New type of quantum criticality in the pyrochlore iridates

Physical Review X

Volumn 4, Issue 4, 2014, Pages

  Savary, Lucile ^a   Moon, Eun Gook ^a   Balents, Leon ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANTIFERROMAGNETISM; CRITICALITY (NUCLEAR FISSION); FERMI LIQUIDS; STATISTICAL MECHANICS;

ANTI-FERROMAGNETIC FLUCTUATIONS; CONDUCTING MATERIALS; MAGNETIC FLUCTUATION; NON-FERMI-LIQUID BEHAVIOR; QUANTUM CRITICAL POINTS; RENORMALIZATION GROUP TECHNIQUE; SPIN-ORBIT COUPLINGS; UNCONVENTIONAL SUPERCONDUCTORS;

IRIDIUM COMPOUNDS;

EID: 84921044902     PISSN: None     EISSN: 21603308     Source Type: Journal    
DOI: 10.1103/PhysRevX.4.041027     Document Type: Article

References (37)

1. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, England, 2011).
2. H. v. Löhneysen, A. Rosch, M. Vojta, and P. Wölfle, Fermi-Liquid Instabilities at Magnetic Quantum Phase Transitions, Rev. Mod. Phys. 79, 1015 (2007).
3. J. A. Hertz, Quantum Critical Phenomena, Phys. Rev. B 14, 1165 (1976).
4. A. J. Millis, Effect of a Nonzero Temperature on Quantum Critical Points in Itinerant Fermion Systems, Phys. Rev. B 48, 7183 (1993).
5. S.-S. Lee, Low-Energy Effective Theory of Fermi Surface Coupled with U(1) Gauge Field in 2 + 1 Dimensions, Phys. Rev. B 80, 165102 (2009).
6. M. A. Metlitski and S. Sachdev, Quantum Phase Transitions of Metals in Two Spatial Dimensions. II. Spin Density Wave Order, Phys. Rev. B 82, 075128 (2010).
7. D. F. Mross, J. McGreevy, H. Liu, and T. Senthil, Controlled Expansion for Certain Non-Fermi-Liquid Metals, Phys. Rev. B 82, 045121 (2010).
8. K. B. Efetov, H. Meier, and C. Pépin, Pseudogap State Near a Quantum Critical Point, Nat. Phys. 9, 442 (2013).
9. X. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Topological Semimetal and Fermi-Arc Surface States in the Electronic Structure of Pyrochlore Iridates, Phys. Rev. B 83, 205101 (2011).
10. E.-G. Moon, C. Xu, Y. Baek Kim, and L. Balents, Non-Fermi-Liquid and Topological States with Strong Spin-Orbit Coupling, Phys. Rev. Lett. 111, 206401 (2013).
11. R. Chen, E.-G. Moon, and L. Balents (unpublished).
12. T. Kondo, S. Nakatsuji et al. (unpublished).
13. K. Matsuhira, M. Wakeshima, Y. Hinatsu, and S. Takagi, Metal-Insulator Transitions in Pyrochlore Oxides Ln2Ir2O7, J. Phys. Soc. Jpn. 80, 094701 (2011).
14. W. Witczak-Krempa, A. Go, and Y. Baek Kim, Pyrochlore Electrons under Pressure, Heat, and Field: Shedding Light on the Iridates, Phys. Rev. B 87, 155101 (2013).
15. H. Sagayama, D. Uematsu, T. Arima, K. Sugimoto, J. J. Ishikawa, E. O'Farrell, and S. Nakatsuji, 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).
16. K. Tomiyasu, K. Matsuhira, K. Iwasa, M. Watahiki, S. Takagi, M. Wakeshima, Y. Hinatsu, M. Yokoyama, K. Ohoyama, and K. Yamada, Emergence of Magnetic Long-Range Order in Frustrated Pyrochlore Nd2Ir2O7 with Metal-Insulator Transition, J. Phys. Soc. Jpn. 81, 034709 (2012).
17. 7 (A = Y, Yb), Phys. Rev. B 86, 014428 (2012).
18. K. A. Ross, L. Savary, B. D. Gaulin, and L. Balents, Quantum Excitations in Quantum Spin Ice, Phys. Rev. X 1, 021002 (2011).
