Moiré superlattices produced by the mismatch between two-dimensional (2D) atomic crystals have been an exciting platform for new physics [1–3] since the invention of the technique for manipulating such 2D layers [4]. These superlattices give clean access to a length scale tens or hundreds of times larger than that of the atomic lattice, which when combined with electrostatic gating, give access to moiré bands that can be completely filled or emptied of electrons at the press of a button on a power supply. This simple but powerful idea recently led to the discovery of superconductivity and correlated insulators in magic-angle twisted bilayer graphene (MATBG) [5,6], where two graphene sheets rotated ~1° relative to each other produce a set of eight low-energy flat bands near charge neutrality [7]. Correlated insulators occur at integer fillings of these flat bands, while superconductivity can occur at partial fillings.

In March 2018, Pablo Jarillo-Herrero from MIT came to Princeton to give a talk about his group’s discovery of superconductivity in MATBG. At the time, our team (Kevin Nuckolls, Myungchul Oh, and myself) in Ali Yazdani’s lab at Princeton was building a millikelvin-temperature scanning tunneling microscope (STM) [8]. We were immediately interested in using our ultra-low-temperature STM for investigating the superconducting order parameter, which would provide key insight into the mechanism driving the superconductivity, but that would have to wait until construction was completed. In the meantime, four major papers [9–12] (one of which was from a separate team in the Yazdani lab) would report on STM studies of MATBG above the superconducting transition temperature. These papers described numerous ways strong electron-electron interactions influence the electronic properties of MATBG: the appearance of a gap-like feature [9,10,12], increased separation of the flat bands at charge neutrality [9–11], broadening of the flat bands due to charge fluctuations [9–11], and broken rotational symmetry [9,10,12].

Upon completion of the construction of our STM in March 2019 [8], our team planned to quickly reproduce the previous papers’ findings at higher temperatures (T ≈ 6 K) and then immediately cool down to superconducting temperatures. We made a modification to the experiment that I believe was important: we reduced the effect of the tip as a top gate (“tip-induced band bending”) as much as possible by using a carefully prepared copper-coated tungsten tip (since copper and tungsten have work functions that are somewhat similar to graphene). This, along with improvements in the sample fabrication process, allowed us to very clearly observe a cascade of transitions between the correlated electronic states of MATBG [13]. It turned out that there was much about the electronic properties of MATBG that we still didn’t understand at higher temperatures.

We found a set of dispersing peaks in spectroscopy that we interpreted as the interaction-induced separation of MATBG’s spin/valley degenerate flat bands into multiple sub-bands. From the energies of these peaks, we were able to extract a measure of the on-site Coulomb repulsion strength between electrons, which is believed to control the ground-state properties of MATBG. Furthermore, we indirectly measured the system’s chemical potential, which we found to oscillate as a function of carrier density. The shape of the chemical potential appears to abruptly reset at each integer filling of the flat bands. Our work provides new insight into the high-temperature parent phase of MATBG that precedes superconductivity and insulating behavior.

Please take a look at our paper at https://doi.org/10.1038/s41586-020-2339-0. While writing this paper, we became aware of complementary work from Shahal Ilani’s group at Weizmann Institute that also uncovered this cascade of transitions in MATBG [14]. They performed compressibility measurements with a single-electron transistor, instead of the energy-resolved tunneling spectroscopy that we used. Although we did not share preprints, we coordinated simultaneous submissions to Nature and the arXiv.

References:

1. Dean, C. R. et al. Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices. Nature 497, 598–602 (2013).
2. Ponomarenko, L. A. et al. Cloning of Dirac fermions in graphene superlattices. Nature 497, 594–7 (2013).
3. Hunt, B. et al. Massive dirac fermions and hofstadter butterfly in a van der Waals heterostructure. Science 340, 1427–1430 (2013).
4. Dean, C. R. et al. Boron nitride substrates for high-quality graphene electronics. Nat. Nanotechnol. 5, 722–726 (2010).
5. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).
6. Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).
7. Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl. Acad. Sci. U. S. A. 108, 12233–12237 (2011).
8. Wong, D. et al. A modular ultra-high vacuum millikelvin scanning tunneling microscope. Rev. Sci. Instrum. 91, 023703 (2020).
9. Kerelsky, A. et al. Maximized electron interactions at the magic angle in twisted bilayer graphene. Nature 572, 95–100 (2019).
10. Choi, Y. et al. Electronic correlations in twisted bilayer graphene near the magic angle. Nat. Phys. 15, 1174–1180 (2019).
11. Xie, Y. et al. Spectroscopic signatures of many-body correlations in magic-angle twisted bilayer graphene. Nature 572, 101–105 (2019).
12. Jiang, Y. et al. Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene. Nature 573, 91–95 (2019).
13. Wong, D. et al. Cascade of electronic transitions in magic-angle twisted bilayer graphene. Nature 582, 198–202 (2020).
14. Zondiner, U. et al. Cascade of phase transitions and Dirac revivals in magic-angle graphene. Nature 582, 203–208 (2020).