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# Unconventional free charge in the correlated semimetal Nd2Ir2O7

## Abstract

Nd2Ir2O7 is a correlated semimetal with the pyrochlore structure, in which competing spin–orbit coupling and electron–electron interactions are believed to induce a time-reversal symmetry-broken Weyl semimetal phase characterized by pairs of topologically protected Dirac points at the Fermi energy1,2,3,4. However, the emergent properties in these materials are far from clear, and exotic new states of matter have been conjectured5,6,7. Here, we demonstrate optically that, at low temperatures, the free carrier spectral weight is proportional to T2, where T is the temperature, as expected for massless Dirac electrons. However, we do not observe the corresponding T3 term in the specific heat. That the system is not in a Fermi liquid state is further corroborated by the charge carrier scattering rate approaching critical damping and the progressive opening of a correlation-induced gap at low temperatures. These observations cannot be reconciled within the framework of band theory of electron-like quasiparticles and point towards the effective decoupling of the charge transport from the single particle sector.

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## Data availability

The datasets generated and analysed during the current study are available in ref. 43. These will be preserved for 10 years. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

## References

1. 1.

Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011).

2. 2.

Tian, Z. et al. Field-induced quantum metal–insulator transition in the pyrochlore iridate Nd2Ir2O7. Nat. Phys. 12, 134–138 (2016).

3. 3.

Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018).

4. 4.

Ohtsuki, T. et al. Strain-induced spontaneous Hall effect in an epitaxial thin film of a Luttinger semimetal. Proc. Natl Acad. Sci. USA 116, 8803–8808 (2019).

5. 5.

Pesin, D. & Balents, L. Mott physics and band topology in materials with strong spin–orbit interaction. Nat. Phys. 6, 376–381 (2010).

6. 6.

Moon, E.-G., Xu, C., Kim, Y. B. & Balents, L. Non-Fermi-liquid and topological states with strong spin–orbit coupling. Phys. Rev. Lett. 111, 206401 (2013).

7. 7.

Morimoto, T. & Nagaosa, N. Weyl Mott insulator. Sci. Rep. 6, 19853 (2016).

8. 8.

Dzero, M., Sun, K., Galitski, V. & Coleman, P. Topological Kondo insulators. Phys. Rev. Lett. 104, 106408 (2010).

9. 9.

Kim, D. J., Xia, J. & Fisk, Z. Topological surface state in the Kondo insulator samarium hexaboride. Nat. Mater. 13, 466–470 (2014).

10. 10.

Nakatsuji, S., Kiyohara, N. & Higo, T. Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature. Nature 527, 212–215 (2015).

11. 11.

Kuroda, K. et al. Evidence for magnetic Weyl fermions in a correlated metal. Nat. Mater. 16, 1090–1095 (2017).

12. 12.

Lai, H.-H., Grefe, S. E., Paschen, S. & Si, Q. Weyl–Kondo semimetal in heavy-fermion systems. Proc. Natl Acad. Sci. USA 115, 93–97 (2018).

13. 13.

Xu, Y., Yue, C., Weng, H. & Dai, X. Heavy Weyl fermion state in CeRu4Sn6. Phys. Rev. X 7, 011027 (2017).

14. 14.

Kondo, T. et al. Quadratic Fermi node in a 3D strongly correlated semimetal. Nat. Commun. 6, 10042 (2015).

15. 15.

Cheng, B. et al. Dielectric anomalies and interactions in the three-dimensional quadratic band touching Luttinger semimetal Pr2Ir2O7. Nat. Commun. 8, 2097 (2017).

16. 16.

Tomiyasu, K. et al. Emergence of magnetic long-range order in frustrated pyrochlore Nd2Ir2O7 with metal–insulator transition. J. Phys. Soc. Jpn 81, 034709 (2012).

17. 17.

Guo, H. et al. Magnetic order in the pyrochlore iridate Nd2Ir2O7 probed by muon spin relaxation. Phys. Rev. B 88, 060411 (2013).

18. 18.

Sagayama, H. et al. Determination of long-range all-in-all-out ordering of Ir4+ moments in a pyrochlore iridate Eu2Ir2O7 by resonant X-ray diffraction. Phys. Rev. B 87, 100403 (2013).

