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Magic-angle twisted bilayer graphene (MATBG) is notable as a highly tunable platform for investigating strongly correlated phenomena such as high-$T_c$ superconductivity and quantum spin liquids, due to easy control of doping level through gating and sensitive dependence of the magic angle on hydrostatic pressure. Experimental observations of correlated insulating states, unconventional superconductivity and ferromagnetism in MATBG indicate that this system exhibits rich exotic phases. In this work, using density functional theory calculations in conjunction with the effective screening medium method, we find the MATBG under pressure at a twisting angle of $2.88unicode{xb0}$ and simulate how its electronic states evolve when doping level and out-of-plane electric field are gate-tuned. Our calculations show that, at doping levels between two electrons and four holes per moir{e} unit cell, a ferromagnetic solution with spin density localized at AA stacking sites is lower in energy than the nonmagnetic solution. The magnetic moment of this ferromagnetic state decreases with both electron and hole doping and vanishes at four electrons/holes doped per moir{e} unit cell. Hybridization between the flat bands at the Fermi level and the surrounding dispersive bands can take place at finite doping. Moreover, upon increasing the out-of-plane electric field at zero doping, a transition from the ferromagnetic state to the nonmagnetic one is seen. We also analyze the interlayer bonding character due to the flat bands via Wannier functions. Finally, we report trivial band topology of the flat bands in the ferromagnetic state at a certain doping level.
Strong electron correlation and spin-orbit coupling (SOC) provide two non-trivial threads to condensed matter physics. When these two strands of physics come together, a plethora of quantum phenomena with novel topological order have been predicted t
In the past two years, magic-angle twisted bilayer graphene has emerged as a uniquely versatile experimental platform that combines metallic, superconducting, magnetic and insulating phases in a single crystal. In particular the ability to tune the s
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Graphene, a one-layer honeycomb lattice of carbon atoms, exhibits unconventional phenomena and attracts much interest since its discovery. Recently, an unexpected Mott-like insulator state induced by moire pattern and a superconducting state are obse
Twisting two layers into a magic angle (MA) of ~1.1{deg} is found essential to create low energy flat bands and the resulting correlated insulating, superconducting, and magnetic phases in twisted bilayer graphene (TBG). While most of previous works