Topologically Insulating Properties of Doping-free Bi 2 Se 3 Single Crystals
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1 Topologically Insulating Properties of Doping-free Bi 2 Se 3 Single Crystals POSTECH-APCTP AMS Workshop September 6, 2010; Pohang Hu-Jong Lee Pohang University of Science and Technology (POSTECH) Quantum Transport and Superconductivity Laboratoryry
2 Outline Introduction - Basic characters of topological insulators - Bulk doping High pressure growth technique - Reducing bulk doping - Transport measurements - Estimation of carrier densities - Comparison between different growth schemes Summary
3 Collaborators Dong-Keun Ki Hyun-Sook Lee POSTECH Jun Sung Kim Se Woong Na POSTECH T. Y. Koo PLS Namjung Hur Ki Myung Song Inha University Quantum Transport and Superconductivity Laboratoryory
4 Introduction Phase or State of a Matter ; - Often defined by the characteristic symmetry - Phase transition by breaking of characteristic symmetry of a system - ex) FM ; by breaking of spin symmetry ν=1 ν=3 ν=2 IQHE ; - Broken time-reversal symmetry; Landau levels in the bulk - Topological invariance ; Chern number (v) - Transition between QH conductance plateaus possible without breaking any symmetry - But with changing the topological number (filling factor)
5 Introduction Phase or State of a Matter ; - Often defined by the characteristic symmetry - Phase transition by breaking of characteristic symmetry of a system - ex) FM ; by breaking of spin symmetry Metal Insulator Gapless at E F Gapped at E F Topological Insulators ; - Opening of bulk band gap - Topological number (ν=1) different from that (ν=0) of ordinary insulators - Topologically protected conducting surface state
6 Topology Topology in Real Space Gauss-Bonnet equation Local curvature of the surface 1 2(1 ) 2 KdA = π g S # of holes; genus
7 Topology g ; genus = number of holes g = 0 g = 1
8 Energy Band and Topological Number Energy band can be characterized by topological number ψ ( k ) ; Classified by the Chern topological invariant (Thouless et al., 1982) The Chern topological invariant can change only at a quantum phase transition where the energy gap vanishes. v = 0 v = 1 ordinary insulator gapless interface state topological insulator
9 Surface State of TI - Surface states massless 2D Dirac fermionic E QM + Relativistic Effect k x k y - Surface states are chiral (spin-filtered) comprised of counter-propagating spin states Dirac cone helical structure - Robust against non-magnetic impurities protected from disorder by a large SO interaction (time-reversal symmetry)
10 Suppressed Backward Scattering E k x k y - Surface states are chiral (spin-filtered) comprised of counter-propagating spin states - Robust against non-magnetic impurities protected from disorder by a large SO interaction (time-reversal symmetry)
11 Time-Reversal Symmetry E Θ= e iπ S y / K [ H, Θ ] = 0 kx k y Dirac cone helical structure k =Θ k E( k ) = Ek ( ) [ U, Θ ] = 0 k U k = k U k = k U k = * 0 Back-scattering is suppressed for nonmagnetic impurities
12 Fascinating Emergent Materials - Materials leading to a new quantum world Magnetic Monopole Anyon & Fractional Statistics Quantum Anomalous Hall Effect Majorana Fermions Axion Electromagnetic Effect - Promising materials for future information technology Spintronics Quantum Computing Utilizing charge/spin transport properties of the conducting surface state for a device application is a formidable task
