Shift in cyclotron resonance of electrons on liquid helium surfaces

Polaron impurity states on a liquid helium film

“…Since the helium surface is deformed we have to solve simultaneously the Schrödinger equation for the electron and the mechanical equilibrium equation for the surface. Considering that external electrical and magnetic fields are present, the Schrödinger equation for the electron can be written as 15,17 …”

10.1007/s11447-008-2010-3

“…Other experiments with electrons on a helium surface also show considerable inconsistency between theory and experiment. Thus, the theory in [13] predicts a shift of the cyclotron resonance frequency as a function of the clamping electric field two to three times less than the one experimentally measured in [14] (see [1,2] for a review). The measured linewidth of the "vertical" (i.e., intersubband) electron transitions at low temperature is also considerably larger than that predicted by the theory.…”

“…Assuming the electron scattering amplitude on vapor He atoms and on SLAs to be identical, we use (6) to calculate the electron mobility η e as (12) where we introduce the notation (13) and (14) In a weak clamping field E ⊥ Ӷ 200 V/cm, we can take wavefunction (3) for the ground electron level, which gives…”

“…(3) vanishes at the surface. Therefore, integral (13) depends strongly on the behavior of the electron wavefunction near the helium surface. The surface electron spectrum in (2) and the ground state wavefunction (3) were calculated assuming that the potential barrier at the helium surface is infinite.…”

“…Normalized scattering rate on SLAs, which is proportional to integral(13), as a function of the clamping electric field. This figure shows that the scattering rate on SLAs depends very strongly on the clamping field (I S = I S (E) is calculated numerically and = I S (E = 0) is as given by Eq.…”