Dirac nodal lines protected against spin-orbit interaction in ${\mathrm{IrO}}_2$

The interplay between strong spin-orbit coupling and electron correlations has recently been the subject of intense investigation, due to a number of theoretically predicted phases such as quantum spin liquids, unconventional superconductivity, complex magnetic orders, and correlated topological phases of matter. In particular, iridates have been proposed as a promising family of materials which could host a number of these phases. Here we report the existence of Dirac nodal lines in the binary oxide ${\mathrm{IrO}}_2$, through a combination of reactive oxide molecular beam epitaxy and angle-resolved photoemission spectroscopy. Unlike in other such materials reported to date, these Dirac nodal lines have the unique property of being simultaneously (i) robust against spin-orbit coupling, as they are protected by the nonsymmorphic symmetry of the rutile structure, and (ii) only partially occupied, since they cross the Fermi level. This should have direct implications on the low-energy physics properties tied to the band velocity such as magnetoresistance and spin Hall effect.

Figure 1

(a) Crystal structure of ${\mathrm{IrO}}_2$ and (b) x-ray diffraction $\theta \text{−}2\theta$ scans exhibiting clear thickness fringes from $\sim 15$ nm thick ${\mathrm{IrO}}_2$(110) and ${\mathrm{IrO}}_2$(001) films. The asterisks mark the ${\mathrm{TiO}}_2$ substrate peaks. (c) The calculated band structure by $\mathrm{GGA}+\mathrm{SOC}$ along a selected high symmetry path. The nodal lines discussed in this work are marked by the dashed boxes. The $\mathrm{\Gamma }\text{−}X$ and $R\text{−}A$ directions normal to the lines are shown twice for representing the characteristic Dirac crossings, marked by circles superposed to the band structure. Every path perpendicular to the DNLs will show such a a crossing point, as apparent in the 3D renderings of the band structure along $A-M$ (d) and $X\text{−}M$ (e) where the gray planes represent the location of the Fermi level. The higher binding energy nodal line along $A\text{−}M$ is not the focus of this work. It is not relevant for the low energy physics since it lies $>1$ eV from the Fermi level, and is likely to be difficult to measure accurately due to the broader ARPES linewidth at higher binding energy.

Figure 2

(a) 3D rendering of the calculated Fermi surface, with holelike bands in red and electronlike bands in blue. The gray planes correspond to the BZ center and BZ boundary for the [110] and [001] orientations, and indicate the location of the Fermi surfaces measured by ARPES in (c)–(f), as shown in the insets. (b) The 3D BZ with high symmetry directions hosting the DNLs object of this study, shown in green for the $A\text{−}M$ line and orange for the $X\text{−}M$ line. The energy of the band along the $k$ path is color coded as shown. The photon energies used are (c) 124 eV, (d) 84 eV, (e) 140 eV, and (f) 100 eV, and the inner potential $V_0$ used is 11.5 eV for (110) and 4 eV for (001) films, respectively. The sample temperature was $\sim 70$ K. On the left half of (c)–(f), the calculated Fermi surfaces are shown with a $k_z$ broadening of 0.2 Å${}^{-1}$. For bulk ${\mathrm{IrO}}_2$, $\pi /a=\pi /b\simeq 0.70$ Å${}^{-1}$, $\pi /c\simeq 1.00$ Å${}^{-1}$. The experimental data show a slight mismatch with the drawn bulk BZs in view of the strain on films. In all ARPES plots and in the text we name $xy$ the sample surface plane and $z$ the axis normal, for both orientations. As a consequence, $k_z$ is the out of plane momentum regardless of the surface.

Figure 3

(a) The Fermi surface for the (110) surface at the BZ center, from Fig. 2. The dashed lines and the arrow indicate the locations of the dispersion images for the data in (b)–(g), where the DFT results are superposed as dashed curves. (i) and (j)–(o) The equivalent of (a) and (b)–(g) for the (001) surface. (h) and (p) The nodal line dispersion along $A\text{−}M\text{−}A$ and $X\text{−}M\text{−}X$, respectively. The sample temperature was $\sim 70$ K. The photon energy is 124 eV for $A\text{−}M$ and 140 eV for $X\text{−}M$.