Spin-orbit physics in the Mott regime Leon Balents, KITP “Exotic Insulating State of Matter”, JHU, January 2010 Collaborator Dymtro Pesin UT Austin Topological Insulators Exotic Insulating States of Matter » Scientific Program http://icamconferences.org/jhu2010/scientific-program/ Exotic Insulating States of Matter » Scientific Program http://icamconferences.org/jhu2010/scientific-program/ Exotic Insulating States of Matter » Scientific Program http://icamconferences.org/jhu2010/scientific-program/ 7:30 PM Dinner on own 8:00 AM Breakfast Exotic Insulating States of Matter » Scientific Friday, January 15th Novel States: Program 8:00 AM Breakfast 9:00 AM Moses Chan: Is supersolid a superfluid? 9:30 AM Matthew Fisher: Spin Bose-Metals in Weak Mott Insulators Higher-T superconductors: Thursday, January 14th c 10:00 AM Leon Balents: Spin-orbit physics in the Mott regime 9:00 AM Zlatko Tesanovic: Correlated superconductivity in cuprates and pnictides 8:00 AM Breakfast and Registration 9:30 AM Andrei Bernevig: Nodal and nodeless superconductivity in the iron based 10:30 AM Break 8:55 AM Greeting – Welcome superconductors Transport in Topological Insulators: 10:00 AM John Tranquada: Striped Superconductivity in La2-xBaxCuO4 Topological Insulators: 11:00 AM Ashvin Vishwanath: Topological Defects and Entanglement in Topological Insulators 9:00 AM S.-C. Zhang: Topological insulators and topological superconductors 10:30 AM Break 11:30 AM Phuan Ong: Transport Experiments on topological insulators Bi Se and Bi Te 9:30 AM Charles Kane: Topological Insulators and Majorana Fermions 2 3 2 3 12:00 AM Yoichi Ando: Anomalous Magnetotransport in a Topological Insulator Bi Sb 10:00 AM Zahid Hasan: Experimental discovery of two classes of Topological Insulators and Unusual superconducting and insulating phases in disordered systems: 1-x x related Superconductors using Spin-sensitive methods 11:00 AM Allen Goldman: The Insulating States of Ultrathin Superconducting Films Tuned by Perpendicular Magnetic Fields 12:30 PM Lunch 10:30 AM Break 11:30 AM Nandini Trivedi: Local density of states and response functions for the disorder-driven superconductor-insulator transition Dirac Materials: Topological Insulators (continued): 12:00 PM Frank Kruger: Anomalous suppression of the Bose glass at commensurate fillings in 1:30 PM Michael S. Fuhrer: Charge Transport in Dirac Materials 11:00 AM Yulin Chen: Experimental Realization of a Large Gap 3D Topological Insulator with a the disordered Bose-Hubbard model Single Dirac-Cone on the Surface 2:00 PM Eugene J. Mele: Commensuration and Interlayer Coherence in Twisted Bilayer Graphenes 11:30 AM Ali Yazdani: Visualizing Topological Surface States with Scanning Tunneling 12:30 PM Lunch Microscopy & Spectroscopy 12:00 PM Joe Orenstein: Optics as a probe of spin and charge dynamics in 2D metals Unusual superconducting and insulating phases in disordered systems (continued): Novel States (continued): 1:45 PM Benjamin Sacépé: “Evidence of localized Cooper pairs in disordered superconductors 2:30 PM Liang Fu: Odd-Parity Topological Superconductors 12:30 PM Lunch (Posters go up) 2:15 PM Boris Altshuler: Finite temperature superfluid-“insulator” phase transition for 3:00 PM Joel Moore: