Hello, I was looking for a electrical conductivity and resistivity value of graphene sheet but could not find any. Most of the info says it is superconductive without any value. Will be happy to have some value with reference. Thanks
Graphene is a semi-metal which means its band structure has no forbidden gap the same as for metal in contrast to that of semiconductors. Meanwhile, its conduction band is empty at absolute temperature as for semiconductors in contrast to metal. Its electrical conductivity (resistivity) σ, strongly depends on its doping (its means the number of charge carriers available in the sheet). Either electrons or holes). The relationship σ(n) is linear with the proportionality constant being the mobility. σ(n) = (w/L)xµxen. w, L are the geometrical dimensions of the sheet (w : the width, L the length. Therefore, depending on the density of carriers, σ(n) either decreases or increases. The minimum value of conductivity is reached near the so called Dirac neutrality point where the carrier density in the sheet vanishes (n = 0).
They were many debate regarding the exact fundament value of this minimum conductivity (resistivity). However σ = (4 e^2)/(pi x h) is often reported theoretically (Electronic transport in two-dimensional graphene, Rev. Mod. Phys. 83, 2, 2011. Page 443). While experiments reported a value in the range of 2-12e^2/h. (Measurement of Scattering Rate and Minimum Conductivity in Graphene. Tan et al. PRL 99, 246803 (2007) ). So, one can keep in mean that the minimun conductivity of graphene is the quantum conductivity 2e^2/h that is 7.75 E-5 siemens.
A common way to extimate the transport of graphene (as in any material) is the mobility of carriers, which in principle does depends on the doping although it may vary from sample to sample as a matter of experiemental realities and fabrication processes). One of the highest mobility reported in graphene is 7×10^4 cm^2/v·s (Dielectric screening enhanced performance in graphene FET, Fang Chen et al. Nano. Let 2009). The value of 1 000 000 cm^2/v·s has even been mentioned (https://fr.wikipedia.org/wiki/Mobilit%C3%A9_des_porteurs_de_charge (in French !)). This makes graphene one of the best conductor ever reported.
I hope I have provided enough details for answering your question.