SFB Colloquium

When the relative rotation between two sheets of graphene is set to be close to special angles (referred to in the literature as “magic angles”), the low-energy effective theory features Dirac fermions with very flat bands.  While the role of disorder [1] and electron-electron interactions [2] for the Dirac fermions in monolayer graphene is now well-established, the properties of these Dirac fermions in twisted bilayer graphene can be very different.  In this talk we discuss three recent results showcasing how the Dirac fermions in twisted bilayer graphene is different from those in monolayer graphene.  First, we show using a Boltzmann-RPA theory that for most of the experimental regime, gauge phonons dominate the transport [3].  For monolayer graphene, gauge phonons only dominate over charged impurities only for T>500 K, while for twisted graphene close to magic angle, this crossover temperature drops to T_cr∼5K.  This difference is because although gauge phonons couple to current, they do not induce charge and are therefore unscreened by the large density of states close to magic angle.   Second, starting from a real-space cluster interaction, and using a mean-field analysis, we propose a strong-coupling t-J-D model where fluctuations of the anti-ferromagnetic order in the conducting phase mediates superconducting paring [4].  The properties of this model can be solved self-consistently to reveal chiral d-wave superconductivity and Majorana edge modes.  Third, we show that in the presence of long-range Coulomb interactions, there is a universal square-root renormalization [5] of the band anisotropy, implying that the Dirac fermions in interacting twisted bilayer graphene are more isotropic than what would be predicted from the non-interacting moiré band theory.   

References

1. S. Das Sarma, S. Adam, E. H. Hwang, and E. Rossi, “Electronic transport in two dimensional graphene”, Rev. Mod. Phys. 83, 407 (2011).
2. H.K. Tang, J.N. Leaw, J.N.B. Rodrigues, I. F. Herbut, P. Sengupta, F.F. Assaad, and S. Adam, " The role of electron-electron interactions in two-dimensional Dirac fermions", Science 361 570 (2018).
3. I. Yudhistira, N. Chakraborty, G. Sharma, D.Y.H. Ho, E. Laksono, O.P. Sushkov, G. Vignale and S. Adam, “Gauge phonon dominated resistivity in twisted bilayer graphene near magic angle”, arXiv:1902.01405.
4. X. Gu, C. Chen, J.N. Leaw, E. Laksono, V.M. Pereira, G. Vignale, and S. Adam, “Antiferromagnetism and chiral d-wave superconductivity from an effective t-J-D model for twisted bilayer graphene”, arXiv:1902.00029.
5.  J. N. Leaw, H.K. Tang, M. Trushin, F. F. Assaad, S. Das Sarma and S. Adam.  “Universal Fermi-surface anisotropy renormalization for interacting Dirac fermions with long-range interactions”, arXiv:1809.07775.