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

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

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

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

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)

, PRL 103, 246601 (2009) nonmetallic for 0.002<x<0.

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

- minimum loss of Se content 2 GPa Cubic pressure cell Carbon heater Pyrophillite

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

87 nm - Sharp Bragg peaks - high quality of the single crystals - Dominant surface

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

Temperature Dependence - 50-200-nm-thick flakes mechanically exfoliated on highly doped silicon substrate covered

AP-grown Bi 2 Se 3 In collaboration with Prof. J. S. Kim From Prof. N. Hur in Inha Univ.

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)]

HP-grown Checkelsky et al. PRL 103, 246601 (2009) Bi 2-x Ca x Se 3 (0.002<x<0.

05 single crystal - almost T independence Checkelsky et al.

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

Electric Field Effect Gate-voltage dependence of the

experimental evidence for the dominant surface conduction 2

37 nm TI surface TI bulk SiO 2 180 nm 300 nm 180 nm Si sub

efficiency: ~ 6.2ⅹ10 10 cm -2 V-1, - Geometrical value: ~ 7.

300-nm-thick SiO 2 dielectric layer AP-grown crystal -

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

3x10 19 cm -3 µ~1100 cm 2 V -1 s -1 C SiO V 10-1 -2 BG [V] 7.

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

Magnetoresistance Checkelsky et al. PRL 103, 246601 (2009) Bi 2-x Ca x Se 3 (0.002<x<0.

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

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

~ 2.4 Ω/T HP12 1.56 µm 5.93 µm Non-invasive max( width ) = 1.56 µ m, average( width) = 5.

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]

3D Weyl metallic states realized in the Bi 1-x Sb x alloy and BiTeI. Heon-Jung Kim Department of Physics, Daegu University, Korea

3D Weyl metallic states realized in the Bi 1-x Sb x alloy and BiTeI Heon-Jung Kim Department of Physics, Daegu University, Korea Content 3D Dirac metals Search for 3D generalization of graphene Bi 1-x