We have measured tunneling rates out of an electron layer trapped at a liquid-helium-vacuum interface in the presence of a magnetic field. When the field is transverse to the escape direction we find a striking suppression of the tunneling rates: a field of 3000 G at 40 mK reduces the tunneling current by four orders of magnitude. As the temperature increases the magnetic suppression of tunneling diminishes until it disappears completely above 250 mK. By contrast parallel fields have no effect on the tunneling rates.PACS numbers: 73.40.Gk, 73.20.Dx The transport of electrons through potential barriers in the presence of a magnetic field is a powerful tool for understanding the physics of tunneling in the presence of correlations and in various applications such as the design and control of tunneling devices [1][2][3][4][5]. Experiments on magnetotunneling (MT) have thus far focused on semiconductor heterostructures [1,5] where the magnetic field has only a slight effect on the tunneling rates. The relative importance of the magnetic field may be estimated by comparing the time to complete a cyclotron precession, ~ o^T 1 , to a characteristic time scale of tunneling which is usually taken as [6] T ~ f** dz/sj2 [U(z) -E]/m. Here cv c = eB/m*c is the cyclotron frequency, ra, e, and E are the electronic mass, charge, and total energy, U(z) is its potential energy, B is the magnetic field amplitude, and 21,22 are the turning points of the potential.In this Letter we report on measurements of MT for surface state electrons trapped at a liquid-heliumvacuum interface. In this system the barrier size and the electron densities are readily tuned in situ over a wide range of parameters that are not accessible in heterostructures [7][8][9]. The barriers can be made very wide and shallow so that r ~ 20 psec is two orders of magnitude larger than in heterostructures and the strong magnetic field limit (00 C T > 1) is reached for fields as low as 2500 G. For these barriers we observe a strong suppression of the tunneling rates in the presence of a transverse magnetic field B t (transverse to the direction of tunneling and parallel to the electron layer). As illustrated in Figs. 1-3 the tunneling currents depend exponentially on B*l and exhibit an unexpected temperature and density dependence.Our experimental setup consists of a cylindrical cell of height 2.5=b0.05 mm that is half filled with liquid helium supporting the electron disk. The electrons are prevented from escaping to the sides with a negatively biased guard ring of diameter 18±0.05 mm. A voltage V t applied between the top plate of the cell and the grounded bottom plate creates an external field with which the electrons can be pressed toward or extracted from the surface. The cell is positioned at the center of a double split superconducting magnet that can provide up to 0.5 T of either transverse and/or parallel field. The electron density is determined from the plasmon spectrum of the electron disk which is measured with an rf spectrometer. From the known 2D ...

In order to explain the experimental results on Cu(100), Ag(111), Ag thin films, graphite, and H2 bubbles in Cu, the ortho-para conversion rates of H2 and D2 adsorbed on metal and paramagnetic surfaces at low temperatures have been considered. The conversion rates due to magnetic dipoledipole, Fermi contact, and spin-orbit interaction between the conduction electrons, and nuclear spins of H2 (D2) are calculated to elucidate the role of the metal surface. Although the rates on clean metal surfaces are found to be too slow to account for the observed rates on Ag, they may explain the catalytic conversion on H~bubble surfaces at 1.3 K. Additionally, effects of impurities and defects on the surface are investigated by calculating the conversion rate in two-dimensional solid D2 (H&) by emission of one (two) phonon(s). Fast conversion rates observed on Ag and graphite surfaces as well as on the surfaces of H2 bubbles may be accounted for by paramagnetic impurities or defects. On Grafoil, both in (&3X&3)R30' commensurate and incommensurate solid phase, a temperature-independent conversion rate is predicted if the mobility of the molecules is high enough to prevent concentration gradients.

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We show that the tunneling time~of a localized electron tunneling through a barrier modulated by a microwave field satisfies the relation DE~=Pi, where the uncertainty hE in the energy of the coupled electron-field system is determined by the response of the electron to the time-dependent fields. We express hE as the expectation value of an operator and point out how it can be measured experimentally.