19. Q. Si and E. Abrahams, Strong Correlations and Magnetic Frustration in the High Tc Iron Pnictides, Phys. Rev. Lett. 101, 076401 (2008).
20. J. Kim, A. H. Said, D. Casa, M. H. Upton, T. Gog, M. Daghofer, G. Jackeli, J. van den Brink, G. Khaliullin, and B. J. Kim, Large Spin-Wave Energy Gap in the Bilayer Iridate Sr3Ir2O7: Evidence for Enhanced Dipolar Interactions Near the Mott Metal-Insulator Transition, Phys. Rev. Lett. 109, 157402 (2012).
21. J.W. Kim, Y. Choi, J. Kim, J. F. Mitchell, G. Jackeli, M. Daghofer, J. van den Brink, G. Khaliullin, and B. J. Kim, Dimensionality Driven Spin-Flop Transition in Layered Iridates, Phys. Rev. Lett. 109, 037204 (2012).
22. A. A. Abrikosov and S. D. Beneslavskii, Possible Existence of Substances Intermediate between Metals and Dielectrics, Sov. Phys. JETP 32, 699 (1971).
23. A. A. Abrikosov, Calculation of Critical Indices for Zero-Gap Semiconductors, Sov. Phys. JETP 39, 709 (1974).
24. O. Vafek and A. Vishwanath, Dirac Fermions in Solids: From High-Tc Cuprates and Graphene to Topological Insulators and Weyl Semimetals, Annu. Rev. Condens. Matter Phys. 5, 83 (2014).
25. Y. Huh and S. Sachdev, Renormalization Group Theory of Nematic Ordering in d-Wave Superconductors, Phys. Rev. B 78, 064512 (2008).
26. M. Vojta, Y. Zhang, and S. Sachdev, Renormalization Group Analysis of Quantum Critical Points in d-Wave Superconductors, Int. J. Mod. Phys. B 14, 3719 (2000).
27. Note that a number of technicalities are involved in this calculation, in particular, regarding the convergence of the differentiated functions. They are all discussed in Appendices C 2 and C 3
28. M. Kurita, Y. Yamaji, and M. Imada, Phase Diagram Structure of Topological Mott Transition for Zero-Gap Semiconductors beyond Conventional Landau-Ginzburg- Wilson Scenario, Phys. Rev. B 88, 115143 (2013).
29. W. Witczak-Krempa and Y. Baek Kim, Topological and Magnetic Phases of Interacting Electrons in the Pyrochlore Iridates, Phys. Rev. B 85, 045124 (2012).
30. G. Chen and M. Hermele, Magnetic Orders and Topological Phases from f-d Exchange in Pyrochlore Iridates, Phys. Rev. B 86, 235129 (2012).
31. R. Flint and T. Senthil, Chiral RKKY Interaction in Pr2Ir2O7, Phys. Rev. B 87, 125147 (2013).
32. S. Lee, A. Paramekanti, and Y. Baek Kim, RKKY Interactions and the Anomalous Hall Effect in Metallic Rare-Earth Pyrochlores, Phys. Rev. Lett. 111, 196601 (2013).
33. T. Hahn, Cuba-A Library for Multidimensional Numerical Integration, Comput. Phys. Commun. 168, 78 (2005).
34. D. Binosi and L. Theul, JaxoDraw: A Graphical User Interface for Drawing Feynman Diagrams, Comput. Phys. Commun. 161, 76 (2004).
35. J. M. Luttinger, Quantum Theory of Cyclotron Resonance in Semiconductors: General Theory, Phys. Rev. 102, 1030 (1956).
36. S. Murakami, N. Nagaosa, and S.-C. Zhang, SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors, Phys. Rev. B 69, 235206 (2004).
37. M. Kardar, Statistical Physics of Fields (Cambridge University Press, Cambridge, England, 2007).