I am trying to find an approximate value of the electrical conductivity $\sigma$ of graphene in units of S/m or S/cm. This table on Wikipedia gives $\sigma$ values for a variety of materials (including references), but I do not see graphene.
In the classic 2004 paper on graphene by Novoselov and Geim (Novoselov et al., Science 2004, 306, 666: available here), I see a plot of $\sigma \text{ (m} \Omega^{-1})$ versus $V_g \text{ (V)}$, where $V_g$ is the gate voltage:
Based on that plot, what can we say about the electrical conductivity $\sigma$?
One confusing thing about the above plot is that it is in $\text{m} \Omega^{-1}$. But $1 \text{ S} = 1 \text{ } \Omega^{-1}$, so in the plot is given in units proportional to S, not S/m. Why is this?
Best Answer
Resistivity is the relevant parameter for three-dimensional materials. Sheet resistance (less commonly called "sheet resistivity") is the relevant parameter for two-dimensional materials, and its inverse is called "sheet conductance" or "sheet conductivity". In the Novoselov paper you cited, they talk about sheet resistance and sheet conductance. Please forgive them for the bad habit of using the words "resistivity" and "conductivity" when they mean "sheet resistance" and "sheet conductance" respectively! (When they first define it they do actually use the word "sheet", but then they start leaving it out to be concise.)
The units of sheet resistance are ohms, and sheet conductance is siemens. (Sometimes the unit of sheet resistance is written $\Omega/\Box$, "ohms per square", so that you don't mistakenly think it's an ordinary resistance.)
For most purposes the sheet conductance or sheet resistance of graphene is a far more relevant parameter than the "bulk" conductivity or resistivity. But if you really have to convert one to the other, you would multiply or divide by the thickness of graphene. [The thickness of graphene is not very well defined ... therefore the bulk conductivity and resistivity are not very well defined either. The sheet resistance, on the other hand, is perfectly well defined.]