3D Imaging of the Fermi Surface by Thermal Diffuse Scattering

We use thermal diffuse scattering of x rays to visualize the lens-shaped portions of the Fermi surface in metallic zinc. Our interpretation of the nature of the observed scattered intensity anomalies is supported by the incorporation of inelastic x-ray scattering measurements as well as ab initio calculations of the electronic structure and lattice dynamics. Our work demonstrates that thermal diffuse scattering complements well-established techniques and is a powerful tool in its own right for studying the shape of the Fermi surface through the associated electron-phonon coupling.

Figure 1

Reciprocal space maps for zinc. Sections along the $c^{*}$ axis: (a) $HHL$ and $H0L$, and perpendicular to it: (b) $HK2$ and (c) $HK3$. The upper part of panels show the experimental pattern, and the lower part the calculated pattern. (d) Constant-intensity surfaces for diffuse scattering: general view of the experimental data set and comparison of experiment and theory for the region around the (004) Bragg spot. For visualization purposes a ${cos}^2(2\theta )$ factor is added.

Figure 2

(a) Brillouin zone of zinc with denoted special points; (b) high-symmetry section of the Fermi surface obtained by ab initio calculations; (c) scheme of the assembly of lenslike surfaces centered on strong Bragg spots and their dissection by $HHL$ plane.

Figure 3

Dispersion of transverse acoustic phonons of zinc propagating along $\Gamma \mathrm{\text{−}}K\mathrm{\text{−}}M$ direction and polarized along $\Gamma \mathrm{\text{−}}A$ direction: comparison of IXS and INS [22] data (left axis); corresponding evolution of the inelastic signal intensity scattered on TA phonon (right axis).