19. 19.

Ma, E. Y. et al. Mobile metallic domain walls in an all-in-all-out magnetic insulator. Science 350, 538–541 (2015).

20. 20.

Donnerer, C. et al. All-in-all-out magnetic order and propagating spin waves in Sm2Ir2O7. Phys. Rev. Lett. 117, 037201 (2016).

21. 21.

Chun, S. H. et al. Magnetic excitations across the metal–insulator transition in the pyrochlore iridate Eu2Ir2O7. Phys. Rev. Lett. 120, 177203 (2018).

22. 22.

Go, A., Witczak-Krempa, W., Jeon, G. S., Park, K. & Kim, Y. B. Correlation effects on 3D topological phases: from bulk to boundary. Phys. Rev. Lett. 109, 066401 (2012).

23. 23.

Witczak-Krempa, W. & Kim, Y. B. Topological and magnetic phases of interacting electrons in the pyrochlore iridates. Phys. Rev. B 85, 045124 (2012).

24. 24.

Witczak-Krempa, W., Go, A. & Kim, Y. B. Pyrochlore electrons under pressure, heat, and field: shedding light on the iridates. Phys. Rev. B 87, 155101 (2013).

25. 25.

Shinaoka, H., Hoshino, S., Troyer, M. & Werner, P. Phase diagram of pyrochlore iridates: all-in-all-out magnetic ordering and non-Fermi-liquid properties. Phys. Rev. Lett. 115, 156401 (2015).

26. 26.

Ueda, K. et al. Magnetic-field induced multiple topological phases in pyrochlore iridates with Mott criticality. Nat. Commun. 8, 15515 (2017).

27. 27.

Ueda, K. et al. Variation of charge dynamics in the course of metal–insulator transition for pyrochlore-type Nd2Ir2O7. Phys. Rev. Lett. 109, 136402 (2012).

28. 28.

Ueda, K., Fujioka, J. & Tokura, Y. Variation of optical conductivity spectra in the course of bandwidth-controlled metal–insulator transitions in pyrochlore iridates. Phys. Rev. B 93, 245120 (2016).

29. 29.

Sushkov, A. B. et al. Optical evidence for a Weyl semimetal state in pyrochlore Eu2Ir2O7. Phys. Rev. B 92, 241108 (2015).

30. 30.

Machida, Y., Nakatsuji, S., Onoda, S., Tayama, T. & Sakakibara, T. Time-reversal symmetry breaking and spontaneous Hall effect without magnetic dipole order. Nature 463, 210–213 (2010).

31. 31.

Tabert, C. J. & Carbotte, J. P. Optical conductivity of Weyl semimetals and signatures of the gapped semimetal phase transition. Phys. Rev. B 93, 085442 (2016).

32. 32.

Tabert, C. J., Carbotte, J. P. & Nicol, E. J. Optical and transport properties in three-dimensional Dirac and Weyl semimetals. Phys. Rev. B 93, 085426 (2016).

33. 33.

Lide, D. R. CRC Handbook of Chemistry and Physics 71st edn (CRC Press, 1990).

34. 34.

Hosur, P., Parameswaran, S. A. & Vishwanath, A. Charge transport in Weyl semimetals. Phys. Rev. Lett. 108, 046602 (2012).

35. 35.

Zaanen, J. Planckian dissipation, minimal viscosity and the transport in cuprate strange metals. SciPost Phys. 6, 061 (2019).

36. 36.

Watahiki, M. et al. Crystalline electric field study in the pyrochlore Nd2Ir2O7 with metal–insulator transition. J. Phys. Conf. Ser. 320, 012080 (2011).

37. 37.

Phillips, P. Mottness. Ann. Phys. 321, 1634–1650 (2006).

38. 38.

Wang, R., Go, A. & Millis, A. Weyl rings and enhanced susceptibilities in pyrochlore iridates: kp analysis of cluster dynamical mean-field theory results. Phys. Rev. B 96, 195158 (2017).

39. 39.

