Abstract
Recent theory and experiment have revealed that strong spin–orbit coupling can have marked qualitative effects on the band structure of weakly interacting solids, leading to a distinct phase of matter, the topological band insulator. We show that spin–orbit interaction also has quantitative and qualitative effects on the correlation-driven Mott insulator transition. Taking Ir-based pyrochlores as a specific example, we predict that for weak electron–electron interaction Ir electrons are in metallic and topological band insulator phases at weak and strong spin–orbit interaction, respectively. We show that by increasing the electron–electron interaction strength, the effects of spin–orbit coupling are enhanced. With increasing interactions, the topological band insulator is transformed into a ‘topological Mott insulator’ phase having gapless surface spin-only excitations. The proposed phase diagram also includes a region of gapless Mott insulator with a spinon Fermi surface, and a magnetically ordered state at still larger electron–electron interaction.
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References
Kane, C. & Mele, E. Z(2) topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95, 146802 (2005).
Bernevig, B. A., Hughes, T. L. & Zhang, S.-C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757–1761 (2006).
Moore, J. E. & Balents, L. Topological invariants of time-reversal-invariant band structures. Phys. Rev. B 75, 121306 (2007).
Fu, L., Kane, C. L. & Mele, E. J. Topological insulators in three dimensions. Phys. Rev. Lett. 98, 106803 (2007).
Konig, M. et al. Quantum spin Hall insulator state in HgTe quantum wells. Science 318, 766–770 (2007).
Hsieh, D. et al. A topological Dirac insulator in a quantum spin Hall phase. Nature 452, 970–974 (2008).
Chen, G. & Balents, L. Spin–orbit effects in Na4Ir3O8: A hyper-kagome lattice antiferromagnet. Phys. Rev. B 78, 094403 (2008).
Tovar, M., Raman, K. S. & Shtengel, K. Dzyaloshinskii-Moriya interactions in valence-bond systems. Phys. Rev. B 79, 024405 (2009).
Chen, G., Balents, L. & Schnyder, A. P. Spin-orbital singlet and quantum critical point on the diamond lattice: FeSc2S4 . Phys. Rev. Lett. 102, 096406 (2009).
Kim, B. J. et al. Phase-sensitive observation of a spin-orbital Mott state in Sr2IrO4 . Science 323, 1329–1332 (2009).
Shitade, A. et al. Quantum spin Hall effect in a transition metal oxide Na2IrO3 . Phys. Rev. Lett. 102, 256403 (2009).
Matsuhira, K. et al. Metal–insulator transition in pyrochlore iridates Ln2Ir2O7 (Ln=Nd, Sm, and Eu). J. Phys. Soc. Jpn 76, 043706 (2007).
Okamoto, Y., Nohara, M., Aruga-Katori, H. & Takagi, H. Spin-liquid state in the S=1/2 hyperkagome antiferromagnet Na4Ir3O8 . Phys. Rev. Lett. 99, 137207 (2007).
Fukazawa, H. & Maeno, Y. Filling control of the pyrochlore oxide Y2Ir2O7 . J. Phys. Soc. Jpn 71, 2578–2579 (2002).
Nakatsuji, S. et al. Metallic spin-liquid behavior of the geometrically frustrated Kondo lattice Pr2Ir2O7 . Phys. Rev. Lett. 96, 087204 (2006).
Abragam, A. & Bleaney, B. Electron Paramagnetic Resonance of Transition Ions (Clarendon, 1975).
Jin, H., Kim, H., Jeong, H., Kim, C. H. & Yu, J. Mott insulating ground state and its proximity to spin–orbit insulators in Na2IrO3. Preprint at <http://arxiv.org/abs/0907.0743> (2009).
Slater, J. & Koster, G. Simplified LCAO method for the periodic potential problem. Phys. Rev. 94, 1498–1524 (1954).
Fu, L. & Kane, C. Topological insulators with inversion symmetry. Phys. Rev. B 76, 045302 (2007).
Elhajal, M., Canals, B., Sunyer, R. & Lacroix, C. Ordering in the pyrochlore antiferromagnet due to Dzyaloshinsky-Moriya interactions. Phys. Rev. B 71, 094420 (2005).
Florens, S. & Georges, A. Slave-rotor mean-field theories of strongly correlated systems and the Mott transition in finite dimensions. Phys. Rev. B 70, 035114 (2004).
