Heavy Fermion Pseudo-potential of Twisted Bilayer Graphene: the role of the backgate.

Song and Bernevig (SB) have recently proposed a faithful reformulation of the physics of magic angle twisted bilayer graphene (MATBG) as a topological heavy fermion problem, involving the hybridization of flat band f-electrons with a topological band of conduction electrons[1,2]. Here we explore the consequences of this analogy, using it to reformulate the SB model as a mixed valence model for twisted bilayer graphene[3]. In contrast to previous treatments[4,5] of gate tuned MATBG as a simple capacitor, we argue that the existence of the tight localization of charge inside the moiré unit cells necessarily creates an emergent gate tuned heavy fermion pseudopotential due to the image charges behind the backgate. Our picture allows us to understand why 10-20V backgate voltages are required to tune the Moire potentials on the meV scale. The presence of the heavy fermion pseudopotential stabilizes local moment behavior and ensures the Kondo temperature is small at integer fillings, in contrast to treating gate tuned MATBG as a simple capacitor where the drastic increase in the Kondo temperature at larger filling factors kills the observed local moment behavior.

[1] Zha-Da Song and B. Andrei Bernevig, Phys. Rev. Lett 129 047601 (2022).

[2] Dumitru Călugăru, Maksim Borovkov, Liam L.H. Lau, Piers Coleman, Zhi-Da, Song, B. Andrei Bernevig, Low Temp. Phys 49, 640-654 (2023).

[3] Liam L. H. Lau and Piers Coleman, arXiv 2303.02670v2, (2023)

[4] Yang-Zhi Chou & Sankar Das Sarma, Phys. Rev. Lett 131, 026501 (2023).

[5] H. Hu, G. Rai, L. Crippa, J. Herzog-Arbeitman, D. Călugăru, T. Wehling, G. Sangiovanni, R. Valenti, A. M. Tsvelik, B. A. Bernevig, arXiv:2301.04673(2023).