# The possibility of superconductivity in twisted bilayer graphene

## Abstract

We discuss the possibility of superconductivity in Twisted Bilayer Graphene (TBG). In this study we use TBG model with commensurate rotation θ=1.16° in which the van-Hove singularities (VHS) arise at 6 meV from the Fermi level. We use BCS standard formula that include Density of States (DOS) to calculate the critical temperature (T{sub C}). Based on our calculation we predict that superconductivity will not arise in Pristine TBG because pairing potential has infinity value. In this situation, Dirac Fermions do not interact with each other since they do not form the bound states. Superconductvity may arise when the Fermi level is shifted towards the VHS. Based on this calculation, we predict that T{sub C} has value between 0.04 K and 0.12 K. The low value of T{sub C} is due to highly energetic of in plane phonon vibration which reduce the effective electron-phonon coupling. We conclude that doped TBG is candidate for Dirac Fermion superconductor.

- Authors:

- Jurusan Fisika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Gadjah Mada, Bulaksumur 55281, Yogyakarta (Indonesia)
- (Indonesia)

- Publication Date:

- OSTI Identifier:
- 22488926

- Resource Type:
- Journal Article

- Journal Name:
- AIP Conference Proceedings

- Additional Journal Information:
- Journal Volume: 1677; Journal Issue: 1; Conference: 5. international conference on mathematics and natural sciences, Bandung (Indonesia), 2-3 Nov 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; BOUND STATE; CRITICAL TEMPERATURE; DENSITY OF STATES; DOPED MATERIALS; ELECTRON-PHONON COUPLING; FERMI LEVEL; FERMIONS; GRAPHENE; LAYERS; PHONONS; POTENTIALS; ROTATION; SUPERCONDUCTIVITY; SUPERCONDUCTORS

### Citation Formats

```
Manaf, Muhamad Nasruddin, E-mail: muhamad.nasruddin.manaf@mail.ugm.ac.id, Santoso, Iman, E-mail: iman.santoso@ugm.ac.id, Hermanto, Arief, and Yayasan Hikmah Teknosains, Jl. Kaliurang Km 5,3 Gg. Pamungkas No. 16 A, Yogyakarta.
```*The possibility of superconductivity in twisted bilayer graphene*. United States: N. p., 2015.
Web. doi:10.1063/1.4930708.

```
Manaf, Muhamad Nasruddin, E-mail: muhamad.nasruddin.manaf@mail.ugm.ac.id, Santoso, Iman, E-mail: iman.santoso@ugm.ac.id, Hermanto, Arief, & Yayasan Hikmah Teknosains, Jl. Kaliurang Km 5,3 Gg. Pamungkas No. 16 A, Yogyakarta.
```*The possibility of superconductivity in twisted bilayer graphene*. United States. doi:10.1063/1.4930708.

```
Manaf, Muhamad Nasruddin, E-mail: muhamad.nasruddin.manaf@mail.ugm.ac.id, Santoso, Iman, E-mail: iman.santoso@ugm.ac.id, Hermanto, Arief, and Yayasan Hikmah Teknosains, Jl. Kaliurang Km 5,3 Gg. Pamungkas No. 16 A, Yogyakarta. Wed .
"The possibility of superconductivity in twisted bilayer graphene". United States. doi:10.1063/1.4930708.
```

```
@article{osti_22488926,
```

title = {The possibility of superconductivity in twisted bilayer graphene},

author = {Manaf, Muhamad Nasruddin, E-mail: muhamad.nasruddin.manaf@mail.ugm.ac.id and Santoso, Iman, E-mail: iman.santoso@ugm.ac.id and Hermanto, Arief and Yayasan Hikmah Teknosains, Jl. Kaliurang Km 5,3 Gg. Pamungkas No. 16 A, Yogyakarta},

abstractNote = {We discuss the possibility of superconductivity in Twisted Bilayer Graphene (TBG). In this study we use TBG model with commensurate rotation θ=1.16° in which the van-Hove singularities (VHS) arise at 6 meV from the Fermi level. We use BCS standard formula that include Density of States (DOS) to calculate the critical temperature (T{sub C}). Based on our calculation we predict that superconductivity will not arise in Pristine TBG because pairing potential has infinity value. In this situation, Dirac Fermions do not interact with each other since they do not form the bound states. Superconductvity may arise when the Fermi level is shifted towards the VHS. Based on this calculation, we predict that T{sub C} has value between 0.04 K and 0.12 K. The low value of T{sub C} is due to highly energetic of in plane phonon vibration which reduce the effective electron-phonon coupling. We conclude that doped TBG is candidate for Dirac Fermion superconductor.},

doi = {10.1063/1.4930708},

journal = {AIP Conference Proceedings},

issn = {0094-243X},

number = 1,

volume = 1677,

place = {United States},

year = {2015},

month = {9}

}