Theory of Transport in Graphene

Graphene, a two-dimensional sheet of carbon, is considered one of the materials most likely to produce the next breakthrough in the electronics revolution.  Ideal graphene has the highest electron mobility of any material, giving rise to high electron and thermal conductivities, both of which are important in the next generation of highly efficient electronic devices.  Actual devices never achieve the ideal properties of graphene due to the interactions between the graphene and the other parts of the devices, like the substrate and the contacts.  If graphene is going to be an important part of the next revolution in information processing, it is necessary to fabricate it as cheaply and as well as silicon.  Understanding the consequences of the interaction of graphene with its environment and the consequences of different growth techniques is crucial to developing graphene into an important material.
 

When many graphene layers are stacked on top of each other, the result is graphite. When just a two layers are stacked, the result is referred to as “bilayer graphene” and when there are just a few layers, “few layer graphene.” While single-layer graphene has been studied more than these other forms, the other forms have some potential advantages for applications. One advantage is that some of the growth techniques that are most likely to scale up to device production naturally produce few layer graphene. In addition, it is possible in few layer graphene to create a band gap (one of the important features of a semiconductor for electronic devices) by applying an electric field perpendicular to the layers. We have carried out a number of calculations to understand the transport properties of bilayer and few layer graphene. 

Bilayer and few layer graphene have screening properties to “cover up” defects that are very different from the properties of single layer graphene. Since the screening is very different, the ability to conduct electricity varies significantly as the density of electrons in the material is varied. Therefore, it may be possible to determine the type of graphene just from the way its conductivity varies as a function of the electron density.

One of the earliest methods developed to fabricate graphene likely to meet the needs of the electronics industry is to sublimate silicon from a silicon carbide crystal. The carbon that is left behind forms few-layer graphene sheets with many of the properties of single layer graphene. Surprisingly, scanning tunneling microscopy measurements made in the CNST show that the electrons in the top layer appear to behave as if they are in an isolated layer. The top layer is rotated with respect to the layer below it, and theoretical calculations explain why this leads to small coupling for all but the smallest rotation angles. This decoupling breaks down at the lowest temperatures and highest magnetic fields. Other calculations show that the flow of electrons from layer to layer could also cause this breakdown.

• Semiclassical Boltzmann transport theory for graphene multilayers, H. Min, P. Jain, S. Adam, and M. D. Stiles, Physical Review B 83, 195117 (2011).
  NIST Publication Database          Journal Web Site
• Landau levels and band bending in few-layer epitaxial graphene, H. Min, S. Adam, Y. J. Song, J. A. Stroscio, M. D. Stiles, and A. H. MacDonald, Physical Review B 83, 155430 (2011).
  NIST Publication Database          Journal Web Site
• Temperature dependence of the diffusive conductivity of bilayer graphene, S. Adam and M. D. Stiles, Physical Review B 82, 075423 (2010).
  NIST Publication Database          Journal Web Site

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