Topological insulators in applied fields: magnetoelectric effects and exciton disordered bosons in one dimension condensation Superconductivity in reduced dimensions: 2:45 PM Jongsoo Yoon: Transport Phase Diagram of Homogeneously Disordered 3:30 PM Subir Sachdev: Scaling theory of the nematic ordering transition in two-dimensional 1:45 PM Jean-Marc Triscone: Tuning the Electronic Properties at the LaAlO /SrTiO Interface 3 3 Superconducting Tantalum Thin Films metals. (CANCELED DUE TO GENEVA BLIZZARD) 3:15 PM Jim Valles: Experiments on a Cooper Pair Insulator 2:00 PM Gil Refael: The thin film Giaever transformer – vortex drag in a superconductor thin-film bilayer 3:45 PM Break 2:30 PM Sambandamurthy Ganapathy: Transport behavior near phase transitions in quasi-1D systems Topological phases: 4:15 PM Sankar Das Sarma: Topological Quantum Computation using Non-Abelian Anyons Follow us on Twitter » 3:00 PM Break 4:45 PM Iuliana Radu: Quasiparticle tunneling in the Fractional Quantum Hall Effect: Readability version 0.5.1 Experiments at filling fraction 5/2 Building exotic states in cold-atom systems: 5:15 PM Cenke Xu: Fractionalization in Josephson Junction Arrays Hinged by Quantum Spin 3:45 PM Brian DeMarco: Disordered Insulator in an Optical Lattice Hall edges 4:15 PM Tudor Stanescu: Light-induced vector fields, spin-orbit coupling and topological phases 5:45 PM Anton Burkov: Fractional Quantum Hall Effect and Featureless Mott Insulators in cold atom systems 4:45 PM Ian Spielman: Synthetic electromagnetic fields created with light 6:15 PM Poster Session 5:15 PM Congjun Wu: Exotic orbital band and Mott insulating states in optical lattices 7:30 PM Reception and Conference Dinner at Azafran Cafe Public Lecture 6:30 PM Philip Phillips: From the Vulcanization of Rubber, to Quarks and High-Temperature Saturday, January 16th Superconductivity: Physics at Strong Coupling 1 of 3 1/14/10 11:06 AM 2 of 3 1/14/10 11:06 AM so we should all be experts!3 of 3 1/14/10 11:06 AM Topological Insulators 2d: Kane, Mele (2005); Bernevig, Hughes, Zhang (2006) 3d: L. Fu, C. Kane, E. Mele (2007); J. Moore, LB (2007) Band insulators w/ significant SOI can have hidden topological structure, somewhat similar to the IQHE Exhibit “helical” surface states - chiral Dirac fermions (evades Fermion doubling problem!) Cannot be localized by disorder provided T-reversal is maintained Several experimental examples HgTe quantum wells L. Molenkamp group Bi1-xSbx, Bi2Se3, Bi2Te 3 M.Z. Hasan group, Chen, Yazdani... What about interactions? Some theoretical suggestions Spontaneous TIs in models with S. Raghu et al, 2008 T. Grover + Senthil, 2008 microscopic SU(2) symmetry Y. Zhang et al, 2009 Antiferromagnetism from a TI - A. Shitade et al, 2009 H. Jin et al, arXiv:0907.0743 Na2IrO3 2d Fractionalized QSHE - spin- M. W. Young et al, 2008 charge separated TI Materials perspective U/t Coulomb correlations reduce bandwidth Mott II Spin-orbit enhanced relative to Mott I bandwidth In Mott insulator, Metal TBI? compare SO to J not t. λ/t schematic phase diagram Materials perspective U/t Coulomb correlations reduce bandwidth Mott II Spin-orbit enhanced relative to Mott I bandwidth In Mott insulator, Metal TBI? compare SO to J not t. λ/t schematic