  We analyze the instability of an unpolarized uniform quantum plasma
consisting of two oppositely charged fermionic components with varying mass
ratios, against charge and spin density waves (CDWs and SDWs). Using density
functional theory, we treat each component with the local spin density
approximation and a rescaled exchange-correlation functional. Interactions
between different components are treated with a mean-field approximation. In
both two- and three-dimensions, we find leading unstable CDW modes in the
second-order expansion of the energy functional, which would induce the
transition to quantum liquid crystals. The transition point and the length of
the wave-vector are computed numerically. Discontinuous ranges of the
wave-vector are found for different mass ratios between the two components,
indicating exotic quantum phase transitions. Phase diagrams are obtained and a
scaling relation is proposed to generalize the results to two-component
fermionic plasmas with any mass scale. We discuss the implications of our
results and directions for further improvement in treating quantum plasmas.
