Optical spectroscopy and the nature of the insulating state of rare-earth nickelates

Using a combination of spectroscopic ellipsometry and DC transport measurements, we determine the temperature dependence of the optical conductivity of ${\mathrm{NdNiO}}_3$ and ${\mathrm{SmNiO}}_3$ films. The optical spectra show the appearance of a characteristic two-peak structure in the near-infrared when the material passes from the metal to the insulator phase. Dynamical mean-field theory calculations confirm this two-peak structure and allow us to identify these spectral changes and the associated changes in the electronic structure. We demonstrate that the insulating phase in these compounds and the associated characteristic two-peak structure are due to the combined effect of bond disproportionation and Mott physics associated with half of the disproportionated sites. We also provide insights into the structure of excited states above the gap.

Figure 1

Real part of the dielectric function (top) and optical conductivity (bottom) of ${\mathrm{NdNiO}}_3$ on a ${\mathrm{NdGaO}}_3 \left(110\right)$ substrate (a), ${\mathrm{NdNiO}}_3$ on a ${\mathrm{NdGaO}}_3 \left(101\right)$ substrate (b), and for ${\mathrm{SmNiO}}_3$ on a ${\mathrm{LaAlO}}_3 \left(001\right)$ substrate (c).

Figure 2

Real part of the optical conductivity for selected temperatures and energy/temperature color maps of samples (a) NNO/NGO-110, (b) NNO/NGO-101, and (c) SNO/LAO-001. Metal-insulator phase transitions are indicated by arrows on the color maps. $A$ and $B$ designate two peaks in the insulating phase. Data at 0 eV come from DC measurements.

Figure 3

The bare (GGA) band structure of the monoclinic phase of ${\mathrm{SmNiO}}_3$. The color represents the site character of the states: LB (red) and SB (blue). Note the Peierls splitting at an energy +0.5–0.7 eV. The position of the Fermi level is $\varepsilon =0$.

Figure 4

Calculated optical spectra for several values of $U$ and $J$. The two peaks are denoted by $A$ (constant position) and $B$ (varying position). Inset: Phase boundary of the bond-disproportionated insulating state. The symbols indicate the values of $U,J$, chosen such that the leading edge is kept approximately constant of order $0.5$ eV.

Figure 5

Momentum-resolved spectral function (color intensity map) for two selected parameter sets: $U=1.0$ eV, $J=0.85$ eV (top) and $U=2.0$ eV, $J=0.85$ eV (bottom). The colors represent the site character of a state: red for LB, blue for SB (violet for a mixed LB/SB character). A darker (lighter) tone corresponds to higher (lower) spectral intensity. The circles indicate the energy-momentum locations where the Peierls pseudogap opens. The indirect Mott-like gap is indicated by the black arrow connecting the highest occupied states between $R$ and $Z$ and the lowest unoccupied states at the $\mathrm{\Gamma }$ point. Side panel: momentum-integrated spectral functions (density of states) for LB (red) and SB (blue) sites, with arrows indicating the optical transitions corresponding to the two peaks (see text).

Figure 6

Left-hand side of the quasiparticle equation (3) and graphical construction of the three QP branches. The green (shaded) area shows the region of allowed values of the RHS: $0\le |t_k{|}^2\le W^2/4$, where $W$ is the bandwidth. ${\omega }_i,i=+,-$, and $\omega ={\varepsilon }_{\text{SB}}$ are the roots of the equation for $t_k=0$. The order of the roots ${\omega }_{+}$ and ${\varepsilon }_{\text{SB}}$ depends on the regime (Mott or Mott-Peierls, see text).

Figure 7

Quasiparticle band structure, density of states, and main optical transitions of the simple model discussed in the text. Top: Mott regime, bottom: Mott-Peierls regime. Colors indicate the LB/SB character, as above. The indirect Mott-like gap is indicated with the thin arrow in the main panel.

Figure 8

(a) Sketch of the optical experiment determining the ellipsometric parameters $\mathrm{\Delta }$ (phase shift between $p$- and $s$-polarized component of the light) and $\mathrm{\Psi }$ (argument of the ratio of $p$- and $s$-polarized amplitude). (b) $\mathrm{\Psi }$ and $\mathrm{\Delta }$ spectra of 17-nm-thick ${\mathrm{NdNiO}}_3$ on ${\mathrm{NdGaO}}_3$(101) at 100 K measured with an angle of incidence of 69 degrees, shown with the Drude-Lorentz fit. (c) Thin film dielectric function calculated from panel (b) with the method explained in the main text. The insets of (b) and (c) show the same parameters for the ${\mathrm{NdGaO}}_3$(101) substrate. (d) Optical conductivity corresponding to ${\epsilon }_2\left(\omega \right)$ in panel (c), with the DC conductivity.

Figure 9

Output obtained when applying the thin-film approximation, Eq. (A2), to ellipsometric data $r_p/r_s$ of a film of finite thickness on a substrate (${\epsilon }_{\mathrm{TFA}}$, blue curves). A Drude-Lorentz parametrization (${\epsilon }_{DL}$, orange curves) was used to generate the ellipsometric $r_p/r_s$. Parameters for the substrate dielectric function, film thickness, and angle of incidence are indicated in the legend.

Figure 10

Examples of the analytical fit (LB: red solid, SB: magenta dashed) of the QMC self-energy (LB: blue filled circles, SB: green empty circles). The LB self-energy is fit with a two-pole ansatz given by Eq. (C1), while the SB self-energy is fit with a constant. Top two panels: $U=1.0$ eV; bottom two panels: $U=2.0$ ($J=0.85$ eV in both cases).

Figure 11

Analytical fit of the LB self-energy on the real axis. Green: $U=1.0$, blue: $U=2.0$ ($J=0.85$ eV in both cases). The LB self-energy is fitted with a two-pole ansatz given by Eq. (C1), with parameters presented in Table 4.

Figure 12

$k$-resolved spectral function for the simple 1D model. The parameters for the three panels are taken from the fitted parameters of the self-energies for three cases. Top panel: $J=0.85$ eV, $U=1.0$ eV, middle panel: $J=0.8$ eV, $U=1.2$ eV, bottom panel: $J=0.85$ eV, $U=2.0$ eV. The color represents a site character of states: LB (red) and SB (blue).

Figure 13

$k$-resolved spectral function for ${\mathrm{SmNiO}}_3$ as obtained in the GGA+DMFT calculation. The parameters for the three panels are taken from the fitted parameters of the self-energies for three cases. Top panel: $J=0.85$ eV, $U=1.0$ eV, middle panel: $J=0.8$ eV, $U=1.2$ eV, bottom panel: $J=0.85$ eV, $U=2.0$ eV. The color represents a site character of states: LB (red) and SB (blue).