R1: We showed how convolutional neural networks can be used to extract highly non-trivial microscopic physics from scanning tunneling microscopy data in graphene moiré systems (Nature Communications 14, 5012), using nematic order in twisted double-bilayer graphene as an example.
R2: In an experimental collaboration, the presence of the superconducting diode effect at zero external magnetic field in a twisted graphene moiré system was demonstrated (Nature Physics 18, 1221-1227). On the theory side, we extended our understanding of this effect by developing a theory (Physical Review Letters 132, 046003) based on a back-action mechanism that can explain, for the first time, the extremely large diode effect efficiency observed. We further showed that the superconducting diode effect does not even require finite magnetization and can also be stabilized by altermagnets (Phys. Rev. B 110, 024503), introducing the “altermagnetic diode effect”.
R3: We proposed the first graphene moiré superlattice setup where the strength of spin orbit coupling can be tuned in situ (Phys. Rev. Lett. 130, 066001). We demonstrated that this can lead to “Möbius Fermi surfaces” with semi-classical trajectories that require two full revolutions to be closed, and with consequences for quantum oscillations and superconducting instabilities (Phys. Rev. B 109, 035159).
R4: We have developed two possible explanations for recent tunneling experiments in the superconducting state in twisted bi- and trilayer graphene: In one explanation (Nature Communications 15, 1713), thermal fluctuations are taken into account which naturally lead to interesting “vestigial” pairing states, yielding spectral functions that are consistent with experiment. In a second explanation (Nature Communications 14, 7134), we ask the question whether similar spectral functions can also be obtained in a mean-field picture and identify a novel purely interband pairing state. In a related work (arXiv:2308.00748) we have proposed a model involving “quadratic Dirac cones” yielding highly non-trivial renormalization-group flows.
R5: Inspired by recent experiments demonstrating the creation of atomically sharp moiré interfaces between oxides with different Bravais lattices and finite twist, we developed the, to the best of our knowledge, first systematic band theory for these novel systems (Phys. Rev. B 110, 125143). We present case studies illustrating the huge potential for band engineering and show that there are novel forms of “geometric magic angles”.
R6: We have further extended our understanding of the correlated physics in Chern bands as they are realized in moiré graphene: (a) in Chern-two bands, we showed that CDW phases are competing with a tetrahedral magnet at half-integer filling and uncovered an exotic emergent symmetry (SciPost Phys. 14, 040); (b) we found a novel guiding principle, which we dub the “three-rule”, for ideal Chern bands with strong repulsion (arXiv:2406.09505); (c) we studied the correlated insulators and competing superconductors in the Chern bands of twisted WSe2 (arXiv:2407.02393).
