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We compute electromagnetic, gravitational and mixed linear response functionsof two- dimensional free fermions in external quantizing magnetic field at aninteger filling factor. The results are presented in the form of the effectiveaction and as an expansion of currents and stresses in wave-vectors andfrequencies of the probing electromagnetic and metric fields. We identify theterms in linear response functions coming from geometric Chern-Simons, Wen-Zee,and gravitational Chern-Simons terms in effective action. We derive theexpressions for Hall conductivity, Hall viscosity and find the current andcharge density responses to the spatial curvature as well as stresses caused byinhomogeneous electromagnetic fields.

Electromagnetic and gravitational responses of two-dimensional non-interacting electrons in background magnetic field