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Valleytronics behaviour relies on one or both of the following quantities being nonzero in certain solid state systems. These two are:

Berry curvature

Magnetic moment

In this answer, I will focus on the first part, namely Berry curvature and how it gives rise to the so called valleytronics behaviour (actually the two quantities above are not independent). I will only talk about atomically thin or the so called 2D materials, since that is my field of expertise. Also, I will not consider the interesting effects arising from spin orbit coupling. I will try to keep the language as nontechnical as possible. www.quora.com

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