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We consider a massive fermionic quantum field localized on a plane inexternal constant and homogeneous electric and magnetic fields. The magneticfield is perpendicular to the plane and the electric field is parallel. Thecomplete set of solutions to the Dirac equation is presented. As importantphysical characteristics of the vacuum state, the fermion condensate and theexpectation value of the energy-momentum tensor are investigated. Therenormalization is performed using the Hurwitz function. The results arecompared with those previously studied in the case of zero electric field. Wediscuss the behavior of the vacuum expectation values in different regions forthe values of the problem parameters. Applications of the results include theelectronic subsystem of graphene sheet described by the Dirac model in thelong-wavelength approximation.

Fermionic condensate and the vacuum energy-momentum tensor for planar fermions in homogeneous electric and magnetic fields