13 Topological Insulators 2D TI ; HgTe/CdTe quantum well 3D TI ; Bi 1-x Sb x..s. C. Zhang, Science 2006 Koenig et. al., JPSJ 2008 C. L. Kane, Phys. Rev. Lett Z. Hasan, Nature 2008
14 3D Topological Insulators Sb 2 Se 3 Sb 2 Te 3 Bi 2 Se 3 Bi 2 Te 3 Dai, Fang, Zhang., Nature Physics (2008)
15 Topological Insulators (Self-Flux Method) Bi 1-x Sb x Bi 2 Se 3 Bi 2 Te 3 E F conduction band valence band Hsieh et al. (Princeton) Nature Physics 2008 Xia et al. (Princeton) Nature Physics 2009 Chen et al.,.. (Stanford) Science Dirac cones Impurities 1 Dirac cone Non-stoichiometric -intrinsic doping Large bulk gap 0.3 ev
16 Diverse Schemes to Grow TI s Need to compensate the Se vacancies Thus to replace the E F inside the bulk band gap Allowing one to access the surface conducting state Single Crystal Growth Hole doping with Ca at the Bi sites - Delicate control of low concentration ( %) of Ca via two-step melting Binary melting (sometimes with the excess Se composition) - Yielding the most-reduced bulk carrier density down to about cm -3 Post-growth annealing under the Se partial pressure - Requiring a long highly stable heat treatment after the crystal growth Epitaxial Film Growth MBE growth ; less doping - Bi 2 Se 3 /graphene/sic(0001), Bi 2 Se 3 /sapphire(0001), Bi 2 Te 3 /Si(111), Sb 2 Te 3 /Si(111), Sb 2 Te 3 /graphene/sic(0001)
17 Binary Melting Technique (Bi 2 Se 3 ) - Elemental Bi and Se mixed in alumina crucibles in a molar ratio of (Bi:Se=35:65) n e =5x10 17 cm -3 (Bi:Se=34:66) n e =2.3x10 17 cm -3 (Bi:Se=34:66) n e =3x10 17 cm -3 (Bi:Se=40:60) n e =2.3x10 19 cm -3 - Sealed in quartz ampules and raised to 750 C and cooled slowly to 550 C Metallic R vs T n e =5 x cm -3 Analytis et al., PRB 81, (2010)
18 Binary Melting Technique (Bi 2 Se 3 ) K. Eto, Y. Ando, PRB 81, (2010) n e =5 x cm 3 - Only recently transport measurements emerge to investigate the surface state - Metallic R vs T dominant bulk contribution - SdH oscillations from the bulk Fermi surface unambiguously pin the Fermi level in the bulk conduction band
19 Doping Problem of Self-Flux Method - Bi 2 Se 3 - Large bulk gap (~0.3 ev) ; possible realization of topological quantum states near room RT Bi 2 Se 3 - Bulk properties are sensitive to slight doping; due to the occurrence of selenium vacancies by the high volatility of Se - Compensating the Se vacancies by hole doping with Ca to adjust the E F inside the bulk band gap to access the surface conducting state only - To induce an insulating state in Bi 2-x Ca x Se 3, a delicately low concentration ( %) of Ca should be substituted - Carrier-scattering by the foreign dopants may plague the transport properties
20 Fermi Level Tuning by Doping Bi 2-x Ca x Se 3 n = 0.7~8 x cm -3 Hsieh et al., Nature 460, 1101 (2009)
21 Fermi Level Tuning by Doping caliper area S F of the bulk FS Bi 2-x Ca x Te 3 n = 1.7 x cm -3 Chen et al., Science 325, 178 (2009)
22 Obstacle to Transport Measurements J. G. Checkelsky et al., PRL 103, (2009) nonmetallic for 0.002<x< Se vacancies are the problem. due to bulk impurity bands or coupling between bulk and surface states E F Ca doping
23 Our Scheme : High-Pressure Synthesis High-pressure furnace In collaboration with Prof. Jun Sung Kim pyrophillite pressure medium
24 Our Scheme : High-Pressure Synthesis Cubic multi-anvil press Scheme - Bi:Se = 2:3 - pressurized in a BN crucible 14-mm cubic multi-anvil apparatus 800 º C for min - minimum loss of Se content 2 GPa Cubic pressure cell Carbon heater Pyrophillite pressure medium Insulator Crucible Thermocouple Starting material (Ar) Before and after pressurizing
