By Toshiaki Enoki, Tsuneya Ando
From a chemistry element, graphene is the extrapolated severe of condensed polycyclic hydrocarbon molecules to endless dimension. right here, the idea that on aromaticity which natural chemists make the most of is appropriate. attention-grabbing concerns showing among physics and chemistry are said in nano-sized graphene (nanographene), as we realize the significance of the form of nanographene in figuring out its digital constitution. during this ebook, the basic matters at the digital, magnetic, and chemical houses of condensed polycyclic hyodrocarbon molecules, nanographene and graphene are comprehensively discussed.
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Extra resources for Physics and chemistry of graphene : graphene to nanographene
B) > 0. bulk graphite [49, 50]. The thermodynamic function gs gv = −kB T ϕ(εn ), 2πl 2 n . 49) ϕ(ε) = ln 1 + exp[β(ζ − ε)] , where T is the temperature, kB the Boltzmann constant, β = 1/kB T , and ζ the chemical potential. Let ns be the electron concentration. Then, the free energy is written as F = ns ζ + . 50) With the use of the relation ns = −(∂ /∂ζ ) B , the magnetization is given by ∂F ∂ M =− =− . 51) ∂ B ns ∂B ζ Therefore, susceptibility χ , deﬁned by M = χ B for small B, can be obtained by calculating up to the order of B 2 .
13 shows the minimum conductivity at the Dirac point. For very short-range case dkc < 1, the conductivity is nearly independent of W, where kc is the cufoﬀ momentum given by γ kc ∼ γ0 corresponding to the region where the linear dispersion is approximately valid. For dkc > 1, on the other hand, the conductivity increases with W, depending on dkc . States at the Dirac point have higher k components because of strong forward scattering caused by long-range scatterers. These higher k states are weakly scattered in backward direction and therefore tend to have large contribution to the conductivity.
Bulk graphite [49, 50]. The thermodynamic function gs gv = −kB T ϕ(εn ), 2πl 2 n . 49) ϕ(ε) = ln 1 + exp[β(ζ − ε)] , where T is the temperature, kB the Boltzmann constant, β = 1/kB T , and ζ the chemical potential. Let ns be the electron concentration. Then, the free energy is written as F = ns ζ + . 50) With the use of the relation ns = −(∂ /∂ζ ) B , the magnetization is given by ∂F ∂ M =− =− . 51) ∂ B ns ∂B ζ Therefore, susceptibility χ , deﬁned by M = χ B for small B, can be obtained by calculating up to the order of B 2 .