Magic-angle twisted bilayer graphene hosts two distinct electronic species

During the mid-20th century, the idea of a one-atom-thick layer of graphite was theorized. The term “graphene” was introduced some years later, in 1986, by chemists Hanns-Peter Boehm, Ralph Setton and Eberhard Stumpp. Once single graphene layers were successfully produced, scientists noticed their remarkable properties: they are flexible, light yet strong, excellent thermal and electrical conductors, and host a myriad of intriguing physical phenomena.

However, it turns out that two layers of graphene can create an even more fascinating system. That became evident in March of 2018, when an international team led by Pablo Jarillo-Herrero from MIT reported the discovery of superconductivity after stacking two layers of graphene on top of each other with a twist angle of approximately 1.1 . At this very specific ‘magic angle’, the electronic properties change so dramatically that exotic physical phenomena – like the discovered superconductivity– emerge.

Despite the enormous research effort around magic-angle twisted bilayer graphene (MATBG), many open questions remain. One of them concerns its energy band structure. Normally, in a solid, electrons can move through a range of energy bands, and the curvature of these bands determines how fast the electrons can move—their effective mass. But in MATBG, some of the bands are nearly flat. What are the electrons in the flat bands like? How do they behave, and what are the consequences of such behaviors?

Now, ICFO researchers Dr. Rafael Luque Merino, Dr. Jaime Díez-Mérida (now member of the STM on 2D Quantum Materials group at ICFO), Andrés Díez-Carlón, Dr. Paul Seifert, led by the former ICFO Professor Dmitri K. Efetov, now Professor at Ludwig-Maximilians-Universität and the Munich Center for Quantum Science and Technology (MCQST), together with other research institutions, have provided experimental evidence of the coexistence of two electronic ‘species’ in the flat bands of MATBG. “This had been hinted at experimentally before, but lacked direct evidence, which we have provided for the first time,” shares Dr. Rafael Luque Merino, first author of the article.

One of the species corresponds to itinerant electrons, similar to the ‘usual’ free electrons. Such electrons can move across the material, carrying charge and heat. Due to their high mobility, and low effective mass, they are sometimes referred to as ‘light carriers’. The other species resides in highly localized orbitals and interact very strongly between them, which causes a drastic reduction of their mobility. Consequently, these ‘heavy carriers’ do not contribute significantly to charge and heat transport.

Researchers recorded an unusual thermoelectric response

The interplay between heavy and light carriers, which have very different properties, gave rise to an unusual thermoelectric response. To record it, the researchers used a focused laser beam to locally heat the electrons in the MATBG. By tuning the experimental setup appropriately, they managed to ‘direct’ the heat gradient that the hot electrons followed. As the electrons carry charge, this naturally generated a voltage, that is, a thermoelectric signal. “One might expect that the overall thermoelectric response coming from all the electrons would cancel out at specific fillings of the flat bands.” said Rafael. “But that is not the case. It turns out that, at those specific fillings, heavy carriers are incredibly localized and do not contribute to the thermoelectric signal. This happens due to their localized and strongly-interacting nature.”

The proposed method, based on thermoelectric measurements, served as a powerful tool to probe the asymmetry in the properties of the flat-band electrons. Since the presence of strong interactions between electrons has long been acknowledged as the underlying cause of many correlated physics effects, the technique could thus be applied to many other correlated phases that appear in twisted 2D materials.

Moreover, the team observed that the system behaved differently depending on the temperature. In particular, at low (cryogenic) temperatures, light carriers dominated the response. But, surprisingly, at higher temperatures, the roles were reversed. “We found that these results can be explained naturally in this scenario of two electronic species, through the so-called Topological Heavy Fermion model for twisted bilayer graphene,” says Dr. Luque Merino. Within this model, put forward by Andrei Bernevig and Zhi-Da Song, both the low- and high-temperature thermoelectricity could be understood quite elegantly. “After our discovery, I think more and more people will explore this ‘heavy fermion’ framework to model the properties of twisted graphene, hopefully shedding more light on these intriguing materials.”

Reference:

Merino, R.L., Călugăru, D., Hu, H. et al. Interplay between light and heavy electron bands in magic-angle twisted bilayer graphene. Nat. Phys. (2025).

DOI: https://doi.org/10.1038/s41567-025-02912-x

Acknowledgements:

D.C. acknowledges the hospitality of the Donostia International Physics Center, at which this work was carried out. B.A.B. was supported by DOE grant number DE-SC0016239. D.C. was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 101020833) and by Simons Investigator grant number 404513, the Gordon and Betty Moore Foundation through grant number GBMF8685 towards the Princeton theory programme, the Gordon and Betty Moore Foundation’s EPiQS Initiative (grant number GBMF11070), the Office of Naval Research (ONR grant number N00014-20-1-2303), the Global Collaborative Network Grant at Princeton University, BSF Israel US foundation number 2018226 and NSF-MERSEC (grant number MERSEC DMR 2011750). D.C. also gratefully acknowledges the support provided by the Leverhulme Trust. H.H. was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 101020833) and the Schmidt Fund Grant. P.S. acknowledges support from the Alexander von-Humboldt Foundation and the German Federal Ministry for Education and Research through the Feodor-Lynen programme. J.D.-M. acknowledges support from the INPhINIT ‘la Caixa’ Foundation (ID 100010434) fellowship programme (grant number LCF/BQ/DI19/11730021). D.K.E. acknowledges funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 852927) and the German Research Foundation (DFG) under the priority programme SPP2244 (project number 535146365). K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan (grant number JPMXP0112101001), and JSPS KAKENHI (grant numbers 19H05790, 20H00354 and 21H05233).