Helmut Schober

Superconducting ${\mathrm{MgB}}_2$ shows an $E_{2g}$ zone center phonon, as measured by Raman spectroscopy, that is very broad in energy and temperature dependent. The Raman shift and lifetime show large differences with the values elsewhere in the Brillouin zone measured by inelastic x-ray scattering (IXS), where its dispersion can be accounted for by standard harmonic phonon theory, adding only a moderate electron-phonon coupling. Here we show that the effects rapidly disappear when electron-phonon coupling is switched off by Al substitution on the Mg sites. Moreover, using IXS with very high wave-vector resolution in ${\mathrm{MgB}}_2$, we can follow the dispersion connecting the Raman and the IXS signal, in agreement with a theory using only electron-phonon coupling but without strong anharmonic terms. The observation is important in order to understand the effects of electron-phonon coupling on zone center phonon modes in ${\mathrm{MgB}}_2$, and also in all metals characterized by a small Fermi velocity in a particular direction, typical for layered compounds.

We present neutron scattering measurements of the dynamic structure factor of liquid helium confined to nanoscales in 25 and $34\text{Å}$ mean pore diameter porous media over a range of pressures and temperatures. At low temperature and low pressure we observe well-defined phonon-roton (P-R) modes characteristic of liquid helium containing Bose-Einstein condensation (BEC). As pressure is increased above 25 bars, we observe that the high energy P-R modes broaden and become unobservable. At pressure $p=36.3–36.8\text{bars}$ we observe loss of all modes, including the roton. The observation of modes up to 36.3–36.8 bars indicates that there is liquid containing BEC in the gelsils up to this pressure. The loss of modes at 36.3–36.8 bars indicates loss of BEC in the liquid or significant solidification in the gelsils at this pressure. At a pressure of 31.2 bars, we observe well-defined P-R modes up to $T\simeq 1.4\text{K}$ but loss of all modes above this temperature. At $p\simeq 0$, we have previously observed modes up to $T_{\lambda }=2.17\text{K}$. Yamamoto et al. have reported superfluidity in the same $25\text{Å}$ gelsil up to a pressure $p_c=34\text{bars}$ at $T\simeq 0\text{K}$ and to a maximum temperature of $T_c=1.3\text{K}$ at $p\simeq 0$. The transition at $p_c=34\text{bars}$ and $T\simeq 0\text{K}$ was interpreted as a quantum phase transition. The present observation of P-R modes at temperatures well above $T_c$ (and pressures slightly above $p_c$) indicates that there is a phase containing BEC above $T_c$ $\left(p_c\right)$ that is not superfluid. This is interpreted as a Bose glass phase containing islands of BEC that support P-R modes separated by normal liquid so that there is no phase coherence across the sample as needed for superflow. The Bose glass phase lies between the superfluid and normal liquid at all temperatures and pressures. Measurements of the static structure factor indicate that freezing in the gelsils is predominantly to an amorphous solid.