Electronic band structure of a two-dimensional oxide quasicrystal

The valence band electronic structure of a ${\mathrm{BaTiO}}_3$-derived oxide quasicrystal (OQC) is studied by photoemission using momentum microscopy. An upward-dispersive ${\mathrm{O}}_{2p}$ band is identified, and it can be assigned to a combination of in-plane orbitals according to the symmetry and the overlap of the wave functions. In addition, the signature of ${\mathrm{Ti}}_{3d}$ states near the Fermi level is observed, which results in a metallic character of the OQC with $3d^1$ occupation. Our experiments reveal two-dimensional electronic states within the OQC based on a symmetry-adapted decomposition of photoelectron intensity distribution in the momentum space.

Figure 1

Low energy electron diffraction (LEED) on the OQC at (a) 28 and (b) 66 eV. In both images the intensity is normalized to the [0011] spot of the OQC. In (a) the diffraction spot [1211] of the OQC is located at $q_{\left[1211\right]}=2k_r^{\mathrm{kink}}\approx 1.5{\AA }^{-1}$, which will be discussed later in Fig. 6 and Sec. 3e2. The [1111] spot as well as the [2210] spot in (b) are relevant for the possible umklapp processes and will be discussed in Sec. 3e1.

Figure 2

2D momentum maps of photoelectrons from (a), (c) the OQC and (b), (d) Pt(111). (a), (b) are measured at $E_B=0.5$ eV, and (c), (d) at the Fermi level $\left(E_F\right)$. The $k_{x,y}$ directions and the surface Brillouin zone of Pt(111) are marked in (b) (blue). Insets: Magnified views near the Pt $\overline{M}$ point (yellow), with Pt surface resonance (SR) in (b), (d). Color scale in ${10}^4$ CCD counts.

Figure 3

Energy-momentum distribution of photoelectrons from (a), (c) the OQC and (b), (d) Pt(111). In (a) the dispersive oxygen-derived electronic state is marked. NB: Nonbonding O-$2p$ state; $pd\pi$: $\pi$-bonding state with Ti-$3d$ and O-$2p$ orbitals [22]. Color scale in ${10}^4$ CCD counts.

Figure 4

Momentum- $\left(k_r\right)$ and energy- $\left(E_B\right)$ integrated symmetry-adapted photoemission intensity $I_n(k_r,E_B)$ as a function of the azimuthal order $n$ up to 50 for (a) Pt(111) and (b) the OQC. The numbers indicate clear oscillations with the multiples of the 3-fold symmetry at $n=3m$ orders, with $m$ as an integer. Dashed curves are phenomenological fits with the function $I_n=a{e}^{b/(n+c)}$ for the $n\ne 3m$ orders. The fitting parameters are $a_{\mathrm{Pt}}=6.9\times {10}^5,b_{\mathrm{Pt}}=33,c_{\mathrm{Pt}}=6.4$, and $a_{\mathrm{OQC}}=5.9\times {10}^5,b_{\mathrm{OQC}}=9,c_{\mathrm{OQC}}=0.95$. Dashed vertical line marks $n=12$ as the expected first-order azimuthal symmetry of the OQC dodecagonal structure. In (b) the magnified view for $n\ge 11$ is plotted with respect to the right vertical axis.

Figure 5

Azimuthally decomposed photoemission intensity $I_n(k_r,E_B)$ with $n=0$ to 12 of the OQC in (a)–(g) and (o)–(t), and Pt(111) in (h)–(n) and (u)–(z). $2p_x\text{−}2p_y$: ${\mathrm{O}}_{2p}$ state with combined orbitals in the surface plane. The minimum/maximum color scales are (a) 0.1/2.6, (b) 0/0.4, (c) 0/0.2, (d) 0/0.1, (e) 0/0.04, (f) 0/0.02, (g) 0/0.06, (h) 0.2/7.3, (i) 0/1.6, (j) 0/0.5, (k) 0/1.3, (l) 0/0.3, (m) 0/0.2, (n) 0/0.6, (o)–(p) 0/0.02, (q) 0/0.04, (r)–(t) 0/0.02, (u) 0/0.2, (v) 0/0.1, (w) 0/0.6, (x)–(y) 0/0.1, (z) 0/0.3 in ${10}^4$ CCD counts. In (n), the label SR indicates the surface resonance of Pt(111) at $\overline{M}$ points, which is quenched by the OQC in (g). In (t), the ${\mathrm{S}}_1,{\mathrm{S}}_2$, and ${\mathrm{S}}_3$ indicate pronounced 12-fold features on the OQC.

