scholarly journals Flat bands and gaps in twisted double bilayer graphene

Nanoscale ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 5014-5020 ◽  
Author(s):  
F. J. Culchac ◽  
R. R. Del Grande ◽  
Rodrigo B. Capaz ◽  
Leonor Chico ◽  
E. Suárez Morell
Keyword(s):  
Tight Binding ◽  
Bilayer Graphene ◽  
Continuum Models ◽  
Flat Bands

We explain the behavior of the bandgap for twisted double bilayer graphene for different angles and discuss the two mechanisms involved. We propose corrections to the tight binding and continuum models.

scholarly journals Flat bands in slightly twisted bilayer graphene: Tight-binding calculations

2010 ◽  
Vol 82 (12) ◽  
Author(s):  
E. Suárez Morell ◽  
J. D. Correa ◽  
P. Vargas ◽  
M. Pacheco ◽  
Z. Barticevic
Keyword(s):  
Tight Binding ◽  
Bilayer Graphene ◽  
Flat Bands ◽  
Twisted Bilayer Graphene

scholarly journals Moire Is Different

2021 ◽  
Vol 13 (1) ◽  
pp. 50
Author(s):  
Wenyuan Shi
Keyword(s):  
Electronic Structures ◽  
Tight Binding ◽  
Physical Property ◽  
Large Change ◽  
Bilayer Graphene ◽  
Dirac Fermion ◽  
Dirac Fermions ◽  
Graphene Layers ◽  
Flat Bands ◽  
Twisted Bilayer Graphene

Graphene, as the thinnest material ever found, exhibits unconventionally relativistic behaviour of Dirac fermions. However, unusual phenomena (such as superconductivity) arise when stacking two graphene layers and twisting the bilayer graphene. The relativistic Dirac fermion in graphene has been widely studied and understood, but the large change observed in twisted bilayer graphene (TBG) is intriguing and still unclear because only van der Waals force (vdW) interlayer interaction is added from graphene to TBG and such a very weak interaction is expected to play a negligible role. To understand such dramatic variation, we studied the electronic structures of monolayer, bilayer and twisted bilayer graphene. Twisted bilayer graphene creates different moiré patterns when turned at different angles. We proposed tight-binding and effective continuum models and thereby drafted a computer code to calculate their electronic structures. Our calculated results show that the electronic structure of twisted bilayer graphene changes significantly even by a tiny twist. When bilayer graphene is twisted at special “magic angles”, flat bands appear. We examined how these flat bands are created, their properties and the relevance to some unconventional physical property such as superconductivity. We conclude that in the nanoscopic scale, similar looking atomic structures can create vastly different electronic structures. Like how P. W. Anderson stated that similar looking fields in science can have differences in his article “More is Different”, similar moiré patterns in twisted bilayer graphene can produce different electronic structures.

scholarly journals Topological flat bands and correlated states in twisted monolayer-bilayer graphene

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
Louk Rademaker ◽  
Ivan V. Protopopov ◽  
Dmitry A. Abanin
Keyword(s):  
Bilayer Graphene ◽  
Flat Bands

scholarly journals Dodecagonal bilayer graphene quasicrystal and its approximants

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Guodong Yu ◽  
Zewen Wu ◽  
Zhen Zhan ◽  
Mikhail I. Katsnelson ◽  
Shengjun Yuan
Keyword(s):  
Large Scale ◽  
Lattice Mismatch ◽  
Tight Binding ◽  
Bilayer Graphene ◽  
Dominant Factor ◽  
Honeycomb Lattice ◽  
Fermi Velocity ◽  
Band Theory ◽  
Incommensurate Structures ◽  
Unfolding Method

AbstractDodecagonal bilayer graphene quasicrystal has 12-fold rotational order but lacks translational symmetry which prevents the application of band theory. In this paper, we study the electronic and optical properties of graphene quasicrystal with large-scale tight-binding calculations involving more than ten million atoms. We propose a series of periodic approximants which reproduce accurately the properties of quasicrystal within a finite unit cell. By utilizing the band-unfolding method on the smallest approximant with only 2702 atoms, the effective band structure of graphene quasicrystal is derived. The features, such as the emergence of new Dirac points (especially the mirrored ones), the band gap at $$M$$M point and the Fermi velocity are all in agreement with recent experiments. The properties of quasicrystal states are identified in the Landau level spectrum and optical excitations. Importantly, our results show that the lattice mismatch is the dominant factor determining the accuracy of layered approximants. The proposed approximants can be used directly for other layered materials in honeycomb lattice, and the design principles can be applied for any quasi-periodic incommensurate structures.

scholarly journals Theory of correlated insulating behaviour and spin-triplet superconductivity in twisted double bilayer graphene

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Jong Yeon Lee ◽  
Eslam Khalaf ◽  
Shang Liu ◽  
Xiaomeng Liu ◽  
Zeyu Hao ◽  
...  
Keyword(s):  
Displacement Field ◽  
Twist Angle ◽  
Vertical Displacement ◽  
Bilayer Graphene ◽  
Magic Angle ◽  
Hartree Fock ◽  
Flat Bands ◽  
Half Filling ◽  
Spin Triplet ◽  
Experimental Findings

AbstractTwo graphene monolayers twisted by a small magic angle exhibit nearly flat bands, leading to correlated electronic states. Here we study a related but different system with reduced symmetry - twisted double bilayer graphene (TDBG), consisting of two Bernal stacked bilayer graphenes, twisted with respect to one another. Unlike the monolayer case, we show that isolated flat bands only appear on application of a vertical displacement field. We construct a phase diagram as a function of twist angle and displacement field, incorporating interactions via a Hartree-Fock approximation. At half-filling, ferromagnetic insulators are stabilized with valley Chern number $${C}_{{\rm{v}}}=\pm 2$$Cv=±2. Upon doping, ferromagnetic fluctuations are argued to lead to spin-triplet superconductivity from pairing between opposite valleys. We highlight a novel orbital effect arising from in-plane fields plays an important role in interpreting experiments. Combined with recent experimental findings, our results establish TDBG as a tunable platform to realize rare phases in conventional solids.

scholarly journals Moiré with flat bands is different

2019 ◽  
Vol 50 (3) ◽  
pp. 24-26
Author(s):  
Tero T. Heikkilä ◽  
Timo Hyart
Keyword(s):  
Critical Temperature ◽  
Fermi Surface ◽  
Room Temperature ◽  
Electronic States ◽  
Bilayer Graphene ◽  
Flat Bands ◽  
Twisted Bilayer Graphene

Recent experimental discoveries of superconductivity and other exotic electronic states in twisted bilayer graphene (TBG) call for a reconsideration of our traditional theories of these states, usually based on the assumption of the presence of a Fermi surface. Here we show how such developments may even help us finding mechanisms of increasing the critical temperature of superconductivity towards the room temperature.

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