Atomic-orbital analysis of the Cu Fermi surface by two-dimensional photoelectron spectroscopy

A method for atomic-orbital orientation determination at each $k$ point has been developed. The three-dimensional Cu Fermi surface (FS) structure was measured and visualized by stacking a series of photoelectron intensity angular distribution (PIAD) at different photon energies. PIADs from the Cu(001) surface were obtained using a display-type analyzer and linearly polarized synchrotron radiation. The atomic orbitals composing the FS were determined to be mainly $4p$ orbitals with their axes pointing outward. Atomic orbital orientations at different $k$ coordinates on FS as well as the FS cross-section structures were revealed directly from experiment and were confirmed by ab initio calculation.

Figure 1

PIADs from the Fermi level of Cu(001) surface excited by a normal-incident linearly polarized light. The electric vector of the incident light is in the horizontal direction.

Figure 2

(Color) (a) The Cu FS together with the spheres corresponding to the wave vector of photoelectrons excited with various photon energies. (b)–(e) The top views of Cu FSs and the spheres representing the photoelectron wave vectors together with observed PIADs. FSs labeled $B$ and $C$ are shown in (b) and (c), while FSs labeled $B$ and $D$ are shown in (d) and (e). (f)–(i) Same as (b)–(e), but for sample rotated by 45°. (j) The Cu FS with atomic orbitals constituting each point in $k$ space. The direction of the $p$ orbital axes pointing outward is derived from the experimental analysis. FS is colored according to the $4p$ orbital ratio distribution calculated by using the ab initio code. Blue, red, and green colors correspond to $4p_x$, $4p_y$, and $4p_z$ orbitals, respectively.

Figure 3

(a) PIADs with various azimuthal rotation angles. Photon energy of $45\mathrm{eV}$ is used for exciting the electrons of FS in the $\Gamma XWK$ plane. (b) ADAO from $p_x$, $p_y$, and $p_z$ orbitals. (c) Cross section of the FS at the $\Gamma XWK$ plane. (d) and (e) ADAO and simulated PIADs from $p$ orbitals with their axes pointing radially, respectively.