The role of electron-electron interactions in two-dimensional Dirac fermions: from realistic to toy models.*

In this talk I will review a body of quantum Monte Carlo results aimed at exploring the effect of correlations in Dirac fermions. Emphasis will be placed on the role of the long-ranged Coulomb repulsion at weak coupling and close to the Gross-Neveu transition [1]. I will then move on to more exotic interactions that allow for the dynamical generation of quantum spin Hall states. We will see that Skyrmion defects of the quantum spin Hall order parameter carry charge 2e and can condense to form an s-wave superconducting state [2,3] The relevance of this route to superconductivity for twisted bilayer graphene will be discussed.

[1] H.-K. Tang, J. N. Leaw, J. N. B. Rodrigues, I. F. Herbut, P. Sengupta, F. F. Assaad, and S. Adam, Science, 361, 570, 2018.
[2] Y. Liu, Z. Wang, T. Sato, M. Hohenadler, C. Wang, W. Guo, and F. F. Assaad, Nature Communications, 10, 2658, 2019.
[3] Z. Wang, Y. Liu, T. Sato, M. Hohenadler, C. Wang, W. Guo, and F. F. Assaad. arXiv:2006.13239.