Presentation on theme: "Topological Insulators"— Presentation transcript:
1 Topological Insulators TAR College, Kuala Lumpur, Malaysia13 July 2010Topological InsulatorsYew San Hor1Department of ChemistryandJ. G. Checkelsky2, A. Richardella2,J. Seo2, P. Roushan2, D. Hsieh2, Y. Xia2, M. Z. Hasan2, A. Yazdani2, N. P. Ong2, and R. J. Cava12Department of PhysicsPrinceton UniversityNSF-MRSEC DMR
30 Topology in condensed matter electronic phases… Electron spin property plays an important role.Example:AB
31 Insulator Topological Insulator A new class of insulator material does not conduct electric current1. Band Insulator (valence band completely filled).2. Peierls Insulator (lattice deformation).3. Mott Insulator (Coulomb repulsion).4. Anderson Insulator (impurity scattering).A new class of insulatorTopological Insulator
32 Topological Insulators Bulk band insulators.EBulkConductionBandGapped bulk insulatorE ~ k2kBulkValenceBandGapless Dirac excitations at its boundaries.ESurfaceConductionBandGapless surface stateE ~ kkIngredients:Strong spin-orbit coupling.Time reversal symmetry.SurfaceValenceBand
33 Consider a simpler system 2D electron gas as an analogy
39 Quantum Hall Effect Classical Hall Effect (Klaus von Klitzing, 1980) Quantization ofHall conductancexy = ie2/hLorentz ForceF = -e x Bh/e2 = Hall conductancexy = -ne/B1985 Nobel Prize in Physics
40 Fractional Quantum Hall Effect (discovered in 1982)Daniel TsuiHorst Stormer1998 Nobel Prize in PhysicsQuantization ofHall conductancexy = ie2/hRobert Laughlini = 1/3, 1/5, 5/2, 12/5 ..
41 Devices utilize electron charge property: Semiconductor Transistor, AT&T Bell Labs (1947).Single Crystal Germanium (1952).Single Crystal Silicon (1954).IC device, Texas Instrument (1958).IC Product, Fairchild Camera (1961).Microprocessor, Intel (1971).Personal Computer (1975).
42 Semiconductor crisis *Size limit *Heat dissipation Gorden Moore (co-founder of Intel 1964):Number of transistors doubled every 12 months while price unchanged.In 1980s, number of transistors doubled every 18 months.*Size limit*Heat dissipation
44 New materials utilize electron spin property: Topological Insulators
45 Topological Insulators Spintronic devices- apply electron spin property.Quantum computer- apply quantum mechanical phenomena.- use qubit (quantum bit) instead of bit.
46 Topological Insulator is also important for…1. Quantum Spin Hall Effect.2. The search of Majorana fermion.3. Axion electrodynamic study.4. Magnetic monopole.
47 3D Topological Insulator Strong spin-orbit couplingLLssLsLsLsLsBulk insulatorNo boundaryLarge atomic number → Large orbital moment, L
48 3D Topological Insulator Bulk insulatorStrong spin-orbit coupling
49 3D Topological Insulator EtrapEtrapk x Etrap ~ Bsk1k2sLsBulk insulatorStrong spin-orbit coupling
50 3D Topological Insulator EtrapEtraps-k2-k1sWhen T-operator is applied…Time Reversal SymmetryInvariant!Bulk insulatorsLStrong spin-orbit coupling
51 3D Topological Insulator Electron spinQuantum spin Hall effectSurface Dirac-like spin current.Zero net current, but spin-polarization,protected by Time Reversal SymmetryLsLsLsBulk insulatorStrong spin-orbit coupling
53 (Angle-resolved photoemission spectroscopy) Basics of ARPES(Angle-resolved photoemission spectroscopy)ARPES is surface sensitiveCan measure E vs k of bulk and surface states separatelyhDamascelli et al. RMP 2003
54 E~k E E k Dirac surface state ARPES SCB SVB Surface Dirac-like spin current.Zero net current, but spin-polarization,protected by Time Reversal SymmetrySCBE~kkEDirac surface stateSVBARPES
55 transport measurements Challenging problemforDirac surface statetransport measurementsEEFBCBGaplesssurfacestatekBulk electron is measuredWhy not bulk insulator?
