Electronic energy band parameters of graphite and their dependence on pressure, temperature and acceptor concentration

Dillon, R. O.; Spain, Ian L.; McClure, J. W.

doi:10.1016/0022-3697(77)90231-1

Cited by 63 publications

(25 citation statements)

References 31 publications

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“…A commonly used value for the decay constant is α s = 3.37, which agrees with predictions of the next nearest-neighbor hopping parameter and fits experimental results for dγ 0 (r)/dr [42]. The intralayer hopping parameter for the top layer becomes…”

Section: Triaxial Strainsupporting

confidence: 69%

Piezoelectricity in asymmetrically strained bilayer graphene

et al. 2016

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We study the electronic properties of commensurate faulted bilayer graphene by diagonalizing the one-particle Hamiltonian of the bilayer system in a complete basis of Bloch states of the individual graphene layers. Our novel approach is very general and can be easily extended to any commensurate graphene-based heterostructure. Here, we consider three cases: i) twisted bilayer graphene, ii) bilayer graphene where triaxial stress is applied to one layer, and iii) bilayer graphene where uniaxial stress is applied to one layer. We show that the resulting superstructures can be divided into distinct classes, depending on the twist angle or the magnitude of the induced strain. The different classes are distinguished from each other by the interlayer coupling mechanism, resulting in fundamentally different low-energy physics. For the cases of triaxial and uniaxial stress, the individual graphene layers tend to decouple and we find significant charge transfer between the layers. In addition, this piezoelectric effect can be tuned by applying a perpendicular electric field. Finally, we show how our approach can be generalized to multilayer systems.

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Section: Triaxial Strainsupporting

confidence: 69%

Piezoelectricity in asymmetrically strained bilayer graphene

et al. 2016

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“…The richness of possible stacking configurations is due to the weak van der Waals forces that keep the layers together. Furthermore, the electronic structure of the conduction band in graphene and bulk graphite is well described by a tight binding model which includes hopping between the π orbitals in Carbon atoms, neglecting the remaining atomic orbitals which give rise to the σ bands in graphite 11,15,16,17,18,19,20 . It is known that the low energy electronic structure depends on the stacking order in bulk samples 21,22,23,24,25,26 .…”

Section: Introductionmentioning

confidence: 99%

Electronic states and Landau levels in graphene stacks

2006

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We analyze, within a minimal model that allows analytical calculations, the electronic structure and Landau levels of graphene multi-layers with different stacking orders. We find, among other results, that electrostatic effects can induce a strongly divergent density of states in bi-and tri-layers, reminiscent of one-dimensional systems. The density of states at the surface of semi-infinite stacks, on the other hand, may vanish at low energies, or show a band of surface states, depending on the stacking order.

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“…For comparison, in bulk graphite one usually finds two types of holes and only one type of electrons with m e h Ϸ 0.056m 0 , m h h Ϸ 0.084m 0 or Ϸ0.04m 0 and m h l Ϸ 0.003m 0 . 15,21,22 Theory expects heavy carriers to have g = 2, whereas the location and degeneracy of minority holes are uncertain even for bulk graphite, being sensitive to, e.g., minor changes in the interlayer spacing. The existence of two electron carriers ͑one with g =4͒ and two types of relatively heavy holes clearly distinguish between bulk and surface carriers in graphite.…”

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confidence: 99%

Two-dimensional electron and hole gases at the surface of graphite

et al. 2005

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We report two-dimensional ͑2D͒ electron and hole gases induced at the surface of graphite by the electric field effect. The 2D gases reside within a few near-surface atomic layers and exhibit mobilities up to 15 000 and 60 000 cm 2 / V s at room and liquid-helium temperatures, respectively. The mobilities imply ballistic transport on m scale. Pronounced Shubnikov-de Haas oscillations reveal the existence of two types of charge carries in both electron and hole gases. Two-dimensional ͑2D͒ gases have proved to be one of the most pervasive and reach-in-phenomena systems and, deservedly, they have been attracting intense interest of physicists and engineers for several decades, leading to the discovery of a whole range of applications and phenomena including the field-effect transistor and the integer and fractional quantum Hall effects. So far, all 2D systems ͑2DS͒ have been based on semiconducting materials where charge carriers are induced by either local doping or the electric field effect ͑EFE͒. 1 As concerns metallic materials, many earlier efforts have proven difficult to change intrinsic carrier concentrations by EFE even in semimetals ͑see, e.g., Refs. 2 and 3͒, and a possibility of the formation of 2D gases in such materials was never discussed. The origin of these difficulties lies in the fact that charge densities induced by EFE cannot normally 4 exceed Ϸ10 13 cm −2 , which is several orders of magnitude smaller than area concentrations in nanometer thin films of a typical metal. Accordingly, any possible EFE in metals should be obscured by a massive contribution from bulk electrons. Prospects of the observation of a fully developed 2DS in a metallic material seem to be even more remote, because locally induced carriers could merge with the bulk Fermi sea without forming a distinct 2DS. Furthermore, because the screening length in metals never exceeds a few Å, EFE-induced carriers may also end up as a collection of puddles around surface irregularities rather than to form a continuous 2DS.In this Rapid, we report a strong ambipolar field effect at the surface of graphite. We have investigated EFE-induced carriers in this semimetal by studying their Shubnikov-de Haas ͑SdH͒ oscillations and analyzing the oscillations' dependence on gate voltage V g and temperature T. This has allowed us to fully characterize the carriers and prove their 2D character. The 2D electron and hole gases ͑2DEG and 2DHG, respectively͒ exhibit a surprisingly long mean free path l Ϸ 1 m, presumably due to the continuity and quality of the last few atomic layers at the surface of graphite where 2D carriers are residing. Our results are particularly important in view of current interest in the properties of thin 5-9 and ultrathin 10,11 graphitic films and recently renewed attention to anomalous transport in bulk graphite. 12,13 In our experiments, in order to minimize the bulk contribution, we used graphite films with thickness d from 5 to 50 nm. They were prepared by micromechanical cleavage of highly oriented pyrolytic graphite ͑HOPG...

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Electronic energy band parameters of graphite and their dependence on pressure, temperature and acceptor concentration

Cited by 63 publications

References 31 publications

Piezoelectricity in asymmetrically strained bilayer graphene

Piezoelectricity in asymmetrically strained bilayer graphene

Electronic states and Landau levels in graphene stacks

Two-dimensional electron and hole gases at the surface of graphite

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