The Larsen perturbation method is adopted to study the influence of magnetic fields on polarons in realistic heterojunctions in a quasi-two-dimension approximation. The interaction between an electron and both the bulk longitudinal optical phonons and the two branches of interface optical phonons is taken into account to show the influence of magnetic fields at different ranges on the polaron cyclotron mass due to the coupling of the electron with each branch of phonon modes. The result indicates that not only do the bulk phonons influence the polaron cyclotron mass, but the interface phonons do as well. The pressure effect on the cyclotron mass is also discussed. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 200671.38.Fp Large or Frohlich polarons, 73.20.-r Electron states at surfaces and interfaces, 73.40.Kp III-V semiconductor-to-semiconductor contacts, 62.50.+p High-pressure and shock wave effects in solids and liquids (for high pressure apparatus and techniques),
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