Non-universal Casimir effect in saturated superfluid⁴He films at T_λ

Abstract

Measurements of Casimir effects in 4 He films in the vicinity of the bulk superfluid transition temperature T λ have been carried out, where changes in the film thickness and the superfluid density are both monitored as a function of temperature. The Kosterlitz-Thouless superfluid onset temperature in the film is found to occur just as the Casimir dip in the film thickness from critical fluctuations becomes evident. Additionally, a new film-thickening effect is observed precisely at T λ when the temperature is swept extremely slowly. We propose that this is a non-universal Casimir effect arising from the viscous suppression of second sound modes in the film. PACS numbers: 67.25.dj, 67.25.bh, 67.25.dg, 68.35.Md Copyright 2013. All rights reserved.Saturated liquid 4 He films, in contact with the bulk liquid, form an illuminating model system as a condensed matter analogue of the electromagnetic Casimir effect. Thermal fluctuations in the film are limited by the finite thickness of the film, leading to a free-energy difference with the unlimited fluctuations in the bulk [1]. This causes a change in the film thickness as the atoms move to minimize the free energy. The equilibrium thickness is determined by an energy-balance relation per atom of mass m for a film of thickness d at a height h above the bulk helium surface,where the substrate van der Waals interaction U vdW at the film surface [2], including retardation effects, is given byThis is the main term determining the film thickness, with γ 0 the van der Waals constant equal to 3.59×10 −13 ergÅ 3 for a Cu substrate, and d 1/2 = 193Å . The fluctuation-induced Casimir forces K then produce small additional shifts ∆d as the temperature is swept near the bulk superfluid transition temperature T λ . The force K crit comes from critical fluctuations near the transition temperature, i.e. the vortex loops in the model of Ref. [3]. Finite-size scaling theories [4][5][6] 43Å the amplitude of the coherence length above T λ (using the normalization of Ref.[7]), and V = 45.8Å 3 the volume per helium atom. Experiments [8][9][10][11] have observed a dip in the film thickness corresponding to these critical fluctuations in agreement with simulations [12], and data collapse of films of different thickness confirmed the form of the scaling. One factor not well determined in experiments to date is the location of the Kosterlitz-Thouless (KT) superfluid transition relative to the dip in film thickness. A quartz microbalance oscillator technique at 5 MHz [10] seemed to show the transition as occurring at a temperature somewhat below the bottom of the dip, but the exact location could not be pinpointed because the high frequency greatly broadens the KT transition [13].The term K G in Eq. 1 refers to the free energy difference between bulk and film due to thermally excited Goldstone modes [14]. It was originally proposed that such modes should include the second sound mode in the case of liquid helium [11,15,16], but since we question this we include instead a separate term K 2 fo...