Multicomponent electron-hole liquid in Si/SiGe quantum wells

The density functional theory is used to calculate the energy of an electron-hole liquid in Si/Si$_{1-x}$Ge$_x$/Si quantum wells. Three one-dimensional nonlinear Schrödinger equations for electrons and light and heavy holes are solved numerically. It is shown that, in shallow quantum wells (small $x$), both light and heavy holes exist in the electron-hole liquid. Upon an increase in the Ge content, a transition to a state with one type of holes occurs, with the equilibrium density of electron-hole pairs decreasing by more than a factor of $2$.