General relation between band-gap renormalization and carrier density in two-dimensional electron-hole plasmas

We have analyzed the dependence of the band-gap renormalization due to many-body effects on the carrier density in electron-hole plasmas in quasi-two-dimensional systems. A comparison of the data obtained at low lattice temperatures in various $\mathrm{GaAs}/{\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$, GaSb/AlSb, and ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}/\mathrm{InP}$ multiple-quantum-well structures shows that the band-gap shift, if scaled in effective excitonic units, is independent of the material properties. This new general relation governing the dependence of the band-gap renormalization on the plasma density in two-dimensional systems is confirmed by theoretical considerations.