We report the use of the thermopower technique (Seebeck effect) as an effective tool for discovery of 'hidden' (for standard techniques, like x-ray, synchrotron, Raman, etc) phases of substances. Applying the thermopower technique to a set of GaAs single crystals pressurized in a sintered diamond anvil cell, we found an unknown high-pressure semimetal phase with the electron type of conductivity, similar to that recently discovered in ZnTe. A possible crystal structure of this phase is discussed. The pressure-temperature (P-T) phase diagrams of GaAs and ZnTe are compared.