25 Undoped Bi 2 Se 3 Single Crystals 200 µm Irregular plate-like shapes Easily cleaved with an ab-planar surface
26 Material Characterization XRD at Pohang Light Source Quintuple layer unit cell rhombohedral structure c = 2.855(5) nm a = 0.417(0) nm - Sharp Bragg peaks - high quality of the single crystals
27 Material Characterization EDX HR-TEM Quintuple layer unit cell rhombohedral structure XRD; a=0.417(0) nm, c=2.855(5) nm EDX; Bi:Se ~ 2:3 TEM; a~0.4 nm, c~2.87 nm - Sharp Bragg peaks - high quality of the single crystals - Dominant surface conduction? - due to any possible Se vacancies below the detection limit - Transport measurements required
28 Temperature Dependence nm-thick flakes mechanically exfoliated on highly doped silicon substrate covered with a 300-nm-thick SiO 2 layer - e-beam patterning and low-energy Ar-ion surface cleaning HP-grown Bi 2 Se 3 AP-grown Bi 2 Se 3 In collaboration with Prof. J. S. Kim From Prof. N. Hur in Inha Univ. - Too small for ARPES and STM spectroscopic measurements - Hard to exfoliate on substrate ending up with thick crystals difficult to put contact leads
29 Temperature Dependence HP-grown Bi 2 Se 3 AP-grown Bi 2 Se 3 Non-metallic T dependences E F inside the bulk band gap Hsieh et al., Nature 460, 1101 (2009) Metallic T dependences E F in the bulk conduction band [Park.., PRB 81, (R) (2010)]
30 HP-grown Checkelsky et al. PRL 103, (2009) Bi 2-x Ca x Se 3 (0.002<x<0.0025) Resistance peak - may be related to the metallic surface states 1.7%-Se-rich HP-grown Bi 2 Se 3.05 single crystal - almost T independence Checkelsky et al., PRL 103, (2009) A sample-to-sample variation in the increase of R(T) - probably due to a subtle difference in the doping level - demonstrating the high sensitivity of the transport to a minute doping level
31 Electric Field Effect Gate-voltage dependence of the resistance of HP-grown crystal - providing further experimental evidence for the dominant surface conduction Thomas-Fermi screening length λd = επ 0 / me kf ~ 0.37 nm TI surface TI bulk SiO nm 300 nm 180 nm Si sub 80 nm HP-grown crystal - large gating effect - Backgating efficiency: ~ 6.2ⅹ10 10 cm -2 V-1, - Geometrical value: ~ 7.0x10 10 cm -2 V -1 for the bottom surface with the 300-nm-thick SiO 2 dielectric layer AP-grown crystal - Small gating effect - due to field screening by the high-density carriers in the bulk.
32 Estimation of Bulk Carrier Density (from Electric Field Effect) HP9 t=180 nm n 0 = 1.1x10 18 cm -3 (or 5.5x10 12 cm -2 ) µ~550 cm 2 V -1 s -1 C SiO V BG [V] [V cm ] V -3 G0 (area) e nt 0 n0 [cm ] t[cm] 1 µ = neρ G = 2 BG = 0 0
33 Resistivity changes only over the thickness d. d t=180 nm C SiO2 /(area)=115 af/µm 2 R length 1 width ( t d) width d = ρ, = + width t R ρ length ρ length G R 0 width ( t d) width d ρ0 length = = + / G0 R ρ0 length ρ length width t t d ρ0 d nd 1 CSiO V 1 2 BG d = + = 1+ = 1 + t ρ t n0 t n0 area e d t
34 Estimation of Bulk Carrier Density (from Electric Field Effect) HP9 AP3 t=180 nm n 0 = 1.1x10 18 cm -3 (or 5.5x10 12 cm -2 ) µ~550 cm 2 V -1 s -1 t=80 nm n 0 = 3.3x10 19 cm -3 µ~1100 cm 2 V -1 s -1 C SiO V BG [V] [V cm ] V -3 G0 (area) e nt 0 n0 [cm ] t[cm] 1 µ = neρ G = 2 BG = 0 0 n Hall = 3.8x10 19 cm -3
35 Estimation of Bulk Carrier Density & Mobility HP9 2D density n 0 = 2.0 x cm -2 AP3 n 0 = 2.6 x cm -2
36 Magnetoresistance t ~ 180 nm HP9 1 Rsym = [ RB ( ) + R ( B )] 2 1 Rasym = [ RB ( ) R ( B )] 2
