Multi-Electron Bubbles

Electrons above the surface of liquid helium feel an attractive force (from image charges) towards the surface but are prevented from penetrating the helium surface by a 1 eV energy barrier. The electrons will form a charged film at the helium surface [1]; high densities are achieved by placing grid with a positive potential below the helium surface. There exists a critical density of electrons above which the charged surface becomes unstable, and electrons are subsumed into the bulk helium by formation of a multielectron bubble (MEB) [2, 3]. These bubbles are typically tens of nanometers to a few hundred microns in radius, and contain from a few to more than 10⁸ electrons.

                The diameter scales as N^2/3 where N is the electron number. The MEBs so formed have lifetimes of a several milliseconds as they move to the potential grid where they are annihilated. In experiments by Volodin et al. [2] and by Albrecht and Leiderer [3] the multielectron bubbles were photographed  during their short lifetimes.

It is believed that bubbles with less than 15-20 electrons are unstable to fissioning to single electron bubbles.  On the other hand there are speculations that large bubbles can break up into two smaller bubbles as shown in the figure or movie of fission. For large bubbles the electrons repel each other via Coulomb forces and the electrons form a 2 D gas [4]. on a three dimensional spherical figure of bubble.

              Although known for a few decades, large bubbles have been short-lived due to the manner of production; this has frustrated the study of these fascinating electron balls.  The current program is aimed at stabilizing these balls of electrons in a long-lived state and studying their properties.  We propose to stabilize the multielectron bubbles for long periods of time.  Electrons will be created above liquid helium in a dome shaped cylindrical cell.  The helium liquid is raised to the top of the dome and the electrons find themselves trapped at the top of the dome in the minimum energy state,  a bubble. 

Bubbles are highly compressible and a modest pressure of under 1 bar can lead to an enormous compression.  The two dimensional gas on the surface can have a transition to a solid Wigner lattice figure of Wigner lattice.  This triangular lattice does not fit on a spherical surface so the ground state will have defects built into it.  Very high surface densities should be achievable in bubbles so that not only Wigner solidification can be seen, but also quantum melting at high density.

A spherical bubble can have distortions of the helium surface and such excitations are called spherical ripplons figure of ripplon. The eigenmodes are spherical harmonics Y_Lm  and are characterized by their quantum numbers L, m.   The frequency of ripplon modes can be zero to multi-megaherz [5].  Electrons in the spherical shell have quantum states also characterized by L, m.  The electron energies are discrete and each level has a degeneracy 2L+1.  The fermi energy in a modest sized bubble can be quite high, tens of kelvin, so it is not difficult to form a fermi degerate gas.

Due to the electron-ripplon interaction and the discrete energy levels, we expect an unusual form of superconductivity with Tc oscillating to zero and up as the electron number changes.  We plan to study the statics, dynamics, stability against fission, and tunneling of electrons.  Low temperature techniques and various forms of spectroscopy will be used to study collective (plasmons) [6] and single particle excitations and states.

[1]        M. W. Cole, "Electronic surface states of liquid helium," Rev. Mod. Phys., vol. 46, pp. 451-463, 1974.

[2]        A. P. Volodin, M. S. Khaikin, and V. S. Edel'man, "Multielectron bubbles in helium," JETP Lett., vol. 26, pp. 543, 1977.

[3]        U. Albrecht and P. Leiderer, "Multielectron Bubbles in Liquid Helium," Europhys. Lett., vol. 3, pp. 705-710, 1987.

[4]        M. M. Salomaa and G. A. Williams, " Structure and Stability of Multielectron Bubbles in Liquid Helium," Phys. Rev. Lett., vol. 47, pp. 1730-1733, 1981.

[5]        J. Tempere, I. F. Silvera, and J. T. Devreese, "The effect of pressure on  statics, dynamics, and stability of multielectron bubbles," Phys. Rev. Lett., vol. 87, pp. 275301-277304, 2001.

[6]        J. Tempere, I. F. Silvera, and J. DeVreese, " Fission of multi-electron bubbles in liquid helium." Phys. Rev. B, vol. 67, pp. 35402-35410, 2002