Exciton density pattern formation in laser irradiated quantum wells under electrodes of various shapes

The condensation of indirect excitons in double quantum wells is studied in an electric field created by electrodes of different shapes. The finite value of the exciton lifetime, the pumping and nonuniformity of the electric field under the electrode are taken into account. It is shown that islands of exciton condensed phase emerge under electrodes when the pumping exceeds a certain threshold value. They appear first under the rim where the potential energy of excitons has a dip. Calculations predict a complicated evolution of the exciton density distribution: from the gaseous phase at low laser intensities to the condensed phase in the whole area under the electrode at larger intensities. Therefore, the configurations of the exciton condensed phase may be manipulated by choosing the setups with conductive electrodes of different shapes via forming specific potentials of the electrical field and controlled by the level of the laser irradiation