Possible time-reversal-symmetry-breaking fermionic quadrupling condensate in twisted bilayer graphene

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Prediction of time-reversal-symmetry breaking fermionic quadrupling condensate in twisted bilayer graphene


Ilaria Maccari, Johan Carlström, Egor Babaev


Recent mean-field calculations suggest that the superconducting state of twisted bilayer graphene exhibits either a nematic order or a spontaneous breakdown of the time-reversal symmetry. The two-dimensional character of the material and the large critical temperature relative to the Fermi energy dictate that the material should have significant fluctuations. We study the effects of these fluctuations using Monte Carlo simulations. We show that in a model proposed earlier for twisted bilayer graphene there is a fluctuation-induced phase with quadrupling fermionic order for all considered parameters. This four-electron condensate, instead of superconductivity, shows a spontaneous breaking of time-reversal symmetry. Our results suggest that twisted bilayer graphene is an especially promising platform to study different types of condensates, beyond the pair-condensate paradigm.

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Thanks for the interesting talk and explaining complicated ideas about the multicomponent order parameter. I have a couple of questions though:
1. What is the relation between the generic two-order parameter Ginzburg-Landau action and magic bi-layer graphene? Is there an explicit relation between the parameters of the GL functional and the TBG?
2. What is the nature of time-reversal symmetry breaking in such theories: does it involve spin or it is similar to px+ipy type orbital symmetry breaking in superconductors or something different all-together? Is there some intuition?
Thank you!


Thank you for your comment and sorry for the late reply. Unfortunately, I have noticed it just now. 
Let me answer your questions:
1. The derivation of the GL model is discussed in this work [D. V. Chichinadze et al., Phys. Rev. B. 101, 224513 (2020)]. In a nutshell, the authors start from a 6-patch model for fermions near the VH points, solve the gap equations to find the pairing channels, and finally derive the Landau free energy. 
2. In this specific model, the two components of the model belong to the same two-dimensional irreducible representation (E) giving rise to a d ± id SC order.
Thank you again for your interest! 

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