Grüner, G. The dynamics of charge-density waves. Rev. Mod. Phys. 60, 1129–1181 (1988).

40. 40.

Ishikawa, J. J., O’Farrell, E. C. T. & Nakatsuji, S. Continuous transition between antiferromagnetic insulator and paramagnetic metal in the pyrochlore iridate Eu2Ir2O7. Phys. Rev. B 85, 245109 (2012).

41. 41.

Chen, G. & Hermele, M. Magnetic orders and topological phases from fd exchange in pyrochlore iridates. Phys. Rev. B 86, 235129 (2012).

42. 42.

Ruminy, M. et al. First-principles calculation and experimental investigation of lattice dynamics in the rare-earth pyrochlores R2Ti2O7 (R = Tb, Dy, Ho). Phys. Rev. B 93, 214308 (2016).

43. 43.

Optics, Transport, Specific Heat and Magnetic Susceptibility of the Correlated Semimetal Nd2Ir2O7 (Yareta, 2020); https://doi.org/10.26037/yareta:3k2uscc2bjbqdisikigdjcx2lm

## Acknowledgements

D.v.d.M. acknowledges insightful discussions with D. Abanin and N. Nagaosa. This project was supported by the Swiss National Science Foundation (project no. 200020-179157). This work is partially supported by CREST (JPMJCR18T3), the Japan Science and Technology Agency (JST), by Grants-in-Aids for Scientific Research on Innovative Areas (15H05882 and 15H05883) from the Ministry of Education, Culture, Sports, Science and Technology of Japan and by Grants-in-Aid for Scientific Research (19H00650). Work at JHU was supported through the Institute for Quantum Matter, an EFRC funded by the US DOE, Office of BES (DE-SC0019331).

## Author information

Authors

### Contributions

K.W., B.X., C.W.R., N.B., B.M. and J.T. performed experiments. Y.Q., T.O., B.C. and S.N. prepared samples. K.W., N.B., B.M. and D.v.d.M. analysed data. N.P.A. and D.v.d.M. planned the project. K.W. and D.v.d.M. wrote the manuscript with input and comments from all other authors.

### Corresponding author

Correspondence to D. van der Marel.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Extended data

### Extended Data Fig. 1 Reflectance spectra.

Solid curves: Near normal incidence reflectivity, R=r2, of Nd2Ir2O7 for selected temperatures. Dotted curves below 50 cm−1: Extrapolations using simultaneous Drude–Lorentz fitting to the reflectance spectra and the ellipsometric data beween 4000 and 18000 cm−1 of Extended Data Fig. 2. a, Between 30 and 300 K. b, Between 6 and 30 K.

### Extended Data Fig. 2 Ellipsometric data between 4000 and 18000 cm−1.

a, Real and imaginary part of the dielectric function at room temperature measured using spectroscopic ellipsometry at θ = 65 degrees with the surface normal. b, Phase of the normal incidence reflection coefficient using the Fresnel equation $$| {\rm{r}}| {{\rm{e}}}^{{\rm{i}}\phi }=(1-\sqrt{\varepsilon })/(1+\sqrt{\varepsilon })$$. c, Absolute square of the reflection coefficient.

### Extended Data Fig. 3 Thermodynamic properties of the Nd 4f states.

Model calculation of the exchange potential at the Nd sites Δ(T), entropy per primitive cell sf(T), and specific heat per primitive cell cf(T) (see Methods). a,c,e,f, Δ0 =6.5 K and TN=37 K. b,d,g, Δ0 =15 K and TN =30 K.

### Extended Data Fig. 4 Comparison of the contributions to the specific heat per primitive cell.

Experimental specific heat per primitive cell of Nd2Ir2O7. Red curve: Calculated phonon contribution (see Methods). Olive curve: Calculated contribution of the itinerant Ir 5d band electrons (see Methods). Brown curve: The contribution from the localized Nd 4f electrons (see Methods).

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Wang, K., Xu, B., Rischau, C.W. et al. Unconventional free charge in the correlated semimetal Nd2Ir2O7. Nat. Phys. 16, 1194–1198 (2020). https://doi.org/10.1038/s41567-020-0955-0

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