About ten years ago, a new electronic material appeared – notable not only for its ease of preparation and theoretical simplicity, but also by its promise for future electronic devices. Single monatomic sheets of carbon, known as graphene, are described as weakly interacting massless Dirac fermions and in many ways, are a textbook system to test physical models. In this talk, I will begin by briefly reviewing the theory for graphene at the Dirac point where competing effects of disorder, electron-electron interactions, and quantum interference conspire together to give a surprisingly robust state whose properties can be described using a weakly-interacting semi-classical picture [1]. Motivated by some recent experiments in ultra-clean graphene, we use a combination of nonperturbative numerical and analytical techniques that incorporate both the contact and long-range parts of the Coulomb interaction to address the role of electron-electron interactions at the Dirac point in the absence of disorder. We show that without strain, graphene remains metallic. But that a rather large – but experimentally realistic – uniform and isotropic strain provides a promising route to make graphene an antiferromagnetic Mott insulator [2]. Finally, we address the interaction enhancement of the Fermi velocity. Using quantum Monte-Carlo simulations with a long-range Coulomb tail, we identify the two previously discussed regimes : a Gross-Neveu transition to a strongly correlated Mott insulator, and a semi-metallic state with a logarithmically diverging Fermi velocity accurately described by the random phase approximation. Most interestingly, experimental realizations of Dirac fermions span the crossover between these two regimes providing the physical mechanism that masks this velocity divergence. We explain several long-standing mysteries including why the observed Fermi velocity in graphene is consistently about 20 percent larger than the best values calculated using ab initio and why graphene on different substrates show different behavior [3].

[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. Tang, E. Laksono, J.N.B. Rodrigues, P. Sengupta, F.F. Assaad, and S. Adam, "Interaction driven metal-insulator transition in strained graphene", Phys. Rev. Lett. 115, 186602 (2015) ;

[3] H. 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 graphene", Submitted (2017).

Contact : Shaffique Adam