Bulk Electronic Structure of Quasicrystals

We use hard x-ray photoemission to resolve a controversial issue regarding the mechanism for the formation of quasicrystalline solids, i.e., the existence of a pseudogap at the Fermi level. Our data from icosahedral fivefold Al-Pd-Mn and Al-Cu-Fe quasicrystals demonstrate the presence of a pseudogap, which is not observed in surface sensitive low energy photoemission because the spectrum is affected by a metallic phase near the surface. In contrast to Al-Pd-Mn, we find that in Al-Cu-Fe the pseudogap is fully formed; i.e., the density of states reaches zero at $E_F$ indicating that it is close to the metal-insulator phase boundary.

Figure 1

HAXPES valence band spectra measured with $h\nu =5.95\mathrm{keV}$ at 300 K compared with surface sensitive low energy photoemission spectra from the literature [7, 9] for (a) $i$-Al-Pd-Mn and (b) $i$-Al-Cu-Fe. The spectra have been normalized to the same intensity at the Pd $4d$ and Cu $3d$ main peak for Al-Pd-Mn and Al-Cu-Fe, respectively. The near-$E_F$ region is shown along with the Au Fermi edge (black open circles) for (c) Al-Pd-Mn and (d) Al-Cu-Fe.

Figure 2

HAXPES valence band spectra (black open circles) of (a) Al-Pd-Mn and (b) Al-Cu-Fe in the near-$E_F$ region. The experimental valence band spectra, fitted with a Lorentzian function [$S(E)$, thick green line] broadened by the instrumental resolution and multiplied by the Fermi function, show the deep pseudogap at $E_F$. The resulting fitted curve is shown as a black line. The residuals are shown at the top of each panel. $S(E)$ for low energy photoemission (dashed blue line) is obtained from the parameters given in Ref. 7. The near-$E_F$ region of Al-Pd-Mn and Al-Cu-Fe HAXPES valence band spectra measured with 7.93 keV at 40 K and 5.95 keV at 300 K are directly compared in (c) and (d), respectively.

Figure 3

The near-$E_F$ region of the HAXPES valence band spectra of Al-Cu-Fe measured with (a) 7.93 keV photon energy at 40 K and 300 K and (b) 7.93 and 5.95 keV photon energies at 300 K.