Low-frequency electronic and optical properties of rhombohedral graphite

Chiu, Chi-Tsung; Huang, Yu‐Wen; Chen, Szu-Chao; Lin, Ming–Fa; Shyu, Feng–Lin

doi:10.1039/c0cp01830a

Cited by 8 publications

(6 citation statements)

References 56 publications

(70 reference statements)

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“…As compared to the bulk bands of rhombohedral graphite with DFT 7,[23][24][25] and tight binding 25 calculations, and to the evolution of graphene to graphite with tight binding calculation 19 , it is clear that these states are surface states of the few-layer rhombohedral graphene. In order to understand the amount of charge needed to fill the flat surface band and close the gap, we have integrated first peak of the density of states above the gap.…”

Section: Appendix C: Metallic and Paramagnetic Bandsmentioning

confidence: 99%

Magnetic gap opening in rhombohedral-stacked multilayer graphene from first principles

et al. 2017

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We investigate the occurrence of magnetic and charge density wave instabilities in rhombohedralstacked multilayer (three to eight layers) graphene by first principles calculations including exact exchange. Neglecting spin-polarization, an extremely flat surface band centered at the special point K of the Brillouin zone occurs at the Fermi level. Spin polarization opens a gap in the surface state by stabilizing an antiferromagnetic state. The top and the bottom surface layers are weakly ferrimagnetic in-plane (net magnetization smaller than 10 −3 µB), and are antiferromagnetic coupled to each other. This coupling is propagated by the out-of-plane antiferromagnetic coupling between the nearest neighbors. The gap is very small in a spin-polarized generalized gradient approximation, while it is proportional to the amount of exact exchange in hybrid functionals. For trilayer rhombohedral graphene it is 38.6 meV in PBE0, in agreement with the 42 meV gap found in experiments. We study the temperature and doping dependence of the magnetic gap. At electron doping of n ∼ 7 × 10 11 cm −2 the gap closes. Charge density wave instabilities with √ 3 × √ 3 periodicity do not occur.In a solid, at low enough density, the Coulomb energy dominates the single particle energy and electronic instabilities such as magnetic phases or even Wigner crystallization become possible. A reduction of the singleparticle energy, and a consequent enhancement of the electron-electron interaction, can be obtained by considering a metallic system with a very flat single-particle band-dispersion. This unfortunately does not happen in graphene where the high Fermi velocity prevents electronic instability. The situation is different, however, in weakly doped Bernal-stacked (AB) even-multilayer graphene (see Fig. 1), as the single-particle bands become massive. Indeed, a spontaneously gapped ground state is already observed in suspended bilayer 1,2 and fourlayer graphene (1.5 meV gap) 3 .Even more favorable to electronic instabilities is rhombohedral-stacked (ABC) multilayer graphene. Neglecting spin polarization, tight-binding and density functional theory (DFT) calculations find bulk rhombohedral graphite to be metallic with a high Fermi velocity (see grey region in Fig. 1). On the contrary, within these approximations, rhombohedral-stacked multilayer graphene (RSMG) displays the occurrence of an extremely flat surface state at the Fermi level (see Fig. 1) located at the K point of the graphene Brillouin zone (BZ) 4-9 . The extension of the surface state in the BZ increases with increasing thickness and saturates at ≈ 7 layers. Its bandwidth is at most 2 meV for flakes of fewer than eight layers. The extremely reduced bandwidth makes RSMG one of the strongest correlated systems known nowadays and an ideal candidate for correlated states even in the absence of d orbitals.On the experimental side, only recently has it been possible to synthesize RSMG. Ouerghi et al.10 found fivelayer RSMG on top of a cubic SiC substrate to be metallic with a very high d...

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Section: Appendix C: Metallic and Paramagnetic Bandsmentioning

confidence: 99%

Magnetic gap opening in rhombohedral-stacked multilayer graphene from first principles

et al. 2017

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“…As a matter of fact, in graphite, it has been known that the interlayer hybridization at special points of the BZ is much affected by the stacking pattern [20][21][22][23]. By carefully examining electronic band structures in the literature, one can find the quasi-two-dimensional states due to this effect in a variety of works not only on graphite [20][21][22][23][24][25][26][27][28][29][30][31]. In addition, it has recently been experimentally demonstrated that this interference can be utilized for controlling the interlayer motion of electrons and holes by the stacking geometry [32,33].…”

Section: Introductionmentioning

confidence: 99%

Interference of the Bloch phase in layered materials with stacking shifts

et al. 2017

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In periodic systems, electronic wave functions of the eigenstates exhibit the periodically modulated Bloch phases and are characterized by their wave numbers k. We theoretically address the effects of the Bloch phase in general layered materials with stacking shift. When the interlayer shift and the Bloch wave vector k satisfy certain conditions, interlayer transitions of electrons are prohibited by the interference of the Bloch phase. We specify the manifolds in the k space where the hybridization of the Bloch states between the layers is suppressed in accord with the stacking shift. These manifolds, named stacking-adapted interference manifolds (SAIM), are obviously applicable to general layered materials regardless of detailed atomic configuration within the unit cell. We demonstrate the robustness and usefulness of the SAIM with first-principles calculations for layered boron nitride, transition-metal dichalcogenide, graphite, and black phosphorus. We also apply the SAIM to general three-dimensional crystals to derive special k-point paths for the respective Bravais lattices, along which the Bloch-phase interference strongly suppresses the band dispersion. Our theory provides a general and novel view on the anisotropic electronic kinetics intrinsic to the periodic-lattice structure.

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“…The consistency of two methods is very useful in the further studies on the other essential properties, e.g. the optical [63], magnetic [64] and transport properties [65] of guest-atom-substituted silicenes/germaneness.…”

Section: Spatial Distribution Of Charge Densitymentioning

confidence: 99%

Rich p -type-doping phenomena in boron-substituted silicene systems

Pham

Nguyen

et al. 2020

R. Soc. open sci.

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The essential properties of monolayer silicene greatly enriched by boron substitutions are thoroughly explored through first-principles calculations. Delicate analyses are conducted on the highly non-uniform Moire superlattices, atom-dominated band structures, charge density distributions and atom- and orbital-decomposed van Hove singularities. The hybridized 2 p z –3 p z and [2s, 2 p x , 2 p y ]–[3s, 3 p x , 3 p y ] bondings, with orthogonal relations, are obtained from the developed theoretical framework. The red-shifted Fermi level and the modified Dirac cones/ π bands/ σ bands are clearly identified under various concentrations and configurations of boron-guest atoms. Our results demonstrate that the charge transfer leads to the non-uniform chemical environment that creates diverse electronic properties.

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Low-frequency electronic and optical properties of rhombohedral graphite

Cited by 8 publications

References 56 publications

Magnetic gap opening in rhombohedral-stacked multilayer graphene from first principles

Magnetic gap opening in rhombohedral-stacked multilayer graphene from first principles

Interference of the Bloch phase in layered materials with stacking shifts

Rich p -type-doping phenomena in boron-substituted silicene systems

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