Figure 6

(a) $I_1(k_r,E_B)$ spectra with $2p_x\text{−}2p_y,pd\pi$, and NB states and the bottom of the bulk Pt-$d$ bands along $\mathrm{\Lambda }$ [36]. Dashed lines and circles are guides to the eye. (b) Two spectra from (a) fitted with three Gaussian functions for the $pd\pi$ and the $2p_x\text{−}2p_y$ states, as well as the NB state with a possible contribution from Pt. Red curves are sums of the three peaks and a linear background (bg). Curves in (a) and (b) are shifted by 200 and 1700 CCD counts. (c) $E\left(\vec{k}\right)$ of ${\mathrm{O}}_{2p}$ bands. Circles: $2p_x\text{−}2p_y$ and $pd\pi$ states in $I_1(k_r,E_B)$. Squares: NB and $pd\pi$ states in Figs. 3 and 3. R, W, and E: Regions of ${\mathrm{O}}_{2p}$ bands and ${\mathrm{Ti}}_{3d}\text{−}{\mathrm{O}}_{2p}pd\sigma$ bonding bands on ${\mathrm{BaTiO}}_3$ crystals and films [22, 37, 38]. Pt: Bulk transitions in Pt [36]. Filled area: Surface-projected bands on Pt(111) [27]. $k_r^{\mathrm{kink}}$ is related to the [1211] LEED spot in Fig. 1.

Figure 7

2D momentum map on (a), (d) the OQC and (b), (e) Pt(111), with (a), (b) at $E_F$ and (d), (e) at $E_B=0.5$ eV. In (c), (f) their momentum distributions along $k_y$ integrated over $k_x=\pm 0.5{\AA }^{-1}$ are shown, and the full width at half maximum near $k_y=0$ for OQC (filled regions) is estimated by the arrows. The minimum/maximum color scales are (a) 4.5/6, (b) 7/16, (d) 7.5/9, (e) 6/12, in ${10}^3$ CCD counts. The Ti-$3d^1$ occupation in OQC is estimated by the circle in (a).

Figure 8

Energy-momentum distribution of photoelectrons from periodic ${\mathrm{BaTiO}}_3$(111) islands on Pt(111) for comparison with Fig. 3. Color scales are in ${10}^4$ CCD counts.

Figure 9

Azimuthally decomposed photoemission intensity $I_1(k_r,E_B)$ of (a) Pt(111), (b) ${\mathrm{BaTiO}}_3$-derived oxide quasicrystal (OQC), and (c) ${\mathrm{BaTiO}}_3$(111) islands on Pt(111). The line profiles of $I_1(k_r,E_B)$ from (a), (b), and (c) at $k_r=0.7$ to $1.3{\AA }^{-1}$ are shown in (d), (e), and (f), respectively. The minimum/maximum color scales in (a) and (c) are 0/1.6 and $0/1.3\times {10}^3$ CCD counts. The color scale for (b) is the same as in Fig. 5. For clarity, curves in (d)–(f) are shifted vertically.

Figure 10

Azimuthally decomposed photoemission intensity $I_{12}(k_r,E_B)$ of (a) Pt(111), (b) the ${\mathrm{BaTiO}}_3$-derived OQC, and (c) ${\mathrm{BaTiO}}_3$(111) islands on Pt(111). Features ${\mathrm{S}}_{1,2,3}$ of the OQC in (b) are marked as in Fig. 5. The color scales for (a), (b) are the same as in Figs. 5, 5 and for (c) the minimum/maximum scales are $0/5\times {10}^2$ CCD counts.

Figure 11

2D momentum distribution of photoelectrons from (a) the OQC and (b) the ${\mathrm{BaTiO}}_3$ islands on Pt(111) at the binding energy $E_B=5.0$ eV. Color scales are in ${10}^4$ CCD counts. Dashed circles in (a) enclose the region for the $2p_x\text{−}2p_y$ state.