Experimental conditions for the observation of electron-hole superfluidity in GaAs heterostructures

The experimental parameter ranges needed to generate superfluidity in optical and drag experiments in GaAs double quantum wells are determined using a formalism that includes self-consistent screening of the Coulomb pairing interaction in the presence of the superfluid. The very different electron and hole masses in GaAs make this a particularly interesting system for superfluidity with exotic superfluid phases predicted in the BCS-Bose-Einstein condensation crossover regime. We find that the density and temperature ranges for superfluidity cover the range for which optical experiments have observed indications of superfluidity but that existing drag experiments lie outside the superfluid range. We also show that, for samples with low mobility with no macroscopically connected superfluidity, if the superfluidity survives in randomly distributed localized pockets, standard quantum capacitance measurements could detect these pockets.

Figure 1

Conduction and valence bands for a sample from Ref. [32] in the presence of gate potentials and a bias between the wells [35] as obtained using a self-consistent Poisson-Schrödinger solver [36]: quantum well widths: $w=15\mathrm{nm}$ and ${\mathrm{Al}}_{0.9}{\mathrm{Ga}}_{0.1}\mathrm{As}$ barrier thickness: $t_B=10\mathrm{nm}$. The dashed green line: Fermi-level $E_F$. The vertical black dotted lines mark the centers of the wells. ${\varphi }_e\left(z\right)$ and ${\varphi }_h\left(z\right)$ are the resulting electron and hole single-particle wave functions confined in the wells. Note that the separation of the peaks in ${\varphi }_e\left(z\right)$ and ${\varphi }_h\left(z\right)$ is larger than the distance between the centers of the two wells.

Figure 2

${\mathrm{\Delta }}_{\max }$ is the maximum value of the zero-$T$ momentum-dependent superfluid gap as a function of $n$, the equal electron, and hole densities. The solid red line: $w=8$ and $t_B=4\mathrm{nm}$ (sample: Refs. [28, 29, 30]); dashed-dotted purple line: $w=12$ and $t_B=1.1\mathrm{nm}$ (sample: Ref. [31]). The horizontal black bar indicates the density range over which anomalous behavior was observed in Refs. [28, 29, 30].

Figure 3

(a) ${\mathrm{\Delta }}_{\max }$ as a function of $n$. The solid blue line: $w=15$ and $t_B=10\mathrm{nm}$ (sample: Ref. [32]); the dashed-dotted green line: $w=7$ and $t_B=8\mathrm{nm}$; the dotted red line: $w=10$ and $t_B=5\mathrm{nm}$. (b) Corresponding inverse of total capacitance $C_m^{-1}$ as a function of density $n$. The inverse of total capacitance in the normal state ${\left(C_m^N\right)}^{-1}$ is indicated.