Pseudogap and electron localization in the $4d$ shell of ${\mathrm{NbO}}_2$ bulk crystal

We present a detailed study of correlation-induced electronic reconstruction in ${\mathrm{NbO}}_2$ bulk crystal. Using density functional plus dynamical mean-field theory $(\mathrm{DFT}+\mathrm{DMFT})$, we show the importance of multiorbital Coulomb interactions in concert with first-principles band structure calculations for a consistent understanding of emergent pseudogap and incipient Mott localization in ${\mathrm{NbO}}_2$. We explain the pseudogapped incoherent metal to a Mott-localization-like transition seen in experiment. We trace its origin to changes in orbital polarization, itself renormalized from its DFT value by sizable multiorbital electron correlations. Our results should be of interest for future studies on electronic switching in Mott memristors for neuromorphic computing devices.

Figure 1

Comparison between DFT [14] and $\mathrm{DFT}+\mathrm{DMFT}$ orbital resolved and total density of states (DOS) for the $t_{2g}$ orbitals of rutile ${\mathrm{NbO}}_2$. While all $t_{2g}$ bands span across the Fermi level, an important feature to be seen is the pseudogap [20] behavior at $E_F$ and the emergence of lower Hubbard bands with increasing the on-site Coulomb interaction $U$. While the metal-insulator transition in ${\mathrm{NbO}}_2$ is found at temperatures between 810 and 1081 K [3, 20, 23], here all $\mathrm{DFT}+\mathrm{DMFT}$ (MO-IPT) spectral functions are computed at zero temperature to avoid thermal broadening effects.

Figure 2

Orbital-resolved self-energies imaginary (main panels) and real (insets) parts of ${\mathrm{NbO}}_2$ bulk crystal, showing their evolution with increasing the on-site Coulomb interaction $U$. Particular features to be seen are the Fermi-liquid-like behavior for $U=2.5$ eV and its suppression with increasing $U$. Also interesting is the particle-hole asymmetry [13] and the presence of poles in the self-energy imaginary parts [12].

Figure 3

Orbital-resolved $\mathrm{DFT}+\mathrm{DMFT}$ DOS of ${\mathrm{NbO}}_2$, showing their evolution with increasing $U$. Apart from orbital-selective Mott localization at $U=3.5$ eV in the regular rutile phase ($\mathrm{\Delta }=0.0$ eV), a particular interesting feature to be seen is the large spectral weight transfer for $U=4.5$ eV and $\mathrm{\Delta }=0.0$ eV within the $xz$ and $x^2\text{−}{y}^2$ orbitals. Also noteworthy is the evolution of the orbital-resolved DOS of distorted rutile ${\mathrm{NbO}}_2$ with increasing the orbital field $\mathrm{\Delta }$ for fixed $U=4.5$ eV. Apart from Mott localization, a relevant feature to be seen is the spectral weight transfer among different orbitals with increasing $\mathrm{\Delta }$. Right-lower panel displays the $\mathrm{\Delta }$ dependence of the Nb-$t_{2g}$ orbital occupations $n_a$. Notice the orbital switching, inducing enhanced charge carrier concentration in the $xz$ channel above ${\mathrm{\Delta }}_c=0.42$ eV.

Figure 4

Orbital-resolved self-energies imaginary (main panels) and real (insets) parts of ${\mathrm{NbO}}_2$, showing their evolution with increasing the on-site Coulomb interaction $U$ and the orbital field $\mathrm{\Delta }$. Particular features to be seen are the clearly visible particle-hole asymmetry and the presence of poles associated with Mott localization in the self-energy imaginary parts [12].

Figure 5

Theory-experiment comparison between the $\mathrm{DFT}+\mathrm{DMFT}$ results and hard x-ray photoelectron spectroscopy (HAXPES) measurements taken from Refs. [21] (dashed curve) and [20] (dot and dot-dashed curves). The dashed and doted curves correspond to the regular rutile phase. Notice the good qualitative theory-experiment agreement between 0.2 and 2.5 eV binding energy, particularly the peak position of the lower Hubbard band for the rutile and bct phases.