Abstract
Quasi-two-dimensional electrons on a thin liquid He film, which are strongly coupled to the gravity-capillary waves (ripplonic polarons), are investigated theoretically when a high magnetic field is applied perpendicularly to the surface. The free energy and the absorption line-shape of the cyclotron resonance are calculated with the use of the path-integral method. The expression for the cyclotron mass has the same form as the one for the weak coupling case, and is always smaller than the electron vacuum mass. The line-width has an exponential temperature dependence with a characteristic energy proportional to the coupling constant, and is very narrow. The pre-factor of the line-width is dependent both on the coupling constant and the magnetic field, and is different from that of the inverse DC collision time.
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