Superconductivity, especially high-Tc superconductivity, is one of the most active fields in
condensed matter physics. The discovery of a room temperature and atmospheric pressure
superconductor would be a technological revolution. In 2018, the group of Pablo Jarrillo at
MIT reported superconductivity in “magic-angle twisted bilayer graphene (MA-tBG)” [1].
Since then, other studies have been made [2]. Due to the simplicity of this material and the
easiness to dope it (since it can be done with electrodes, there is no need to chemically
dope the material), together with the similarity between its superconductivity and the one in
high-Tc superconductors [3], makes tBG a new platform to study high-Tc superconductivity.
In this work, our goal is to study superconductivity in MA-tBG. In particular, we aim to use the
classical XY spin lattice model, which is related to superconductivity, and study if it can
properly calculate its critical temperature. The model by itself cannot be applied directly to
the material. We will use a semiclassical approach, that is, an effective lattice and interaction
coefficients (magnetic and electronic) obtained from a quantum mechanical calculation. This
new adapted model is solved by the stochastic Metropolis Monte Carlo algorithm. This is still
a work in progress. The results up to now suggest that the model behaves as it should, but
the critical temperature is a factor of 5 away from the experimental one.
References
[1] Yuan Cao, Valla Fatemi, Shiang Fang, Kenji Watanabe, Takashi Taniguchi, Efthimios
Kaxiras, and Pablo Jarillo-Herrero. Unconventional superconductivity in magic-angle
graphene superlattices. Nature, 556(7699):43–50, April 2018.
[2] Xiaobo Lu, Petr Stepanov, Wei Yang, Ming Xie, Mohammed Ali Aamir, Ipsita Das, Carles
Urgell, Kenji Watanabe, Takashi Taniguchi, Guangyu Zhang, Adrian Bachtold, Allan H.
MacDonald, and Dmitri K. Efetov. Superconductors, orbital magnets and correlated states in
magic-angle bilayer graphene. Nature, 574(7780):653–657, October 2019.
[3] Eva Y. Andrei and Allan H. MacDonald. Graphene bilayers with a twist. Nature Materials,
19(12):1265–1275, December 2020
Superconductivity, especially high-Tc superconductivity, is one of the most active fields in
condensed matter physics. The discovery of a room temperature and atmospheric pressure
superconductor would be a technological revolution. In 2018, the group of Pablo Jarrillo at
MIT reported superconductivity in “magic-angle twisted bilayer graphene (MA-tBG)” [1].
Since then, other studies have been made [2]. Due to the simplicity of this material and the
easiness to dope it (since it can be done with electrodes, there is no need to chemically
dope the material), together with the similarity between its superconductivity and the one in
high-Tc superconductors [3], makes tBG a new platform to study high-Tc superconductivity.
In this work, our goal is to study superconductivity in MA-tBG. In particular, we aim to use the
classical XY spin lattice model, which is related to superconductivity, and study if it can
properly calculate its critical temperature. The model by itself cannot be applied directly to
the material. We will use a semiclassical approach, that is, an effective lattice and interaction
coefficients (magnetic and electronic) obtained from a quantum mechanical calculation. This
new adapted model is solved by the stochastic Metropolis Monte Carlo algorithm. This is still
a work in progress. The results up to now suggest that the model behaves as it should, but
the critical temperature is a factor of 5 away from the experimental one.
References
[1] Yuan Cao, Valla Fatemi, Shiang Fang, Kenji Watanabe, Takashi Taniguchi, Efthimios
Kaxiras, and Pablo Jarillo-Herrero. Unconventional superconductivity in magic-angle
graphene superlattices. Nature, 556(7699):43–50, April 2018.
[2] Xiaobo Lu, Petr Stepanov, Wei Yang, Ming Xie, Mohammed Ali Aamir, Ipsita Das, Carles
Urgell, Kenji Watanabe, Takashi Taniguchi, Guangyu Zhang, Adrian Bachtold, Allan H.
MacDonald, and Dmitri K. Efetov. Superconductors, orbital magnets and correlated states in
magic-angle bilayer graphene. Nature, 574(7780):653–657, October 2019.
[3] Eva Y. Andrei and Allan H. MacDonald. Graphene bilayers with a twist. Nature Materials,
19(12):1265–1275, December 2020
