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saaskis is offline
Jun21-09, 01:20 AM
P: 66

two dirac cones are described by two bi-spinors of different chirality

The "valley isotropic representation" is quite often used by Beenakker, take a look at e.g. his colloquium on Klein tunneling: , Eq. (5).

Note that the term "pseudospin" is used (in the paper you referred to) to describe the degree of freedom originating from the two interprenating sublattices, not from the two valleys! So it is just as you said: when intervalley scattering can be neglected, one can work with one valley. Intervalley scattering requires short-range disorder, for example, and is quite often neglected in theoretical papers.

If one has to take the actual spin as well as the valley index into account, there are eight components in the spinor.

So let us now fix the quasi-particles to be at one valley. The conservation of pseudospin means, in my opinion, the conservation of helicity, or chirality. (These two terms are exactly the same thing for massless fermions, and are used interchangeably. Chirality is more common.) I mean that if an electron is turned into a hole in a np-junction, for example, one has to also revert the sign of momentum to keep the helicity the same.

Remember that helicity is defined [tex] \Sigma = \sigma \cdot p/|p| [/tex], so the eigenstates of the Hamiltonian are eigenstates of helicity. The eigenstates are [tex] \psi_{sk} = [1,s \cdot \exp(i \phi_k)] [/tex], multiplied by a plane-wave in the position representation.

You should take a look at the original papers by Ando, 1998 and Ando, 2002 if you really want to understand the absence of backscattering in clean graphene. But this is not necessary if you just want to understand Klein tunneling at an introductory level.