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Register a new userDislocation Mobility and Anomalous Shear Modulus Effect in $^4$He Crystals
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We calculate the dislocation glide mobility in solid $^4$He within a model that assumes the existence of a superfluid field associated with dislocation lines. Prompted by the results of this mobility calculation, we study within this model the role that such a superfluid field may play in the motion of the dislocation line when a stress is applied to the crystal. To do this, we relate the damping of dislocation motion, calculated in the presence of the assumed superfluid field, to the shear modulus of the crystal. As the temperature increases, we find that a sharp drop in the shear modulus will occur at the temperature where the superfluid field disappears. We compare the drop in shear modulus of the crystal arising from the temperature dependence of the damping contribution due to the superfluid field, to the experimental observation of the same phenomena in solid $^4$He and find quantitative agreement. Our results indicate that such a superfluid field plays an important role in dislocation pinning in a clean solid $^4$He at low temperatures and in this regime may provide an alternative source for the unusual elastic phenomena observed in solid $^4$He.
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The shear stress relaxation modulus $G(t)$ may be determined from the shear stress $tau(t)$ after switching on a tiny step strain $gamma$ or by inverse Fourier transformation of the storage modulus $G^{prime}(omega)$ or the loss modulus $G^{primeprime}(omega)$ obtained in a standard oscillatory shear experiment at angular frequency $omega$. It is widely assumed that $G(t)$ is equivalent in general to the equilibrium stress autocorrelation function $C(t) = beta V langle delta tau(t) delta tau(0)rangle$ which may be readily computed in computer simulations ($beta$ being the inverse temperature and $V$ the volume). Focusing on isotropic solids formed by permanent spring networks we show theoretically by means of the fluctuation-dissipation theorem and computationally by molecular dynamics simulation that in general $G(t) = G_{eq} + C(t)$ for $t > 0$ with $G_{eq}$ being the static equilibrium shear modulus. A similar relation holds for $G^{prime}(omega)$. $G(t)$ and $C(t)$ must thus become different for a solid body and it is impossible to obtain $G_{eq}$ directly from $C(t)$.
We conducted series of experiments on observing a Stark-type effect in superfluid $^4$He in presence of relative laminar flows of the normal and superfluid components. It is designed a measurement cell which allows us to simultaneously create hydrodynamic flows in the liquid and to carry out high-frequency radio-measurements at external electric field. We used a dielectric disk resonator that made possible to cover a wide frequency range. In our experiments it was registered the spectrum of the dielectric disk resonator modes, as well as narrow lines of absorption of a microwave radiation in He II on its background and in different conditions. We discovered that having in the liquid helium a relative motion of the normal and superfluid fractions in the temperature range of 1.4$div$2.17 K the narrow line of absorption/radiation is observed in the EM spectrum, the frequency of which - 180 GHz - corresponds to the roton minimum. This line splits in a constant electric field. Note that in a weak electric field the value of splitting depends linearly on the electric field strength, i.e. the linear Stark effect is detected. It is found that with the external electric field increasing both split lines are displaced towards more low frequencies side. The obtained data set could be described by an empirical formula, taking into account as the linear part of the Stark effect, as well as a quadratic addition, related to the polarization part. The data point out on having particles or excitations in the liquid helium with the dipole moment $sim 10^{-4}$ D, that in four order less of the characteristic dipole moment of polar molecules. The comparison of our findings to values of the electric dipole moment (EDM) of elementary particles and nuclei is also performed. We sum up with brief discussion of extensions of the known theoretical models and possible mechanisms of the EDM production.
Equation of state of He-4 hcp crystals with vacancies is determined at zero temperature using the diffusion Monte Carlo technique, an exact ground state zero-temperature method. This allows us to extract the formation enthalpy and isobaric formation energy of a single vacancy in otherwise perfect helium solid. Results were obtained for pressures up to 160 bar. The isobaric formation energy is found to reach a minimum near 57 bar where it is equal to $10.5pm 1.2$ K. At the same pressure, the vacancy formation volume exhibits a maximum and reaches the volume of the unit cell. This pressure coincides with the pressure interval over which a peak in the supersolid fraction of He-4 was observed in a recent experiment.
We demonstrate that crystal defects can act as a probe of intrinsic non-Hermitian topology. In particular, in point-gapped systems with periodic boundary conditions, a pair of dislocations may induce a non-Hermitian skin effect, where an extensive number of Hamiltonian eigenstates localize at only one of the two dislocations. An example of such a phase are two-dimensional systems exhibiting weak non-Hermitian topology, which are adiabatically related to a decoupled stack of one-dimensional Hatano-Nelson chains. Moreover, we show that strong two-dimensional point gap topology may also result in a dislocation response, even when there is no skin effect present with open boundary conditions. For both cases, we directly relate their bulk topology to a stable dislocation skin effect. Finally, and in stark contrast to the Hermitian case, we find that gapless non-Hermitian systems hosting bulk exceptional points also give rise to a well-localized dislocation response.
We investigate the origin of a resonant period drop of a torsional oscillator (TO) containing solid ${}^{4}$He by inspecting its relation to a change in elastic modulus. To understand this relationship directly, we measure both phenomena simultaneously using a TO with a pair of concentric piezoelectric transducers inserted in its annulus. Although the temperature, ${}^{3}$He concentration, and frequency dependence are essentially the same, a marked discrepancy in the drive amplitude dependence is observed. We find that this discrepancy originates from the anisotropic response of polycrystalline solid ${}^{4}$He connected with low-angle grain boundaries by studying the shear modulus parallel to and perpendicular to the driving direction.
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