Specific Heat of Disordered SuperfluidHe3

Abstract

The specific heat of superfluid 3 He, disordered by a silica aerogel, is found to have a sharp discontinuity marking the thermodynamic transition to superfluidity at a temperature reduced from that of bulk 3 He. The magnitude of the discontinuity is also suppressed. This disorder effect can be understood from the Ginzburg-Landau theory which takes into account elastic quasiparticle scattering suppressing both the transition temperature and the amplitude of the order parameter. We infer that the limiting temperature dependence of the specific heat is linear at low temperatures in the disordered superfluid state, consistent with predictions of gapless excitations everywhere on the Fermi surface.PACS numbers: 67.57.Bc, 67.57.Pq Two essential characteristics of superconductors are manifest in the specific heat. First, there is a jump at the transition temperature of magnitude that depends on the strength of the electron pair interactions that lead to superconductivity. Secondly, the temperature dependence at low temperature gives a fingerprint of the energy gap structure. Consequently, the measurement of the specific heat is one of the most fundamental to understanding the nature of superconductivity. In fully gapped superconductors, such as aluminum, the specific heat decreases exponentially with decreasing temperature following an Arrhenius relation[1], thereby demonstrating unambiguously the existence of a full gap in the electron quasiparticle excitation spectrum and providing a direct measurement of its size. Both of these basic thermodynamic behaviors conform to predictions of the Bardeen, Cooper, and Schrieffer theory[2] and can be expected to hold in general for any condensate of fermion pairs into a state that is fully gapped. This is precisely what is expected [3] and observed [4] for the B-phase of superfluid 3 He, a pwave superfluid with an isotropic energy gap, similar to conventional s-wave superconductors.Shortly after the success of BCS theory it was sought to understand how perturbations, such as impurities, modify superconducting behavior. It was found [5] that magnetic scattering of quasiparticles suppresses both the transition temperature and the gap magnitude leading to 'gapless superconductivity' [2]. The same should be true for all superconductors and fermion superfluids even those that do not have s-wave states in which case all forms of elastic scattering will produce these suppression effects [6]. In particular it should be true for superfluid 3 He. In this letter we present systematic measurements of the heat capacity in the B-phase of superfluid 3 He, disordered by impurities, demonstrating suppression of the transition temperature, suppression of the order parameter, and gapless superfluid behavior.Superfluid 3 He is a unique example of a Cooper pair condensation. It was the first unconventional pairing state discovered. By unconventional we mean that there are symmetries of the normal Fermi liquid that are spontaneously broken in the superfluid phases in addition to gauge symmetry, ...

Impurity Effects of Aerogel in Superfluid3He

“…16 and compared with the calculations of Sharma and Sauls. 53) For these data they found 35) a best fit value of ¼ 150 nm. Evidence for gapless behavior can also be found in the low temperature magnetic susceptibility, 18,30,57) the thermal conductivity, 74) and the attenuation of sound.…”

“…Later analysis by Haard,25) based on independent measurements of the magnetization, confirmed the earlier conclusions. Additionally, Sprague et al found very little inhomogeneous broadening of their spectra, in inferred from specific heat measurements of Choi et al 35) compared with calculations from the HISM. The non-zero spectral weight at the Fermi energy is attributed to overlapping bound states.…”

“…which can be directly determined from the specific heat jump, ÁC=C, such as measured by Choi et al 35) Additionally, measurements of the NMR frequency shift, Á!, where Á 2 / Á!, can be taken from Sprague et al 8,9) to infer suppression of the order parameter. The two experiments, shown in Fig.…”

“…The linear slopes with magnetic field are rather similar for pure and aerogel superfluids. the B-phase of a 98% aerogel from Choi et al 35) Fitting to the data gives the scattering parameters for the IISM of Sauls and Sharma 52) of meanfree-path ¼ 160 nm and a ¼ 40 nm. The fits are not sensitive to the correlation length, a as shown here, in contrast to the transition temperature, Figs.…”

“…In addition to the specific heat jump, Choi et al 35) determined the temperature dependence of the specific heat and in particular accurate measurements of the temperature derivative of the specific heat just below T ca . They argued on the basis of the third law of thermodynamics that entropy should be conserved, meaning that the two shaded areas in Fig. 14 must be equal and consequently if the specific heat is a monotonic function of temperature that there is a non-zero intercept of C Ba =T at T ¼ 0.…”