Mizusaki, T. & Imada, M. Gapless quantum spin liquid, stripe, and antiferromagnetic phases in frustrated Hubbard models in two dimensions. Phys. Rev. B 74, 014421 (2006).
Motrunich, O. Variational study of triangular lattice spin-1/2 model with ring exchanges and spin liquid state in κ-(ET)2Cu2(CN)3 . Phys. Rev. B 72, 045105 (2005).
Sahebsara, P. & Sénéchal, D. Hubbard model on the triangular lattice: Spiral order and spin liquid. Phys. Rev. Lett. 100, 136402 (2008).
Raghu, S., Qi, X.-L., Honerkamp, C. & Zhang, S.-C. Topological Mott insulators. Phys. Rev. Lett. 100, 156401 (2008).
Young, M. W., Lee, S.-S. & Kallin, C. Fractionalized quantum spin Hall effect. Phys. Rev. B 78, 125316 (2008).
Qi, X., Li, R., Zang, J. & Zhang, S. Inducing a magnetic monopole with topological surface states. Science 323, 1184–1187 (2009).
Qi, X., Hughes, T. & Zhang, S. Topological field theory of time-reversal invariant insulators. Phys. Rev. B 78, 195424 (2008).
Essin, A., Moore, J. & Vanderbilt, D. Magnetoelectric polarizability and axion electrodynamics in crystalline insulators. Phys. Rev. Lett. 102, 146805 (2009).
Wilczek, F. Two applications of axion electrodynamics. Phys. Rev. Lett. 58, 1799–1802 (1987).
Podolsky, D., Paramekanti, A., Kim, Y. B. & Senthil, T. Mott transition between a spin-liquid insulator and a metal in three dimensions. Phys. Rev. Lett. 102, 186401 (2009).
Ioffe, L. B. & Larkin, A. I. Gapless fermions and gauge fields in dielectrics. Phys. Rev. B 39, 8988–8999 (1989).
Yamashita, S. et al. Thermodynamic properties of a spin-1/2 spin-liquid state in a κ-type organic salt. Nature Phys. 4, 459–462 (2008).
Lawler, M. J., Paramekanti, A., Kim, Y. B. & Balents, L. Gapless spin liquids on the three-dimensional hyperkagome lattice of Na4Ir3O8 . Phys. Rev. Lett. 101, 197202 (2008).
Zhou, Y., Lee, P. A., Ng, T.-K. & Zhang, F.-C. Na4Ir3O8 as a 3D spin liquid with fermionic spinons. Phys. Rev. Lett. 101, 197201 (2008).
Senthil, T. Theory of a continuous Mott transition in two dimensions. Phys. Rev. B 78, 045109 (2008).
Kyung, B. & Tremblay, A.-M. S. Mott transition, antiferromagnetism, and d-wave superconductivity in two-dimensional organic conductors. Phys. Rev. Lett. 97, 046402 (2006).
Morita, H., Watanabe, S. & Imada, M. Nonmagnetic insulating states near the Mott transitions on lattices with geometrical frustration and implications for κ-(ET)2Cu2(CN)3 . J. Phys. Soc. Jpn 71, 2109–2112 (2002).
Lee, H. & Monien, H. Mott transition in the Hubbard model on the hyper-kagome lattice. Preprint at <http://arxiv.org/abs/0903.3005> (2009).
Yoshikawa, T. & Ogata, M. Role of frustration and dimensionality in the Hubbard model on the stacked square lattice: Variational cluster approach. Phys. Rev. B 79, 144429 (2009).
Halperin, B. I. & Rice, T. M. Possible anomalies at a semimetal–semiconductor transition. Rev. Mod. Phys. 40, 755–766 (1968).
Halperin, B. I., Lubensky, T. C. & Ma, S.-K. First-order phase transitions in superconductors and smectic-A liquid crystals. Phys. Rev. Lett. 32, 292–295 (1974).
Acknowledgements
This work was supported by the DOE through Basic Energy Sciences grants DE-FG02-08ER46524 (L.B.) and DEFG02-07ER46452 (D.P.). The research facilities at the KITP were supported by the National Science Foundation grant NSF PHY-0551164.
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Pesin, D., Balents, L. Mott physics and band topology in materials with strong spin–orbit interaction. Nature Phys 6, 376–381 (2010). https://doi.org/10.1038/nphys1606
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DOI: https://doi.org/10.1038/nphys1606
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