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

 · Invited

Abstract

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.

*Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter ct.qmat (EXC 2147, project-id 390858490)
Deutsche Forschungsgemeinschaft under the grant number AS 120/15-1 and SFB 1170 on Topological and Correlated Electronics at Surfaces and Interfaces.

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Presenters

  • Fakher Assaad

    • Institut f\"ur Theoretische Physik und Astrophysik, University of Wurzburg
    • University of Wurzburg
    • Institute for Theoretical Physics and Astrophysics, University of Wurzburg

Authors

  • Fakher Assaad

    • Institut f\"ur Theoretische Physik und Astrophysik, University of Wurzburg
    • University of Wurzburg
    • Institute for Theoretical Physics and Astrophysics, University of Wurzburg