Bistability and discontinuity in the tunnel current of two-dimensional electron-hole layers

We present a detailed study of a recently reported discontinuity and bistability in a 12-nm GaAs/AlAs single-barrier $p-i-n$ heterostructure, where a system of spatially separated two-dimensional electron and hole $(e-h)$ layers of equal and tunable density is realized. Both features appear at $T\lesssim 300\hspace{0.5em}\mathrm{mK}$ and are strongly enhanced in a magnetic field $B\gtrsim 10\hspace{0.5em}\mathrm{T}$ perpendicular to the layers, whereas they are suppressed by $B\sim 1\hspace{0.5em}\mathrm{T}$ parallel to the layers. They correspond to a discontinuity in the $e-h$ density and in the phase of the current magneto-oscillations. Whereas the high-current state has the expected properties of the uncoupled $e-h$ layers, the low-current state behaves anomalously under all circumstances, and we identify them with a gas of spatially indirect excitons with binding energy $0.03\hspace{0.5em}\mathrm{meV}\lesssim E_b\lesssim 0.3\hspace{0.5em}\mathrm{meV}$ and $0.5\hspace{0.5em}\mathrm{meV}\lesssim E_b\lesssim 5\hspace{0.5em}\mathrm{meV}$ at $B=0\mathrm{}$ and $B=10\mathrm{}\hspace{0.5em}\mathrm{T},$ respectively. We interpret the bistability as a transition between the two regimes, which arises because of the competition between the in-plane screening, determined by the average $e-e\hspace{0.5em}(h-h)$ distance and the magnetic length, and the interlayer $e-h$ attraction.