The Maths of Graphene

Graphene was made in 2004 by Andre Geim and other scientists. It a carbon allotrope consisting of a single molecule thick layer of carbon atoms held together by strong covalent bonds. Graphene has been described as a 2D material. It is the first material to be so-called and throws up certain theoretical questions.

Previously all matter was considered, no matter how small as belonging in 3 dimensions. This was the flaw of traditional paper based geometry – it was only in 2 dimensions and so could only exist in a theoretical form, much in a similar way that Plato’s ideal forms could not exist in the real world but somehow informed all matter and allowed us to grasp the beauty of things that approximated closer to the ideal form.

In physics graphene is viewed as a 2 dimensional substance that exists in 3D euclidean space. It sometimes referred to as an abstract surface. However, to exist such 2 dimensional surfaces must be curved and strained. This curvature and strain act on the charge carriers to create fields. These fields set up a magnetic influence that form cycles comparable to ’Lamor Cycles’.

The mathematician M. V. Karasev at the Moscow Insistute of Electronics and Mathematics has written up much of the math formulas to map the resulting forces caused by the curvature and strain set up by a two dimensional surface. You can find a copy of his important paper at: springerlink.com.

Discussing the math involved in dealing with 2D material also gives rise the possibility of being able to study and mathematically fix materials that can be detected in 4 or more dimensions. What magentic and and electrical characteristics would such material have?

The future may be a mystery, but the future seems to be always providing us with new ways to test our theoretical understanding of the world.

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