Unexpected Density Dependence of Mobility of Electron Bubbles Trapped Below the Free Surface of Normal 3 He

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Unexpected Density Dependence of Mobility of Electron Bubbles Trapped Below the Free Surface of Normal 3 He H. Ikegami · T. Matsumoto · K. Kono

Received: 29 June 2012 / Accepted: 24 August 2012 / Published online: 6 September 2012 © Springer Science+Business Media, LLC 2012

Abstract We have performed mobility measurements of electron bubbles trapped below the free surface of normal 3 He at temperatures between 5 and 100 mK. We find that the mobility increases with increasing temperature, and that the increase at high temperatures is more significant for higher densities of electron bubbles. The observed mobility has no dependence on depth of the electron bubbles, indicating that the surface excitations have no contributions to the mobility. The observed increase of mobility as a function of density suggests that the Coulomb interaction between electron bubbles has some role in the momentum transfer from the electron bubble to 3 He quasiparticles. Keywords Normal 3 He · Ions 1 Introduction Transport of charged impurities, such as negative and positive ions, immersed in normal and superfluid 3 He have long been used as nonperturbing microscopic probes for investigating elementary excitations of Fermi liquid and anisotropic superfluid [1, 2]. A negative ion, or often called electron bubble, is a state of an electron self-trapped in a spherical open cavity created by the Pauli exclusion of electrons in the shell of surrounding helium atoms. Its radius R is 2.0 nm at zero pressure [1, 3], and its effective mass M− is about 300m3 (m3 is the atomic mass of 3 He). Transport properties of an electron bubble in bulk normal 3 He have been elucidated by the time-of-flight methods [3–6]. At temperatures higher than about 1 K, a traveling electron bubble experiences the Stoke’s drag from the viscous liquid 3 He. The mobility μ is then inversely proportional to the viscosity of the liquid [6]. With H. Ikegami () · T. Matsumoto · K. Kono Advanced Science Institute, RIKEN, Wako, Saitama 351-0198, Japan e-mail: [email protected]

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J Low Temp Phys (2013) 171:159–164

Fig. 1 Schematic diagram of the experimental cell for transport measurements of ions trapped below the free surface (Color figure online)

lowering temperature T , the mean-free-path of 3 He quasiparticles increases due to the Fermi degeneracy, and eventually exceeds the size of the electron bubble. In this long mean-free-path limit (or Knudsen limit) below 100 mK, the mobility is independent of temperature (μ ∼ 1 × 10−6 m2 /V s) [4, 5], which is accounted for in terms of collisions with 3 He quasiparticles. However, this temperature-independent mobility seems to be puzzling since, if the electron bubble is assumed to recoil as a free particle, the mobility should rise as T −2 below T0 = (m∗3 /M)TF ∼ 10 mK because of the inhibited scatterings due to the Fermi degeneracy (m∗3 is the effective mass of a 3 He quasiparticle and TF is Fermi temperature). This discrepancy was resolved by considering the recoil not as a free particle but as a particle undergoing Brownian

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