37 Magnetoresistance t ~ 80 nm AP3 1 Rsym = [ RB ( ) + R ( B )] 2 1 Rasym = [ RB ( ) R ( B )] 2
38 Magnetoresistance HP9 AP3 Anti-weak localization Universal conductance fluctuation Classical magneto-resistance No UCF observed HP9 - Low-field anomaly MR deepens to a sharp cusp at H= 0 AP3 - Conventional Kohler's rule, R(B)/R(B=0 T) ~ 1 + (µb) 2
39 Magnetoresistance Checkelsky et al. PRL 103, (2009) Bi 2-x Ca x Se 3 (0.002<x<0.0025) Sample size: 2 mm x 2 mm x 50 µm n H = 5 x cm -3 Large conductance fluctuations ~ 10e 2 /h
40 Estimation of Bulk Carrier Density from Asymmetric Part of MR) R n H max 1 Rxy W = = t ne B W ' 1 1 W ' 18-3 = = cm R R H e xy W t e for HP9 B
41 T offset : 5 Ω PRL 103, (2009)
42 Crystal Bulk Carrier Density References Ca doped 0.7~8x10 18 cm -3 Princeton group: PRL x10 18 cm -3 Princeton group: Nature 2009 Bi 2 Se 3 nanoribbon 3x10 13 ~ 3x10 14 cm -2 Cui group: Nature Mater Nano Lett 2010 metallic R(T) undoped sample 5x10 18 cm -3 Ando group: PRB 2010 metallic R(T) other than 2:3 ratio 2.3~5x10 17 cm -3 PRB 81, (2010) 3.3x10 17 ~2.3x10 19 cm -3 arxiv: R(T) metallic films grown on STO substrate 1x10 16 ~1x10 19 cm x10 13 cm -2 (undoped) 1.1ex10 13 cm -2 (Ca doped) PRB 81, (2010) - metallic arxiv: Bi 0.91 Sb x10 18 cm -3 Ando group: PRB 2009; arxiv: Sn-doped 1.7x10 18 cm -3 Science 325, 178 (2009) Bi 2 Te 3 nanoplate 7.2x10 13 cm -2 Cui group: Nano Lett 2010 HgTe/CdTe 1.2x10 11 cm -2 (electron at -1 V bg ) 1.0x10 10 cm -2 (hole at -2 V bg ) Science (2007) Science (2009)
43 Summary Non-metallic Bi 2 Se 3 single crystals by adopting high-pressure growth method without introducing foreign dopants Minimal loss of volatile Se elements takes place, leading to almost stoichiometric growth of Bi 2 Se 3 single crystal Contrasting transport properties between HP- and AP-grown crystals, dominant conduction of the topologically-protected surface states - - High-pressure growth provides a promising route to precise vacancy control for the Bi-chalcogenide-based TI s without foreign dopants A crucial step towards utilizing topologically protected surface conduction while keeping the bulk insulating state intact - Determination of carrier density (by Hall and SdH measurements) with crystals prepared by optimized growth condition is required
44
45 Summary II Non-metallic Bi 2 Se 3 without doping!
46 Materials Classified by Energy Bands Metal Insulator Gapless at E F Gapped at E F
47 50 nm Onsager relation Gate dependence 이현우교수 - Onsager relation 을확인할필요. 다시 cool-down 후실험 : 만족함. 박기수박사아이디어 ; Linear 한 MR - 기존 Ag 2+δ Se 나 Ag 2+δ Te 에서관측
48 carrier type: electron V BG 1/R H = n H x e
49 carrier type: electron V BG 1/R H = n H x e
50 Q=C SiO2 ⅹV Q= nⅹeⅹ(volumn)= nⅹeⅹ(areaⅹthickness) d t=180 nm C SiO2 /(area)=115 af/µm 2 Suppose Q is distributed uniformly over a thickness of d. n=c SiO2 /(area)ⅹv/eⅹ1/d = 7.2ⅹ10 10 [V -1 cm -2 ]ⅹV [V]/d [cm]
51 Resistivity changes only over the thickness d. d t=180 nm C SiO2 /(area)=115 af/µm 2 G [V cm ] V [V] [V cm ] = = V BG [V] G n t n BG [cm ] ( = [cm]) 0[cm ] d dependence disappears µ = σ 0 e n0
52 HP9 Invasive ~ 6 Ω/T R R n xy H V E xy y = = width I j width thickness 1 Ey Rxy width = = = thickness ne j B B width 1 1 = = cm 6.0 [ /T] [m] [C] max max 9 19 RH e Ω 18-3
53 HP3 Invasive n 1 1 = = cm 7.5 [ /T] [m] [C] max max 9 19 RH e Ω 18-3
54 ~ 2.4 Ω/T HP µm 5.93 µm Non-invasive max( width ) = 1.56 µ m, average( width) = 5.93 µ m n max 1 1 = = cm max R 5.93 H e [ Ω /T] [m] [C]
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