We demonstrate a method to determine energy level degeneracies using non-equilibrium electronic transport through voltage-biased quantum dots. We establish the general validity of this approach using single and double quantum dots in bilayer graphene and GaAs. Unlike established methods based on entropy measurements or time-resolved tunneling statistics, our approach achieves comparable precision without requiring calibrated electron heating or real-time charge detection. We resolve the predicted symmetric shell structure in bilayer graphene quantum dots, including a singlet ground state at half filling and the ground state degeneracies of the first 13 carriers. Extending the method to double quantum dots, we observe degeneracy doubling associated with bonding and antibonding orbitals for a single carrier and a fourfold degeneracy for two carriers, previously inaccessible with existing techniques. These results establish a conceptually general and experimentally straightforward approach for probing energy level degeneracies in complex quantum systems.
@article{arxiv.2603.00762,
title = {Non-equilibrium transport reveals energy level degeneracy},
author = {Artem O. Denisov and Christoph Adam and Hadrien Duprez and Jessica Richter and Zhuoyu Chen and Andrea Hofmann and Kenji Watanabe and Takashi Taniguchi and Thomas Ihn and Klaus Ensslin},
journal= {arXiv preprint arXiv:2603.00762},
year = {2026}
}