Person:

Feldman, Benjamin Ezekiel

Bilayer graphene has attracted considerable interest due to the important role played by many-body effects, particularly at low energies. Here we report local compressibility measurements of a suspended graphene bilayer. We find that the energy gaps at filling factors v = 4 do not vanish at low fields, but instead merge into an incompressible region near the charge neutrality point at zero electric and magnetic field. These results indicate the existence of a zero-field ordered state and are consistent with the formation of either an anomalous quantum Hall state or a nematic phase with broken rotational symmetry. At higher fields, we measure the intrinsic energy gaps of broken-symmetry states at v = 0, +/-1 and +/-2, and find that they scale linearly with magnetic field, yet another manifestation of the strong Coulomb interactions in bilayer graphene.

Mono- and bilayer graphene have generated tremendous excitement owing to their unique and potentially useful electronic properties(^1). Suspending single-layer graphene flakes above the substrate({^2}{^,}{^3}) has been shown to greatly improve sample quality, yielding high-mobility devices with little charge inhomogeneity. Here we report the fabrication of suspended bilayer graphene devices with very little disorder. We observe quantum Hall states that are fully quantized at a magnetic field of 0.2 T, as well as broken-symmetry states at intermediate filling factors ν=0, ±1, ±2 and ±3. In the ν=0 state, the devices show extremely high magnetoresistance that scales as magnetic field divided by temperature. This resistance is predominantly affected by the perpendicular component of the applied field, and the extracted energy gap is significantly larger than expected for Zeeman splitting. These findings indicate that the broken-symmetry states arise from many-body interactions and underscore the important part that Coulomb interactions play in bilayer graphene.

Graphene provides a rich platform to study many-body effects, owing to its massless chiral charge carriers and the fourfold degeneracy arising from their spin and valley degrees of freedom. We use a scanning single-electron transistor to measure the local electronic compressibility of suspended graphene, and we observed an unusual pattern of incompressible fractional quantum Hall states that follows the standard composite fermion sequence between filling factors ν = 0 and 1 but involves only even-numerator fractions between ν = 1 and 2. We further investigated this surprising hierarchy by extracting the corresponding energy gaps as a function of the magnetic field. The sequence and relative strengths of the fractional quantum Hall states provide insight into the interplay between electronic correlations and the inherent symmetries of graphene.

The nature of fractional quantum Hall (FQH) states is determined by the interplay between the Coulomb interaction and the symmetries of the system. The unique combination of spin, valley, and orbital degeneracies in bilayer graphene is predicted to produce novel and tunable FQH ground states. Here we present local electronic compressibility measurements of the FQH effect in the lowest Landau level of bilayer graphene. We observe incompressible FQH states at filling factors (\nu = 2p + 2/3) with hints of additional states appearing at (\nu = 2p + 3/5), where p = -2,-1, 0, and 1. This sequence of states breaks particle-hole symmetry and instead obeys a (\nu \rightarrow \nu + 2) symmetry, which highlights the importance of the orbital degeneracy for many-body states in bilayer graphene.

Graphene and its multilayers have attracted considerable interest because their fourfold spin and valley degeneracy enables a rich variety of broken-symmetry states arising from electron-electron interactions, and raises the prospect of controlled phase transitions among them. Here we report local electronic compressibility measurements of ultraclean suspended graphene that reveal a multitude of fractional quantum Hall states surrounding filling factors (\nu =−1/2) and (−1/4). Several of these states exhibit phase transitions that indicate abrupt changes in the underlying order, and we observe many additional oscillations in compressibility as (\nu ) approaches (−1/2), suggesting further changes in spin and/or valley polarization. We use a simple model based on crossing Landau levels of composite fermions with different internal degrees of freedom to explain many qualitative features of the experimental data. Our results add to the diverse array of many-body states observed in graphene and demonstrate substantial control over their order parameters.

In materials systems with flat energy bands and limited disorder, interactions among electrons dominate and can dramatically alter physical behavior. Traditionally, two-dimensional electron gases (2DEGs) have offered excellent platforms to study these effects because the kinetic energy of the electrons is effectively quenched by a perpendicular magnetic field. The recent discovery of graphene, a two-dimensional form of carbon, has opened the door for further exploration into many-body phenomena. Graphene, unlike conventional 2DEGs, has fourfold degenerate electronic states due to its spin and valley degrees of freedom. This thesis describes several experiments that show how these underlying symmetries combine with electron-electron interactions to produce novel and tunable correlated electronic phases of matter.