Emergent momentum scale, localization, and van Hove singularities in the graphene twist bilayer

Shallcross, S.; Sharma, S.; Pankratov, Oleg

doi:10.1103/physrevb.87.245403

Cited by 61 publications

(93 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…3). This picture is quite consistent with many previous studies utilizing different approaches [11][12][13][14][15][17][18][19][20][21] . The gap may be viewed as a consequence of hybridization between the states located at the Dirac points of two graphene layers K θ and K ′ (and K and K ′ θ ).…”

Section: Large Twist Angles θ > θCsupporting

confidence: 93%

“…(27) decreases when θ decreases (see Fig. 3), in good agreement with previous theoretical [11][12][13]15,17,[19][20][21] , and experimental 1,5 studies. For angles close to θ c = 1.89…”

Section: Small Twist Angle θ < θCsupporting

confidence: 91%

“…It is clearly seen from these figures that the Fermi surfaces are similar to each other, and the total size (length) of the Fermi surface sheets for the structure (18, 1) is smaller than that for the (17, 1). The band flatness, the non-zero density of states for small θ, as well as the existence of the 'magic' angles where the density of states vanishes is consistent with many previous studies using both low-energy 20,21,24 and tight-binding calculations 11,[15][16][17] . Our calculations show that no gap exists between the low-energy bands and the lower or upper bands.…”

Section: Small Twist Angle θ < θCsupporting

confidence: 91%

“…For such angles, numerical studies based on density functional theory and tight-binding calculations [11][12][13][14][15][16][17] were performed. Since the number of atoms in an elementary unit cell of the tBLG superlattice may be quite substantial, especially at small twist angles, the ab initio calculations incur a significant computational cost.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Electronic spectrum of twisted bilayer graphene

et al. 2015

View full text Add to dashboard Cite

We study the electronic properties of twisted bilayers graphene in the tight-binding approximation. The interlayer hopping amplitude is modeled by a function, which depends not only on the distance between two carbon atoms, but also on the positions of neighboring atoms as well. Using the Lanczos algorithm for the numerical evaluation of eigenvalues of large sparse matrices, we calculate the bilayer single-electron spectrum for commensurate twist angles in the range 1• . We show that at certain angles θ greater than θc ≈ 1.89• the electronic spectrum acquires a finite gap, whose value could be as large as 80 meV. However, in an infinitely large and perfectly clean sample the gap as a function of θ behaves non-monotonously, demonstrating exponentially-large jumps for very small variations of θ. This sensitivity to the angle makes it impossible to predict the gap value for a given sample, since in experiment θ is always known with certain error. To establish the connection with experiments, we demonstrate that for a system of finite sizeL the gap becomes a smooth function of the twist angle. If the sample is infinite, but disorder is present, we expect that the electron mean-free path plays the same role asL. In the regime of small angles θ < θc, the system is a metal with a well-defined Fermi surface which is reduced to Fermi points for some values of θ. The density of states in the metallic phase varies smoothly with θ.

show abstract

Section: Large Twist Angles θ > θCsupporting

confidence: 93%

“…(27) decreases when θ decreases (see Fig. 3), in good agreement with previous theoretical [11][12][13]15,17,[19][20][21] , and experimental 1,5 studies. For angles close to θ c = 1.89…”

Section: Small Twist Angle θ < θCsupporting

confidence: 91%

Section: Small Twist Angle θ < θCsupporting

confidence: 91%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Electronic spectrum of twisted bilayer graphene

et al. 2015

View full text Add to dashboard Cite

show abstract

“…[84] The density of states of twisted graphene bilayers showed an angle-dependent set of vHSs. [85] First, the vHS of graphene monolayer appeared at the M point was split into an increasing number of distinct peaks as the twist angle was reduced. Second, the flattening of the p bands generated the lowenergy vHSs, which approached to the Fermi level for the small angles.…”

Section: Stacked Graphene Layersmentioning

confidence: 99%

Many‐body effects in optical response of graphene‐based structures

Bulusheva

Sedelnikova

Окотруб

2015

Int J of Quantum Chemistry

View full text Add to dashboard Cite

Graphene is an exciting material for optoelectronics and plasmonics. Its optical response may be changed under mechanical action, such as stretching or corrugation, and with confinement of a size in a certain direction. Theoretical investigations play an important role in interpretation of experimental data and stimulating a search for novel graphene architectures. Thereby, it is important to analyze restrictions of modern approaches in calculation of optical properties of graphene-based objects and, particularly, to reveal an impact of electron-electron and electron-hole interactions on the position and shape of optical features. Here, we review the recent progress in quantum-chemical calculations of monolayer and few-layer graphenes, graphene ripples, and dots in a light of optical excitations.

show abstract

Substrate Doping Effect and Unusually Large Angle van Hove Singularity Evolution in Twisted Bi‐ and Multilayer Graphene

et al. 2017

View full text Add to dashboard Cite

Graphene is a 2D honeycomb carbon crystal that exhibits unusual electronic structures and physical properties [1][2][3][4] that make it attractive for high-performance devices, such as transistors, [5][6][7][8] optical modulators, [9,10] and photodetectors. [9,11] Compared to single layer graphene, when two or more layers of graphene are stacked together with a twist angle, their electronic structure can be further enriched, giving rise to the van Hove singularity (vHS) with greatly enhanced carrier density of states, thus leading to enhanced optical absorption for selective photon energies. [12][13][14][15][16][17][18] With large tuning range of the twist angle and vHS binding energy, twisted bi-and multilayer graphene provide a promising material base for fabricating broad band wavelength-selective ultrafast photodetectors from the infrared to the ultraviolet regime.Graphene has demonstrated great potential in new-generation electronic applications due to its unique electronic properties such as large carrier Fermi velocity, ultrahigh carrier mobility, and high material stability. Interestingly, the electronic structures can be further engineered in multilayer graphene by the introduction of a twist angle between different layers to create van Hove singularities (vHSs) at adjustable binding energy. In this work, using angleresolved photoemission spectroscopy with sub-micrometer spatial resolution, the band structures and their evolution are systematically studied with twist angle in bilayer and trilayer graphene sheets. A doping effect is directly observed in graphene multilayer system as well as vHSs in bilayer graphene over a wide range of twist angles (from 5° to 31°) with wide tunable energy range over 2 eV. In addition, the formation of multiple vHSs (at different binding energies) is also observed in trilayer graphene. The large tuning range of vHS binding energy in twisted multilayer graphene provides a promising material base for optoelectrical applications with broadband wavelength selectivity from the infrared to the ultraviolet regime, as demonstrated by an example application of wavelength selective photodetector.

show abstract

Emergent momentum scale, localization, and van Hove singularities in the graphene twist bilayer

Cited by 61 publications

References 17 publications

Electronic spectrum of twisted bilayer graphene

Electronic spectrum of twisted bilayer graphene

Many‐body effects in optical response of graphene‐based structures

Substrate Doping Effect and Unusually Large Angle van Hove Singularity Evolution in Twisted Bi‐ and Multilayer Graphene

Contact Info

Product

Resources

About