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What are spin and valley symmetries in graphene?

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I have been assigned a presentation on a part of a paper ( http://arxiv.org/ftp/arxiv/papers/1303/1303.6942.pdf ). My task is to present on the spin and valley symmetries in graphene, and relate it back to the paper above.

However, after looking at many papers detailed spin and valley degeneracy lifting and symmetry breaking, I still can't get my head round what spin and valley symmetries in graphene actually are.

So if anyone could give me a description of what these are and maybe any other relevant properties that are worth presenting on that would be incredibly helpful.

I apologise for the vagueness of my question, if I could be more specific I probably wouldnt need to ask in the first place!!

Thanks in advance!

This post imported from StackExchange Physics at 2014-10-11 09:49 (UTC), posted by SE-user Tom Rylands

asked Oct 10, 2014 in Theoretical Physics by Tom Rylands (5 points) [ no revision ]

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