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English is not my native language and I have some hard time translating this word. I was searching in couple dictionaries(both paper and online) and could not find it. Could anyone provide me definition of word "Valley". example usage:

Suggest using only the valley degree of freedom

valley and spin degeneracy

Valley relaxation


Thanks in advance!

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    $\begingroup$ It seems like it just means a minimum energy state. Something from a higher energy state could "roll" down the potential to a lower energy state which could be called a valley. $\endgroup$ – Brandon Enright Mar 4 '14 at 21:39
  • $\begingroup$ In my opinion it do not fit to example sentences. I have found definition like Yours in dictionary. $\endgroup$ – user117937 Mar 4 '14 at 22:01
  • $\begingroup$ @BrandonEnright No, that's not right. Valley in this case refers to Dirac points as noted below. Why valley? Because in the most commonly analyzed example of graphene, at zero doping, all the states in the bottom Dirac cone are filled, which leaves the top Dirac cone empty. This empty Dirac cone looks like a valley, like the letter 'V', and the interesting physics comes from exciting electrons into V. $\endgroup$ – nervxxx Mar 5 '14 at 0:21
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Sounds like graphene physics or something similar. You won't find it in a dictionary.

In the band structures of many materials, it is common to find multiple similar points in reciprocal (momentum) space. For example, in silicon's band structure there are six distinct conduction bands that all have similar behaviour. These six points came to be known as valleys. Among other details, the "valley degeneracy" of 6 is an important factor to take into account when calculating electronic properties of silicon.

Graphene's band structure has two distinct bands. These are often known as the K and K' valleys, and they are centered around the K and K' points in reciprocal space. They are very symmetric and also are closely related to a spin-like property of the electrons in the graphene, known as pseudospin. In essence, you can imagine the K valley as being "pseudospin up" and the K' valley as being "pseudospin down". An electron can also be in a superposition of pseudospin up and down, so you can imagine "pseudospin left", "pseudospin right", and so on. The resemblance with spin comes from the fact that scattering processes between the two valleys are fairly rare, and so pseudospin is conserved over some distance. Also, it means that besides the normal factor of 2 degeneracy from real spin, the electrons in graphene have a further factor of 2 degeneracy from the valleys / spin. On the other hand, pseudospin is not associated with a magnetic moment, unlike real spin.

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