Point defects in twisted bilayer graphene: A density functional theory study

Abstract

We have used ab initio density functional theory, incorporating van der Waals corrections, to study twisted bilayer graphene (TBLG) where Stone-Wales defects or monovacancies are introduced in one of the layers. We compare these results to those for defects in single layer graphene or Bernal stacked graphene. The energetics of defect formation is not very sensitive to the stacking of the layers or the specific site at which the defect is created, suggesting a weak interlayer coupling. However signatures of the interlayer coupling are manifested clearly in the electronic band structure. For the "γγ" Stone Wales defect in TBLG, we observe two Dirac cones that are shifted in both momentum space and energy. This up/down shift in energy results from the combined effect of a charge transfer between the two graphene layers, and a chemical interaction between the layers, which mimics the effects of a transverse electric field. Charge density plots show that states near the Dirac points have significant admixture between the two layers. For Stone Wales defects at other sites in TBLG, this basic structure is modified by the creation of mini gaps at energy crossings. For a monovacancy, the Dirac cone of the pristine layer is shifted up in energy by ∼ 0.25 eV due to a combination of the requirements of the equilibration of Fermi energy between the two layers with different numbers of electrons, charge transfer, and chemical interactions. Both kinds of defects increase the density of states at the Fermi level. The monovacancy also results in spin polarization, with magnetic moments on the defect of 1.2 -1.8 µB.PACS numbers: 73.22. Pr, 71.15.Mb

Sodium adsorption and intercalation in bilayer graphene from density functional theory calculations

“…The defective formation energy E defect f was calculated as follows where E pristine and E defect are the total energies of pristine BLG and defective BLG, respectively; μ C is the chemical potential of carbon and taken as the total energy per carbon atom of pristine graphene. E defect f of the MV defects is 8.042 eV per carbon atom shown in Table 4, which is well agreed with the previous studies (7.42-8.05 eV) [27,28,60]. cutting through the diagonal of the 3 × 3 supercell with Na atom are shown in the right side of a-f, where the red and the blue regions correspond to accumulation (0.02 e/Å 3 or more) and depletion (−0.02 e/ Å 3 or less), respectively.…”

“…cutting through the diagonal of the 3 × 3 supercell with Na atom are shown in the right side of a-f, where the red and the blue regions correspond to accumulation (0.02 e/Å 3 or more) and depletion (−0.02 e/ Å 3 or less), respectively. Gray and purple circles represent C and Na atoms, respectively Table 4 Defective formation energy E defect f and average interlayer distance (D g-g ) for the BLG with MV defects a LDA, M06-L, vdW-DF implemented in the CASTEP [60] b DFT-D2 implemented in the QUANTUM ESPRESSO [28] c LDA implemented in the CASTEP [ The ∆E f of intercalation/adsorption of Na atoms at inequivalent hollow sites around the point defect regions are shown in Fig. 6a-c.…”

“…Bilayer graphene (BLG) as a gapless semiconductor is similar to the monolayer and has widespread potential applications in various fields [24]. However, the BLG has drawn special attention mainly due to the controlled band gap and the magnetic properties from twisting, lattice vacancies and doping/inserting N, B and metal atoms [25][26][27][28][29][30]. BLG was expected to be a good candidate of anode material for LIB, and the Li ions in BLG were surrounded by two exterior graphene layers [31][32][33].…”

Electronic properties of graphene-based bilayer systems

“…The modification of the tBLG electron spectrum by point defects has been studied, also using DFT, in Ref. [419].…”

Raman signature of defected twisted bilayer graphene

“…As defects are introduced in one or both layers of TBG, the atomic and electronic structures of http://dx.doi.org/10.1016/j.carbon.2015.05.076 0008-6223/Ó 2015 Elsevier Ltd. All rights reserved. each layer, and of the coupled system, are altered [24]. As a result, an improved understanding of the Raman spectra of defective TBG is necessary to facilitate the study of defective or chemically-modified TBG and to extend earlier studies of ion irradiated graphene [19,25] and carbon nanotubes [26,27].…”