Effects of Low-Energy Excitations on Spectral Properties at Higher Binding Energy: The Metal-Insulator Transition of ${\mathrm{VO}}_2$

The effects of electron interaction on spectral properties can be understood in terms of coupling between excitations. In transition-metal oxides, the spectral function close to the Fermi level and low-energy excitations between $d$ states have attracted particular attention. In this work we focus on photoemission spectra of vanadium dioxide over a wide (10 eV) range of binding energies. We show that there are clear signatures of the metal-insulator transition over the whole range due to a cross coupling of the delocalized $s$ and $p$ states with low-energy excitations between the localized $d$ states. This coupling can be understood by advanced calculations based on many-body perturbation theory in the $GW$ approximation. We also advocate the fact that tuning the photon energy up to the hard-x-ray range can help to distinguish fingerprints of correlation from pure band-structure effects.

Figure 1

(a) Experimental HAXPES spectra at $h\nu =8\mathrm{keV}$ [25] (similar results have been obtained in Ref. [26]) and XPS spectra at $h\nu =700\mathrm{eV}$ [13]. (b) ${\mathit{G}}_0{\mathit{W}}_0$ PDOS for metallic and insulating ${\mathrm{VO}}_2$, weighted by photoionization cross sections at 8 keV (upper curves) and 700 eV (bottom curves). (c) Total spectral functions $A(\omega )$ in the energy-self-consistent $GW$ approximation (solid lines). Spectral functions where the excitations of energy less than 2.7 eV have been suppressed in $W$ (dashed lines). (Inset) $A(\omega )$ summed over states that have the largest V $4s$ contribution. In (b) and (c) the same 0.25 eV Gaussian broadening has been used.

Figure 2

Spectral functions $A(\omega )$ and self-energy $\mathrm{\Sigma }(\omega )$ for the top-valence state at $\mathrm{\Gamma }$ for the metallic phase, calculated in ${\mathit{G}}_0{\mathit{W}}_0$ (double-dot-dashed lines) and energy-self-consistent $GW$ approximations (solid lines). Vertical orange arrow: Energy of the LDA Kohn-Sham state. Vertical dotted line: Fermi energy in LDA. The zero of the energy axis is at the Fermi energy calculated in the energy-self-consistent $GW$ approximation. ${\mathrm{\Delta }}_F$ is the shift of the Fermi energy.