• Corpus ID: 55549814

# Theory of Emergent Josephson Lattice in Neutral Twisted Bilayer Graphene (Moiŕe is Different)

@article{Baskaran2018TheoryOE,
title={Theory of Emergent Josephson Lattice in Neutral Twisted Bilayer Graphene (Moiŕe is Different)},
journal={arXiv: Superconductivity},
year={2018}
}
• Published 2 April 2018
• Physics
• arXiv: Superconductivity
`More is Different' (Anderson, 1972) in graphene. A bilayer and a twist spring surprises. Recently discovered superconductivity (T$_c\approx$ 1.7 K) at an ultra low doping density $\sim 10^{11}$cm${}^{-2}$ has alerted the community to look for an electron-electron interaction based mechanism, as phonon-induced attraction seems inadequate. We suggest a mechanism of superconductivity, where an important role is played by the dense (density $\approx$ 2 $\times$ 10${}^{15}$cm$^{-2}$) $\pi$-electron…
18 Citations

## Figures from this paper

Pairing in twisted double-bilayer graphene and related moiré superlattice systems
• Physics
• 2019
We present a systematic classification and analysis of possible pairing instabilities in graphene-based moire superlattices. Motivated by recent experiments on twisted double-bilayer graphene showing
Pressure-induced metal-insulator transition in twisted bilayer graphene
• Physics
Physical Review B
• 2019
Recent experiments [arXiv: 1808.07865] on twisted bilayer graphene (TBLG) show that under hydrostatic pressure, an insulating state at quarter-filling of the moir\'e superlattice (i.e., one charge
Pairing symmetry and spontaneous vortex-antivortex lattice in superconducting twisted-bilayer graphene: Bogoliubov-de Gennes approach
• Physics
Physical Review B
• 2018
We study the superconducting pairing symmetry in twisted bilayer graphene by solving the Bogoliubov-de Gennes equation for all electrons in moir\'{e} supercells. With increasing the pairing
Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization, Not Mott Insulation.
• Medicine, Physics
Nano letters
• 2018
We devise a model to explain why twisted bilayer graphene exhibits insulating behavior when ν = 2 or 3 charges occupy a unit moiré cell, a feature attributed to Mottness per previous work but not for
Flatbands and Perfect Metal in Trilayer Moiré Graphene.
• Physics, Medicine
Physical review letters
• 2019
It is proved that the system is a perfect metal in the sense that it is gapless at all energies and holds quite generally for multilayer graphene with an odd number of planes under the condition of C_{2z}T symmetry.
Tuning superconductivity in twisted bilayer graphene
This study demonstrates twisted bilayer graphene to be a distinctively tunable platform for exploring correlated states by inducing superconductivity at a twist angle larger than 1.1°—in which correlated phases are otherwise absent—by varying the interlayer spacing with hydrostatic pressure.
High-TC Superconductivity Originating from Interlayer Coulomb Coupling in Gate-Charged Twisted Bilayer Graphene Moiré Superlattices
• Materials Science, Physics
Journal of Superconductivity and Novel Magnetism
• 2019
Unconventional superconductivity in bilayer graphene has been reported for twist angles θ near the first magic angle and charged electrostatically with holes near half filling of the lower flat
Superconductivity from valley fluctuations and approximate SO(4) symmetry in a weak coupling theory of twisted bilayer graphene
• Physics
npj Quantum Materials
• 2019
AbstarctThe recent discovery of the Mott insulating and superconducting phases in twisted bilayer graphene has generated tremendous research interest. Here, we develop a weak coupling approach to the
Phases of a phenomenological model of twisted bilayer graphene
• Physics
Physical Review B
• 2018
We propose a lattice scale two-band generalized Hubbard model as a caricature of the electronic structure of twisted bilayer graphene. Various possible broken symmetry phases can arise, including a
Triangular antiferromagnetism on the honeycomb lattice of twisted bilayer graphene
• Physics, Materials Science
Physical Review B
• 2018
We present the electronic band structures of states with the same symmetry as the three-sublattice planar antiferromagnetic order of the triangular lattice. Such states can also be defined on the

## References

SHOWING 1-10 OF 57 REFERENCES
Electronic structure of turbostratic graphene
• Physics
• 2010
We explore the rotational degree of freedom between graphene layers via the simple prototype of the graphene twist bilayer, i.e., two layers rotated by some angle $\ensuremath{\theta}$. It is shown
Theory of Ultra Low Tc Superconductivity in Bismuth: Tip of an Iceberg ?
Superconductivity with an ultra low Tc $\sim$ 0.5 mK was discovered recently in bismuth, a semimetal. To develop a model and scenario for Bi we begin with a cubic reference lattice, close to A7
Resonating-valence-bond contribution to superconductivity in MgB 2
We view ${\mathrm{MgB}}_{2}$ as electronically equivalent to (nonstaggered) graphite $({\mathrm{B}}^{\ensuremath{-}}$ layer) that has undergone a zero-gap-semiconductor-to-superconductor phase
Unconventional superconductivity in magic-angle graphene superlattices
The realization of intrinsic unconventional superconductivity is reported—which cannot be explained by weak electron–phonon interactions—in a two-dimensional superlattice created by stacking two sheets of graphene that are twisted relative to each other by a small angle.
Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene
• Kyounghwa Kim, +7 authors E. Tutuc
• Materials Science, Medicine
Proceedings of the National Academy of Sciences
• 2017
It is demonstrated that at small twist angles, the electronic properties of bilayer graphene moiré crystals are strongly altered by electron–electron interactions.
Resonating Valence Bonds and Mean-Field d-Wave Superconductivity in Graphite
• Physics
• 2007
We investigate the possibility of inducing superconductivity in a graphite layer by electronic correlation effects. We use a phenomenological microscopic Hamiltonian which includes nearest neighbor
Correlated insulator behaviour at half-filling in magic-angle graphene superlattices
It is shown experimentally that when this angle is close to the ‘magic’ angle the electronic band structure near zero Fermi energy becomes flat, owing to strong interlayer coupling, and these flat bands exhibit insulating states at half-filling, which are not expected in the absence of correlations between electrons.
QUANTUM COMPLEXITY IN GRAPHENE
Carbon has a unique position among elements in the periodic table. It produces an allotrope, graphene, a mechanically robust two dimensional semimetal. The multifarious properties that graphene
Single-layer behavior and its breakdown in twisted graphene layers.
High magnetic field scanning tunneling microscopy and Landau level spectroscopy of twisted graphene layers grown by chemical vapor deposition observe an unexpected electron-hole asymmetry which is substantially larger than the asymmetry in either single or untwayer graphene.
Quantum Hall effect in twisted bilayer graphene.
The measured Hall conductivity exhibits the same plateau values as for a commensurate Bernal bilayer, which implies that the eightfold degeneracy of the zero energy mode is topologically protected despite rotational disorder as recently predicted.