Entropy spectroscopy of a bilayer graphene quantum dot

We measure the entropy change of charge transitions in an electrostatically defined quantum dot in bilayer graphene. Entropy provides insights into the equilibrium thermodynamic properties of both ground and excited states beyond transport measurements. For the one-carrier regime, the obtained entropy shows that the ground state has a two-fold degeneracy lifted by an out-of-plane magnetic field. This observation is in agreement with previous direct transport measurements and confirms the applicability of this novel method. For the two-carrier regime, the extracted entropy indicates a non-degenerate ground state at zero magnetic field, contrary to previous studies suggesting a three-fold degeneracy. We attribute the degeneracy lifting to the effect of Kane-Mele type spin--orbit interaction on the two-carrier ground state, which has not been observed before. Our work demonstrates the validity and efficacy of entropy measurements as a unique, supplementary experimental tool to investigate the degeneracy of the ground state in quantum devices build in materials such as graphene. This technique, applied to exotic systems with fractional ground state entropies, will be a powerful tool in the study of quantum matter.