Photoelectron dispersion in metallic and insulating ${\mathrm{VO}}_2$ thin films

The underlying mechanism behind the metal-to-insulator transition in ${\mathrm{VO}}_2$ is still a topic of intense debate. The two leading theoretical interpretations associate the transition with either electron-lattice or electron-electron correlations. Novel experimental results are required to converge towards one of the two scenarios. Here we report on a temperature-dependent angle-resolved photoelectron study of ${\mathrm{VO}}_2$ thin films across the metal-to-insulator transition. The obtained experimental results are compared to density functional theory calculations. We find an overall energy shift and compression of the electronic band structure across the transition while the overall band topology is conserved. The results demonstrate the importance of electron-electron correlations in establishing the insulating state.

Figure 1

Structural model (left) and one octant of the Brillouin zone (right) for rutile ${\mathrm{VO}}_2$. The sizes of vanadium (blue) and oxygen atoms (red) are not to scale. High-symmetry points are indicated in the BZ.

Figure 2

Atomic positions in ${\mathrm{VO}}_2$ alongside its BZ projected onto the $xz$ plane. Borders of the conventional unit cell are illustrated in black and gray for the rutile and monoclinic phases, respectively. Note that for the rutile structure, three unit cells are shown. The oxygen and vanadium atoms in the rutile phase are represented by red and blue circles with dashed borders. The corresponding atoms in the monoclinic phase are represented by yellow and cyan circles with solid borders. The color brightness for each atom increases with its $y$ position. Sphere sizes were chosen arbitrarily, but the atomic displacements are scaled to the lattice dimensions.

Figure 3

Four-probe resistivity results for a virgin ${\mathrm{VO}}_2$ film (film A, shown in blue) and for another film from the same batch after the ARPES experiment (film B, shown in red). The black arrows show the acquisition temperature for the ARPES data. Red and blue arrows indicate the scan direction of time during the measurements.

Figure 4

ARPES data from a 20-nm-thick ${\mathrm{VO}}_2$ film grown on ${\mathrm{TiO}}_2$ substrates. The data were collected at (a)–(c) 340 K and (d)–(f) 280 K and averaged over $k_z=\pm 4{\sigma }_z$ with Gaussian weights using ${\sigma }_z=60\mathrm{m}{\text{Å}}^{-1}$ centered at $k_z=6.45{\text{Å}}^{-1}$ for (a) and (d), which is slightly off $\mathrm{\Gamma }$. (b) and (e) and (c) and (f) show data averaged using ${\sigma }_x=30\mathrm{m}{\text{Å}}^{-1}$ around $k_x=-1.38{\text{Å}}^{-1}$ and $k_x=0.00{\text{Å}}^{-1}$ (i.e., at normal emission), respectively. Each energy distribution curve in the original data matrix has been shifted to zero mean intensity above the Fermi level and normalized to have equal integrated intensity. An inner potential of $V_0=7\mathrm{eV}$ and the free-electron mass was used for the energy to momentum conversion prior to computing the $k_x$ integrated spectral intensity $\langle I\rangle$, seen to the left. This intensity map was subtracted from the data to emphasize dispersing features. Calculated band structures unfolded in the extended-zone scheme for the rutile ($R$) and monoclinic ($M_1$) phases, respectively, are superimposed as black lines for comparison. The thickness and opacity of the lines are proportional to the square of the plane-wave components of the Bloch crystal wave functions as defined in Eq. (1). The calculated Kohn-Sham eigenenergies of the oxygen bands are rigidly shifted downwards by 0.19 and $1.0\mathrm{eV}$ for the rutile and monoclinic phases, respectively, as explained in Sec. 3.

Figure 5

Local intensity maxima from the data in Fig. 4 for which $k_z$-dispersive data from two different BZs are overlaid. Red circles in (a) and (c) are data taken from the ARPES map shown in Figs. 4 and 4, respectively. Data in (b) and (d) originate from scans shown in Figs. 4 and 4 and 4 and 4, where green triangles and blue squares are from $k_x=-1.38{\text{Å}}^{-1}$ and $k_x=0$, respectively. Calculated bands from Fig. 4, with opacity proportional to $P_{k,K}$ and unfolded in the extended-zone scheme, are overlaid on top of the experimental data.

Figure 6

Calculated spin-polarized $\mathrm{LSDA}+U$ band structures. Solid blue line are bands for spin-up electrons, while dotted red lines are for spin-down electrons. $E_F$ denotes the Fermi level. (a), (d), and (g) are the calculated band structures with $U=0.0$, 2.0, $5.0\mathrm{eV}$, respectively, for the nonmagnetic rutile phase, while (c), (f), and (i) are those for the antiferromagnetic monoclinic phase, in which each dimer forms an antiferromagnetic pair. (b), (e), and (h) are the calculated band structures of a hypothetical system which has a rutile structure, in which the two V atoms forming the unit cell are antiferromagnetically coupled with $U=0.0$, 2.0, $5.0\mathrm{eV}$, respectively.

Figure 7

Calculated spin-polarized $\mathrm{LSDA}+U$ band structures along the $\mathrm{\Gamma }\text{−}X$ direction for the nonmagnetic rutile phase for $U=0.0\mathrm{eV}$ [red, Fig. 4] and the antiferromagnetic monoclinic phase for $U=0.0\mathrm{eV}$ (green) and $2.0\mathrm{eV}$ [blue, Fig. 4]. The opacity of the bands is proportional to the projection of these calculated Bloch bands onto free-electron final states, as described in Sec. 3. As in Figs. 4 and 5, the bands have been shifted to fit experimental data.

Figure 8

Band structure plot similar to Fig. 7, but along the $\mathrm{\Gamma }\text{−}Z$ direction at $k_x=-1.37{\text{Å}}^{-1}$ for the nonmagnetic rutile phase for $U=0.0\mathrm{eV}$ [red, Fig. 4] and the antiferromagnetic monoclinic phase for $U=0.0\mathrm{eV}$ (green) and $2.0\mathrm{eV}$ [blue, Fig. 4].

Figure 9

Band structure plot similar to Fig. 7, but along the $\mathrm{\Gamma }\text{−}Z$ direction at normal emission (i.e., $k_x=0.00{\text{Å}}^{-1}$) for the nonmagnetic rutile phase for $U=0.0\mathrm{eV}$ [red, Fig. 4] and the antiferromagnetic monoclinic phase for $U=0.0\mathrm{eV}$ (green) and $2.0\mathrm{eV}$ [blue, Fig. 4].

Figure 10

Illustration of the effective masses for features A and B using data taken from Table 2. The center line represents the estimated value, with the error given by the lighter region behind it. The equation for the ellipses is ${(x/m_x^{*})}^2+{(z/m_z^{*})}^2=1$ in the three plots where both projections could be estimated.