###### user

Summarize the paper

**AI:**The papers discuss different aspects of superconducting systems in two dimensions, with a particular focus on twisted bilayer graphene. Multiple models are used to investigate the behavior of these systems, including the Ginzburg-Landau free-energy density and Monte Carlo simulations. The authors study the critical temperatures, including those of the Berezinskii-Kosterlitz-Thouless and $Z_2$ phase transitions, as well as the presence of fermionic quadrupling condensates and the relationship between defects in the $U(1)$ and $Z_2$ sectors. The potential for detecting fermion quadrupling order is also discussed. The papers suggest that the behavior of these systems can be better understood through further experimental and theoretical research.

## Authors

Ilaria Maccari, Johan Carlström, Egor Babaev

## Abstract

We study the effective model for superconducting magic-angle twisted bilayer graphene beyond mean-field approximation by using Monte Carlo simulations. We consider the parameter regime where the low-temperature phase is a superconductor that spontaneously breaks time-reversal symmetry. When fluctuations are taken into account, it is shown that a fluctuations-induced phase with a fermion quadrupling order appears, where a different condensate, formed by four electrons, breaks time-reversal symmetry.

#### 2 comments

###### alexlee-1984

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!

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!

###### ilaria-maccari

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.

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!

Thank you again for your interest!