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. Interest in understanding the competing mechanisms at play was reignited recently with the experimental observations of superconductivity and strongly correlated insulating phases in such twisted moiré heterostructures. In this talk, I will first discuss the effect of electron-electron interactions on Dirac fermions. Using a combination of nonperturbative numerical and analytical techniques, I will show that the properties of interacting Dirac fermions are governed by two very different fixed points: a Gross-Neveu phase transition to a Mott insulator controlled mostly by the contact interaction, and a semi-metallic state with a diverging Fermi velocity dependent only on the long-range part of the Coulomb interaction [1]. While the various experimental realizations of Dirac fermions span the crossover between these two regimes, changing the twist angle allows one to controllably tune from one regime to another. In the semi-metallic regime, I will show that there is a universal square-root renormalization of the band anisotropy [2], implying that the Dirac fermions in interacting twisted bilayer graphene are more isotropic than predicted from the non-interacting moiré band theory. Using a Boltzmann-RPA theory, I will argue that for small twist angle, gauge phonons dominate the transport properties [3]. For example, at large twist angle, gauge phonons only dominate over charged impurities only for T>500 K, while close to magic angle, this crossover temperature drops to Tcr5 K. Finally, I provide a perspective on some of the unexplained experimental observations in this system.
References
• 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).
• J. N. Leaw, H.K. Tang, M. Trushin, F. F. Assaad, and S. Adam. “Universal Fermi-surface anisotropy renormalization for interacting Dirac fermions with long-range interactions”, Proceedings of the National Acadmy of Sciences, USA, in press (2019); arXiv:1809.07775.
• 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”, Phys. Rev. B 99 140302 (2019).
• † This work is supported by the Singapore Ministry of Education AcRF grants (MOE2017-T2-1-130, MOE2017-T2-2-140).
About the speaker
Shaffique Adam is currently an Associate Professor, Yale-NUS College and an NRF Fellow. A/Prof Adam is an expert in the theoretical physics of Dirac systems. Within FLEET, he is working on gaining an understanding of the electronic transport and other properties of novel Dirac semimetals, as well as the conventional insulator to topological insulator transition in such systems.