Order formation and superfluidity of excitons in type-II semiconductor quantum wells

The condensed state and superfluidity of excitons in type-II semiconductor quantum wells (QW’s) are investigated theoretically. Since the excitons in type-II QW’s have translational motion along the layer, the assembly of them is regarded as an interacting dilute quasi-two-dimensional Bose gas. This system is advantageous for our purpose because those excitons have a long lifetime of the order of ${10}^{-6}\mathrm{s},$ and their transport mechanism can be directly studied in experiments by observing electric current since the excitons consist of spatially separated electron-hole pairs. Using the exciton wave functions obtained by the variational method, the exciton-exciton interaction is calculated and found to be repulsive when the thickness of the QW is thinner than a critical value. To illustrate the situation, we carry out the numerical computation adopting a model system with material constants appropriate to GaAs/AlAs type-II QW’s. The basic equation for the phase of the condensate wave function is derived when the exciton system is irradiated by a weak laser light at zero temperature. Solving the equation in the presence of the external current $J_{\mathrm{ex}},$ we study the stationary spatial pattern of the phase of the condensate wave function. It is shown that there appears a vortex lattice with a net supercurrent when $J_{\mathrm{ex}}$ is larger than a critical value; the period of the lattice is determined as a function of $J_{\mathrm{ex}}.$ We calculate the magnetic field induced by the current in the vortex lattice, and discuss a possibility of an experimental observation of the critical current. Such a direct observation of the exciton transport will provide unambiguous experimental evidence for the superfluidity of excitons.