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Dynamic response of partially spin- and valley-polarised two-dimensional electron liquids

The growing field of valleytronics provides new promising physics. Here, we focus on the collective modes of an infinitely thin electron layer with a binary valley degree of freedom that is unequally occupied. The spin populations are allowed to be imbalanced, too. This system can support four collective modes and two anti-resonances emerge. We study this copious dynamics in the spin- and valley-sensitive random phase approximation (RPA) and explain the uncommon behaviour by building a bridge from the many-fermion system to its bosonic counterpart. For completeness, we also report the RPA exchange and correlation energies for arbitrary spin and valley polarisation. A phase transition occurs at from the four-component to the ferro-magnetic, single-valley-occupation state.