[Physics] Valley meaning explanation for foreigner

quantum mechanicsterminology

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!

Best Answer

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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