phase diagram Strong Mott Insulators with strong SOIs some Fe and Co compounds, e.g. FeSc2S4 - orbitally degenerate spinel 4d and 5d double perovskites - Ba2NaOsO6, Ba2LiOsO6 etc. However, even in strong MIs with “weak” SOIs (e.g. Dzyaloshinskii-Moriya coupling at few % level), the SOIs can control the ground state when the exchange interactions are frustrated e.g. triangular Cs2CuCl4, and probably most kagome materials Materials perspective U/t Mott II intermediate regime Mott I Metal TBI? λ/t schematic phase diagram Weak Mott Insulators with strong SOIs Most 5d TM ions have smallish U≈1eV, and hence tend to be either metallic or weak Mott insulators together, SOI and U can conspire to produce an insulating state e.g. 5d iridates - Sr2IrO4, Na2IrO3, Na4Ir3O8 (hyperkagome), Ln2Ir2O7 (pyrochlores) Mott transition with SOIs U/t Mott II Study this phase diagram in a concrete Mott I case Metal TBI? λ/t schematic phase diagram Introduction Resistivity (polycrystalline samples) pyrochlore oxides Ln2Ir2O7 107 106 Ln3+: (4f)n Localized moment 6 5 10 10 Dy Magnetic frustration Ho 104 Ir4+: 5d5 Conduction electrons 105 Tb Pyrochlore iridates 103 Ir[t2g]+O[2p] conduction band 104 Dy 60 80 100 300 Itinerant electron system cm) " Ho on the pyrochlore lattice (m 103 ! Tb Gd Eu 2 IrO6 10 Sm Formula: Ln2Ir2O7 Nd 101 Pr Ln2Ir2O7 100 both Ln and Ir 0 50 100 150 200 250 300 Ln T(K) atoms occupy O! Metal Insulator Transition pyrochlore lattices (Ln=Nd, Sm, Eu, Gd, Tb, Dy, Ho) Cubic, FCC Bravais K. Matsuhira et al. : J. Phys. Soc. Jpn. 76 (2007) 043706. (Ln=Nd, Sm, Eu) 1 lattice Ln carry localized moments only important at low T Continuous Metal Insulator Transitions in Ln2Ir2O7 Phase Diagram Semiconductor Semi-metal Metal ・These MIT are a second-orderMetal-Insulator transition. 160 ・The insulating phase involves a magnetic Ho Dy Ln Ir O 140 Tb Gd 2 2 7 ordering driven by 5d electrons. Eu Sm 120 Weak FM PM Transition 100 Metal A difference of M(T) between FC and ZFC K. Matsuhira et al, 2007 (K) 80 MI Ir AFM Continuous Metal Insulator Transitions in Ln2Ir2O7 T The resistivity depends on the ionic radius of Ln. 60 Insulator ・ Decreasing Ir-O-Ir Nd 40 As Ir-O-Ir bond angle becomes decreases, Phase Diagram t2g bandbond width becomesangle narrower. makes Semiconductor Semi-metal Metal ・These MIT are a second-order transition. 20 Pr Ln moreheavy rare-earth insulating Mott insulator 160 0 ： ・The insulating phase involves a magnetic 1 1.02 1.04 1.06 1.08 1.1 1.12 1.14 Ho Dy 140 Tb Gd Ln2Ir2O7 3+ Electronic correlation effect is important. ordering driven by 5d electrons. Ln ionic radius (Å) Eu Sm 120 Weak FM O PM 100 Metal The MIT temperature TMI does not depend on A difference of M(T) between FC and ZFC 3+ Ir Ir the de Gennes factor and the magnetism of Ln . (K) 80 MI Ir AFM T 60 ・The resistivity depends on the ionic radius of Ln. TMI tends to increase as the ionic radius of Insulator 3+ Nd Ln becomes smaller. 40 As Ir-O-Ir bond angle becomes decreases, 2 t2g band width becomes narrower. 20 Pr 0 Ln：heavy rare-earth Mott insulator 1 1.02 1.04 1.06 1.08 1.1 1.12 1.14 Electronic correlation effect is important. Ln3+ ionic radius (Å) O The MIT temperature TMI does not depend on Ir the de Gennes factor and the magnetism of Ln3+.