Hundness in twisted bilayer graphene: correlated gaps and quantum criticality

We study the topological heavy fermion (THF) model of magic-angle twisted bilayer graphene (MATBG)[1], with and without electron-phonon coupling, using dynamical mean-field theory (DMFT) with the numerical renormalization group (NRG) impurity solver[2,3]. In the presence of symmetry breaking associated with valley-orbital ordering (time-reversal symmetric or Kramers intervalley coherent, or valley polarized), we observe that spin anti-Hund and orbital-angular momentum Hund couplings, induced by the dynamical Jahn–Teller effect, lead to (i) a robust pseudogap[2], and (ii) two types of quantum criticality[3], heavy-fermion type and BKT type.

[1] Z.-D. Song and B. A. Bernevig, Magic-angle twisted bilayer graphene as a topological heavy fermion problem, Phys. Rev. Lett. 129, 047601 (2022)

[2] Seongyeon Youn, Beomjoon Goh, Geng-Dong Zhou, Zhi-Da Song, and Seung-Sup B. Lee, “Hundness in twisted bilayer graphene: correlated gaps and pairing,” (2024), arXiv:2412.03108 [cond-mat].

[3] Seongyeon Youn, Beomjoon Goh, Geng-Dong Zhou, Yi-Jie Wang, Zhi-Da Song, and Seung-Sup B. Lee, “Hundness in twisted bilayer graphene: phase classification and quantum criticalities,” In preparation