According to "Nat. Nanotechnol., vol. 7, no. 8, pp. 488–489, 2012 (http://www.nature.com/nnano/journal/v7/n8/full/nnano.2012.117.html?WT.ec_id=NNANO-201208)": Valley quantum number is associated with different crystal axes that differ only in their orientations. Such axes can support electron waves that are also identical apart from their direction (or, more precisely, their momentum),so an additional discrete index known as the valley quantum number is needed to fully describe these waves. This argument raises a question: Si and Ge have the same crystal structure. Therefore according to this statement they have to have the same valleys. However Si has 6 valleys in the ##\Gamma X## direction while Ge has 4 valleys in the ##\Gamma L## direction. I don'n know what goes wrong with my thought.