Oxygen vacancy-driven orbital multichannel Kondo effect in Dirac nodal line metals IrO2 and RuO2

Abstract

Strong electron correlations have long been recognized as driving the emergence of novel phases of matter. A well recognized example is high-temperature superconductivity which cannot be understood in terms of the standard weak-coupling theory. The exotic properties that accompany the formation of the two-channel Kondo (2CK) effect, including the emergence of an unconventional metallic state in the low-energy limit, also originate from strong electron interactions. Despite its paradigmatic role for the formation of non-standard metal behavior, the stringent conditions required for its emergence have made the observation of the nonmagnetic, orbital 2CK effect in real quantum materials difficult, if not impossible. We report the observation of orbital one- and two-channel Kondo physics in the symmetry-enforced Dirac nodal line (DNL) metals IrO₂ and RuO₂ nanowires and show that the symmetries that enforce the existence of DNLs also promote the formation of nonmagnetic Kondo correlations. Rutile oxide nanostructures thus form a versatile quantum matter platform to engineer and explore intrinsic, interacting topological states of matter.

Fig. 1. Atomic arrangement around an oxygen vacancy in MO₂ rutile structure.

a Schematics for MO₂ in the rutile structure. The olive and red spheres represent transition-metal ions M⁴⁺ and oxygen ions O²⁻, respectively. V_O1 represents an oxygen vacancy. b The metal ions M1, M2, and M3 surrounding V_O1 form an isosceles triangle. c The four oxygen ions surrounding M2, labeled O4, O9, O10, and O8, form an almost perfect planar square (while O1${}^{\prime }$, O5${}^{\prime }$, O3${}^{\prime }$, and O4${}^{\prime }$ only form a rectangle, cf. Supplementary Note 4 for details). d The d_xz and d_yz orbitals at M2 next to V_O1, with $\widehat{z}$ perpendicular to the O4, O8, O10, and O9 plane, remain essentially degenerate as a result of mirror and C₄ rotation symmetry around M2. (Due to the non-symmorphic rutile structure, $\widehat{z}$∦${\widehat{z}}^{\prime }$, where ${\widehat{z}}^{\prime }$ is parallel to the C₄ axis at M1.).

Fig. 2. Orbital 2CK resistivity of IrO₂ NWs.

ρ versus $\sqrt{T}$ for IrO₂ NWs A, B1 and B2 in magnetic fields B = 0, 6, and 9 T, as indicated. For clarity, the data of NWs B1 and B2 are shifted by 34.7 and 33.6 μΩ cm, respectively. A $\rho \propto \sqrt{T}$ law, which is B independent, is observed between  ~0.5 and  ~20 K in all three NWs. The straight solid lines are linear fits to the 2CK resistivities calculated by the dynamical large-N method (see text). Top left inset: a scanning electron microscopy image of NW A. The scale bar is 1 μm. Top right inset: Low-T ρ(T) curves of NW A and a reference, oxygenated NW 3 (diameter d = 330 nm, ρ(300 K) = 124 μΩ cm).

Fig. 3. Orbital 1CK resistivity of RuO₂ NWs.

a Time-averaged Kondo resistivity 〈ρ_K〉 versus $\log T$ for NW C. The straight line in the inset, which shows a low-T zoom-in, is a guide to the eye. b ρ versus $\log T$ in B = 0 and 4 T for NW E. For clarity, the B = 0 data are time-averaged, while the 4-T data are non-averaged to demonstrate the temporal resistivity fluctuations at low T. The inset shows the time-averaged B = 4 T data (red symbols), which closely overlap the B = 0 data. c ρ versus $\log T$ for NW A in B = 0, 3, and 5 T. Occasional resistivity jumps, or random telegraph noise, are observed. The dash-dotted curves depict the magnetoresistance predicted by the spin-$\frac{1}{2}$ Kondo impurity model (see text). Note that the experimental data are independent of B. Inset: Low-T ρ(T) curves of NW A and a reference, oxygenated NW 4 (d = 150 nm, ρ(300 K) = 336 μΩ cm). In a–c, the solid curve shows the B = 0 numerical renormalization group result for 1CK effect.

Fig. 4. Comparison of 2CK and 1CK resistivities.

a Normalized Kondo resistivity 〈ρ_K〉/ρ_K0 versus T/T_K for RuO₂ NWs A–E manifests the 1CK scaling form (solid curve) for over three decades of reduced temperature. b 〈ρ_K〉/ρ_K0 versus $\sqrt{T/T_{\mathrm{K}}}$ for IrO₂ NW A and RuO₂ NWs B–E. The data of IrO₂ NW A obeys a $\sqrt{T}$ law between 0.39 and 21 K. For clarity, the experimental data points for RuO₂ NWs are plotted with small open symbols. c 〈ρ_K〉/ρ_K0 of IrO₂ NW B1 obeys a $\sqrt{T/T_{\mathrm{K}}}$ law between 0.66 and 22 K, distinctively deviating from the 1CK function. d Results for the resistivity of a diluted system of 2CK impurities in a metallic host evaluated using a dynamical large-N limit (black symbols), which follows a $\sqrt{T/T_{\mathrm{K}}}$ law at low T (see text and Supplementary Note 5). The ordinate is plotted in unit of half-bandwidth W = 4 eV (ref. ).