Criterion of superfluidity, elementary excitations, and heat capacity singularity in superfluid helium

V B Bobrov,S A Trigger

doi:10.1093/ptep/ptt012

Abstract

We proceed from the premise that the spectrum of elementary excitations in the normal component in the Landau theory of superfluidity should depend on the superfluid helium temperature. This leads to generalization of the Landau superfluidity criterion. On this basis, taking into account available experimental data on inelastic neutron scattering, it is shown that, in addition to phonon–roton excitations, there is another type of elementary excitation in superfluid helium, which we called helons. The energy spectrum with such momentum dependence was first proposed by Landau. The helon energy spectrum shape and its temperature dependence make it possible to explain the singular behavior of the heat capacity of superfluid helium near its phase transition to the normal state.

Highlights

According to the seminal phenomenological Landau theory [1,2], superfluid helium is a liquid consisting of superfluid and normal components
The normal component moves with friction and is involved in heat transport. In this case, according to the Landau theory [1], the normal component is a gas of elementary excitations, which are characterized by the dependence of the energy spectrum ε( p) on the momentum p
We show the necessity of the existence of new elementary excitations in the normal component of superfluid helium, with the spectrum essentially dependent on temperature

Summary

Introduction

According to the seminal phenomenological Landau theory [1,2], superfluid helium is a liquid consisting of superfluid and normal components (see Ref. [3]). We believe that the spectrum of excitations for helons is defined by relations (6)–(8); instead of superscript r we write (h) in the quantities r and μr This is not a formal replacement, since the helon’s spectrum is defined, according to (6), by the roton’s mass μ(h) and by the gap (h) related to the critical velocity Vcr (7), since the latter tends to zero at T = Tλ, according to the generalized temperature-dependent Landau criterion. The existence of helons with the spectrum (6)–(8) is confirmed by experiments on inelastic neutron scattering [27,28] (see Fig. 2), in which, in addition to the maxima in the dynamic structure factor of superfluid helium, corresponding to the phonon–roton spectrum of elementary excitations, maxima were detected, whose positions appeared close to the spectrum of the free helium atom εa( p) = p2/2m (here m is the helium atom mass) for the region of the momentum-transferred values q > 0.5 A−1. For dimensionality reasons, to determine the quantity (h)(T ), several quantities with an energy dimension can be constructed, based on the superfluid component density ns, in particular, 2n2s/3(T )/m and 2 Lns(T )/m, where L is the so-called scattering length, which is completely defined by the interparticle interaction potential of helium atoms

Thermodynamics and the heat capacity divergence

Conclusions