Strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides [1-4]. Here, in the pyrochlore iridate Pr₂Ir₂O₇, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behavior is predicted, for which we observe some evidence. Our discovery implies that Pr₂Ir₂O₇ is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.

Fig. 1. Quadratic Fermi node state of Pr₂Ir₂O₇ tunable into interacting topological phases. In the lower part of the diagram, the bottom half of the blue circle and its reflection form a caricature of the quadratically dispersion conduction and valence bands touching at the zone centre, while at the same time the darker-blue upper circle suggests how Pr₂Ir₂O₇, with non-negligible Coulomb interactions, is a strongly correlated non-Fermi liquid analogue of HgTe, shown as a pale-blue reflection. Arrows indicate the perturbations that convert the nodal non-Fermi liquid state to diverse topological phases.

Fig. 2. Fermi node state of Pr₂Ir₂O₇ revealed by ARPES with synchrotron radiation source. (a) Brillouin zone, showing measured momentum sheets. (b,c) ARPES intensities at E_F in the k_x-k_y sheet crossing Γ and L measured at hv=52eV and 39eV, respectively. The calculated band dispersion in the k_x-k₍₁₁₁₎ sheet. Energy dispersions determined by ARPES are plotted on it. (e) ARPES dispersion map crossing Γ, measured at an elevated temperature (T=75K).

The experimental evidence for a quadratic Fermi node state in Pr₂Ir₂O₇ is demonstrated in Fig. 2. In the panel (d), we observe that a parabolic energy-dispersion approaches E_F with increasing photon energies (or k_z values), and finally touches it at the Γ point (a red curve). We have confirmed that, with further increase of k_z, the dispersion gets away from E_F again, which signifies that the 3D band structure of Pr2Ir₂O7 has a single Fermi point (Fig. 2(b)). Other scans of different k_z values up to the L point (Fig.(c)) revealed no other states touching or crossing E_F. This circumstance satisfies the charge neutrality, and it could be a further evidence for the realization of nodal state. We also find that the broad spectral weight emerges beyond E_F as seen in the Fermi-function-divided image for the 75K data (arrow in Fig. 2(e)). This observation is compatible with the predicted existence of a quadratic band touching on the unoccupied side.

References

• [1] B. J. Kim et al., Science 323, 1329 (2009).
• [2] Y. Machida et al., Nature 463, 210 (2009).
• [3] D. Pesin et al., Nature Physics 6, 376 (2010).
• [4] X. Wan et al., Phys. Rev. B 83, 205101 (2011).
• [5] T. Kondo et al., Nature communications 6, 10042 (2015).

Authors

• T. Kondo, M. Nakayama, R. Chen^a, J. J. Ishikawa, E.-G. Moon^a, T. Yamamoto, Y. Ota, W. Malaeb, H. Kanai, Y. Nakashima, Y. Ishida, R. Yoshida, H. Yamamoto, M. Matsunami^b, S. Kimura^b, N. Inami^c, K. Ono^c, H. Kumigashira^c, S. Nakatsuji, L. Balents^a, and S. Shin
• ^aUniversity of California
• ^bUVSOR Facility, Institute for Molecular Science
• ^cHigh Energy Accelerator Research Organization (KEK)