57 Defect chemistry in Bi2Se3 SeSe → VSe●● + Se (gas) + 2 e-e-BiSeBiSeSeBiSeBiSeSe10 nmdefectBiSTMn-type Bi2Se3Se
58 STM Ca-doped in Bi2Se3 → 2CaBi’ + 2h• 2Ca Se e- e- Bi Se Bi Se Se Bi 10 nmdefectBiSTMn-type Bi2Se3p-type Bi2Se3Se
59 Bi2-xCaxSe3 Crystal growth 1st step: (i) stoichiometric mixture of Bi and Se in vacuum quartz tube.(ii) melting at 800 oC for 16 hours.(iii) air-quenching to room temperature.2nd step: (i) add Ca to Bi2-xSe3 and sealed in vacuum quartz tube.(ii) 400 oC for 16 hours.(iii) 800 oC for 1 day.(iv) 1 day slow coolingto 550 oC.(v) stay at 550 oC for3 days.PRB (2009)
60 n- to p-type Bi2-xCaxSe3 topological insulator Can we perform the fine tuning in order to bring the Fermi level to lie in the band gap and hit the Dirac point?X=0.02kkx = 0x = 0.005,0.02, 0.05PRB (2009)
61 Fine tuning in Bi2-xCaxSe3 How about transport properties?Bi2Se3Bi1.9975Ca0.0025Se3Bi1.99Ca0.01Se3Nature 460, 1101 (2009)
62 Bi2-xCaxSe3 transport properties Non-metallic.Onset at T~130 K.Metallic behavior.PRL 103, (2009)
69 CuxCuxBi2Se3CuxWe did a little different approach in doping on Bi2Se3.Cux
70 Cu-doped Bi2Se3 crystal growth Mixtures of high purity elements Bi, Cu, Se in sealed vacuum quartz tubes.Melt at 850 oC overnight.Slow cooling: 850 → 620 oC for 24 hours.Quench in cold water at 620 oC.
71 STM topography of Cu0.15Bi2Se3 T = 4.2 KCu clusters on surface.Cu atoms intercalated between layers
72 Superconductivity of CuxBi2Se3 Superconductivity only found in 0.1 < x < 0.3Tc~3.8 K~20 %SC phaseWe focus on the superconductivity of CuxBi2Se3.
73 Superconductivity of CuxBi2Se3 SC phase is not fully connected.PRL (2010)
74 Strongly type II superconductor Upper critical field Hc2 is anisotropic
76 Topological magnetic insulators Motivated by:Axion electrodynamics theory → E x B.Magnetic monopole → symmetries of Maxwell’s equations.by Zhang group (Stanford), arXiv: v1Ferromagnetism in Bi2-xMnxTe3
77 For axion electrodynamics Point chargeSurface currentinducedVacuumTopologicalinsulatorS. C. Zhang,Science (2009)Magnetic monopole induced1. Quantum Spin Hall Effect: (b) Transport measurements
78 Axion electrodynamics Sharp tip acts as a point chargeInducedsurface currentE fieldGold-copperalloy contactsTI crystalI+V+V-I-Schematic diagram for the studies of axion electrodynamics1. Quantum Spin Hall Effect: (b) Transport measurements
80 STM topography of Bi1.91Mn0.09Te3 Black triangles: substitutional Mn on Bi sites.No Mn-clustering is found.
81 DC Magnetization of Bi2-xMnxTe3 TC ~ 9 – 12 K for x = 0.04 and 0.09
82 ARPES Topological surface state is still present. T=15 KTopological surface state is still present.Dispersion relation of the state is changed in a subtle fashion.PRB 81, (2010)
83 Summary ● Ca-doped Bi2Se3 → Topological “Insulator”. suppress bulk conductance to show up Dirac electron surface state.● Cu-added Bi2Se3 → Superconductor.interface with Bi2Se3 to have proximity effect, Majorana fermionic physics (?).● Mn-doped Bi2Te3 → Magnetic topological insulator.in search for magnetic monopole (?) andaxion electrodynamics studies (?).
84 Acknowledgements References: Thank you Cava group: Funding agencies: Professor Robert CavaTyrel McQueen (JHU)Don Vincent West (U Penn)Anthony WilliamsDavid Grauer (UC Berkeley)Jared AllredShuang JiaSiân DuttonEsteban Climent-PascualMartin BremholmNi NiUlyana SorokopoudLinda PeoplesFunding agencies:Air Force Office ofScientific Research (AFOSR).Materials Research Science &Engineering Centers (MRSEC).References:Bernevig, Hughes, Zhang, Science 2006.Fu, Kane, Mele, PRL 2007.Moore, Nature 2010.Bjorken, Relativistic Quantum Mechanics.Thank you
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