probes. Additionally bilayer graphene offers to us a remarkable opportunity to realize a dramatically new class of integer and fractional quantum Hall states without inversion symmetry that have never been realized experimentally before. This arises because of its near degeneracy of orbitals with N=0 and N=1 cyclotron character. Our project aims to develop the theory of these states in monolayer and bilayer graphene and on understanding their physical properties that can aid their experimental realization and detection.

• DFG Programme: Research Grants