Local Compressibility Measurements of Broken-Symmetry States in Suspended Bilayer Graphene

We have performed local compressibility measurements of a suspended bilayer graphene flake using a scanning single electron transistor. In addition to the expected energy gaps at filling factors \textit{$\nu $} = $\pm $4 and $\pm $8, we observe Landau levels corresponding to broken-symmetry states at \textit{$\nu $} = 0 and $\pm $2. The width of the incompressible region at each filling factor is independent of magnetic field $B$, and is on the order of 10$^{10}$ cm$^{-2}$, indicative of the low disorder in suspended devices. Remarkably, the \textit{$\nu $} = $\pm $4 gaps even persist below 50 mT. The measured energy gap between each Landau levels scales linearly with $B,$ with a magnitude of approximately 4 meV/T for \textit{$\nu $} = $\pm $4 and approximately 1 meV/T for the broken-symmetry states. In addition, the flakes exhibit decreased compressibility near the charge neutrality point at $B$ = 0. Scanning the tip position reveals density variations consistent with estimates from transport and from the width of the incompressible regions around each Landau level.