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.
@article{arxiv.2412.18000,
title = {Entropy spectroscopy of a bilayer graphene quantum dot},
author = {Christoph Adam and Hadrien Duprez and Natalie Lehmann and Antoni Yglesias and Artem Olegovich Denisov and Solenn Cances and Max Josef Ruckriegel and Michele Masseroni and Chuyao Tong and Wei Wister Huang and David Kealhofer and Rebekka Garreis and Kenji Watanabe and Takashi Taniguchi and Klaus Ensslin and Thomas Ihn},
journal= {arXiv preprint arXiv:2412.18000},
year = {2026}
}