Local thermodynamic signatures of interaction-driven topological states in graphene

Abstract

This thesis describes local compressibility measurements in two strongly-interacting topological systems: the nu=1 quantum Hall ferromagnet in monolayer graphene and the Chern insulator states of twisted bilayer graphene. We shed new light on these systems by making use of local chemical potential measurements enabled by scanning single-electron transistor microscopy, which allows us to probe the most pristine, disorder-free parts of the sample on a length scale of approximately 100 nm. This technique provides direct access to the intrinsic properties of the material while minimizing effects due to disorder.

The monolayer graphene nu=1 quantum Hall state is a nearly ideal ferromagnet that, among other remarkable properties, supports all-electrical generation and detection of magnons (spin waves). Such magnons can in principle be exceptionally long-lived due to the absence of nuclear spins and spin-orbit coupling. The system is therefore ideal for simulating aspects of bosonic ensembles. To study the interplay of the neutral and charged degrees of freedom, we study the behavior of the gap of the nu=1 incompressible state as magnons are injected into the system. Remarkably, we observe that introducing magnons results in a reduction of the gap by as much as 20%. This effect is argued to stem from the equilibration between magnons and skyrmionic charged excitations: as magnons are injected, the system favors forming larger skyrmions, which carry with them a reduced exchanged penalty compared to bare quasiparticles and holes. This insight enables us to extract a complete thermodynamic description of the system, including the magnon chemical potential, density, and the number of spins flipped per quasiparticle. These results demonstrate a new method for accessing the thermodynamics of otherwise difficult-to-study bosonic systems and may offer a route toward observing spin superfluidity in the nu=0 state of monolayer graphene.

Magic-angle twisted bilayer graphene, like monolayer graphene in the quantum Hall regime, is a topological strongly-interacting system; unlike monolayer graphene quantum Hall states, however, the topological bands of twisted bilayer graphene are intrinsic and do not require application of an out-of-plane magnetic field. Our local compressibility measurements enable us to uncover a sequence of Chern insulators that we explain in terms of a translation-symmetry breaking mechanism enabled by the peculiar Berry curvature distribution in magic-angle twisted bilayer graphene. Most remarkably, we observe new incompressible states at fractional filling of the Chern bands. These states, termed fractional Chern insulators, are analogues of fractional quantum Hall states that do not require an underlying Landau level structure and emerge from a close competition with doped charge-density waves at moderate magnetic fields. Such states may be of great interest for future applications to topological quantum computing.