Ho-Kin Tang and Jia Ning Leaw
Fri, 02/12/2016 – 11:30am
S16 Level 6 – Theory conference room
The electronic properties of graphene have been extensively studied in the past decade. However, there is still ongoing debate on the role of the electron-electron interactions in graphene. Experimentally, a significant enhancement of the Fermi velocity has been observed. In this work, we adapt the quantum Monte Carlo method to graphene with long range Coulomb interaction. We compute the Fermi velocity of this system’s low-energy excitations and find that its enhancement depends on the distance to the phase transition: away from the Mott insulator phase transition the Fermi velocity is logarithmically enhanced as we approach the Dirac point due to long-range part of the Coulomb potential; close to the phase transition, the Fermi velocity enhancement is suppressed by short- range part of the potential. Interestingly, we find that realistic graphene samples are typically located in an intermediate region where long- and short-range interactions compete.
Besides studying the renormalization of the Fermi velocity, we also look at the Mott insulator phase transition. This phase transition opens a gap in graphene band structure, which may be relevant for its application on low power electronic devices. In the second part of this talk, we will discuss two different Mott insulating phases – the charge- density -wave (CDW) phase and the spin-density- wave (SDW) phase. We will show that the Gross-Neveu phase transition, which is usually considered in the literature, is the CDW phase transition. We will also consider the Gross-Neveu model with spin, and show how the SDW phase transition is different from the CDW phase transition.
 Elias, D. C., et al. ‘Dirac cones reshaped by interaction effects in suspended graphene.’ Nature Physics 7.9 (2011): 701-704.