Topological Insulators Their Spintronics Application Xuesen Wang National

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Topological Insulators & Their Spintronics Application Xue-sen Wang National University of Singapore phywxs@nus. edu.

Topological Insulators & Their Spintronics Application Xue-sen Wang National University of Singapore [email protected]nus. edu. sg Topological Insulator: A piece of material that is an insulator (or semiconductor) in its bulk, but supports spin-dependent conductive states at the boundaries due to spin-orbital coupling

Spintronics in Future Information Technology q Spintronics: Manipulation of electron spin for information storage,

Spintronics in Future Information Technology q Spintronics: Manipulation of electron spin for information storage, transmission & processing q Traditional spintronics: e. g. magnetic disk, size limit q Current spintronics: e. g. GMR, TMR, still with a charge current q Ideal Spintronics: Pure spin current & spin accumulation controlled by electric field/voltage, dissipationless q Quantum spin Hall effect (QSHE): an attractive option (S-Q Shen, AAPPS Bulletin 18(5), 29)

Hall Effect & Spin Hall Effect (SHE) SHE: Separate electrons of different spins without

Hall Effect & Spin Hall Effect (SHE) SHE: Separate electrons of different spins without using a magnetic field Spin current can be generated & controlled with an electric field or voltage, important to spintronics (From Y. K. Kato, Sci. Am. 2007(10) 88; also see Hirsch, PRL 83, 1834)

Observations of Spin Hall Effect SHE Spin accumulation at edges of Ga. As stripe

Observations of Spin Hall Effect SHE Spin accumulation at edges of Ga. As stripe observed by Kerr rotation microscopy (Kato et al. , Science 306, 1910) Reverse SHE E Electronic measurement: A spin Hall voltage VSH generated by Reverse-SHE (Valenzuela & Tinkham, Nature 442, 176; Kent, Nature 442, 143)

Mechanism of SHE: Spin-dependent scattering Extrinsic mechanism: Scattering by magnetic field or magnetic impurities

Mechanism of SHE: Spin-dependent scattering Extrinsic mechanism: Scattering by magnetic field or magnetic impurities Zeeman energy: Stern-Gerlach effect: Intrinsic mechanism: From relativity, an electron moving in an electric field feels a magnetic field

Rashba Effect A moving electric field induces a magnetic field: Intrinsic Rashba spin-orbit coupling:

Rashba Effect A moving electric field induces a magnetic field: Intrinsic Rashba spin-orbit coupling: R: small in light atoms (< 1 me. V), significantly enhanced in narrow-gap semiconductors containing Bi, Hg… More observable in low-D structures, controllable with electric field V: potential gradient in atom, or at a boundary: 1) Edges of a 2 D electron gas 2) Surface or Interface, adjustable with bias voltage

Boundary states & SHE V = 0 in bulk region if it has inversion

Boundary states & SHE V = 0 in bulk region if it has inversion symmetry Major contribution to V still comes from atomic potential A stripe of 2 DEG A thin film Edge Surface × Non-zero and opposite V at two edges (or surfaces) of a 2 DEG channel (or a film) Spin-filtered edge (surface) states

Spin-Orbital Coupling in 2 DEG or on Surface or: s k ARPES of Bi/Ag(111)

Spin-Orbital Coupling in 2 DEG or on Surface or: s k ARPES of Bi/Ag(111) (Sinova et al. , PRL 92, 126603; Ast et al. , PRL 98, 186807)

Quantum Transport in Low-D Systems Quantized conductance through a quantum wire or point contact:

Quantum Transport in Low-D Systems Quantized conductance through a quantum wire or point contact: Quantum conductance unit: G 0 = 2 e 2/h = 7. 75 S Transmitted states (modes) Ntrans, can be changed by gate bias Vg

Edge states & QHE in 2 DEG Channel 2 DEG in a normal B

Edge states & QHE in 2 DEG Channel 2 DEG in a normal B Skipping Orbits To Edge States Four-terminal Hall resistance: or:

Quantum Hall Effect & Quantum Spin Hall Effect in 2 D E Conduction band

Quantum Hall Effect & Quantum Spin Hall Effect in 2 D E Conduction band Valence band k Bulk Insulator with Spin-dependent Kramers-pair gapless edge states Kramers-pair Edge States: elastic backscattering forbidden by time reversal symmetry, robust against weak disorder (Nagaosa, Science 318, 758; Day, Phys. Today 61(1), 19; Kane & Mele, PRL 95, 146802)

Single-layer graphite: Graphene Graphite Zero bandgap Mass-less (relativistic) fermion Semimetal M 3. 4 Å

Single-layer graphite: Graphene Graphite Zero bandgap Mass-less (relativistic) fermion Semimetal M 3. 4 Å K’ Dirac point Γ 1. 42 Å DOS |E| K

QSHE in Graphene Spin-orbit coupling for edge Spin-filtered edge states: Electrons with opposite spin

QSHE in Graphene Spin-orbit coupling for edge Spin-filtered edge states: Electrons with opposite spin propagate in opposite direction; j. S may be non-dissipative states: y x A spin current will flow between leads attached to the opposite edges: Quantized SH conductivity: (from Kane & Mele, PRL 95, 226801)

Graphene: a 2 D Spin Hall insulator Generate a spin current without dissipation Spin-filtered

Graphene: a 2 D Spin Hall insulator Generate a spin current without dissipation Spin-filtered edge states in graphene are insensitive to disorder: Elastic backscattering is prohibited by time reversal Spin Hall gap in graphene: 2 SO ~ 2. 4 K (Kane & Mele, PRL 95, 226801; only ~ 0. 01 K in Yao et al, PRB 75, 041401) Operation temperature not practical! Existence of other spin Hall insulators with stronger SO interaction?

More attractive materials for Spintronics q Bi, Z = 83; Pb, Z = 82;

More attractive materials for Spintronics q Bi, Z = 83; Pb, Z = 82; Hg, Z = 80; strong SOC q Semimetal or narrow-gap semiconductor q Bulk carrier density ~1017 cm-3, low bulk conductivity q Surface carrier density ~1013 cm-2, surface conduction may be dominant q Small effective mass: m* = 0. 002 m 0, ~ 106 cm 2/Vs, Fermi velocity v. F 106 m/s (comparable with graphene) q 2 D & 3 D Topological insulators possible q Hg. Te QW, Bi 1 -x. Sbx , Bi 2 Se 3

QSH Edge States in Hg. Te QW Inverted Normal Inverted ? 5. 5 nm

QSH Edge States in Hg. Te QW Inverted Normal Inverted ? 5. 5 nm Normal Critical QW thickness 6. 3 nm (König et al. , Science 318 (2007) 766) 7. 3 nm

Lattice Structure of Bi Covalent bond Honeycomb bilayer 3. 95 Å c a b

Lattice Structure of Bi Covalent bond Honeycomb bilayer 3. 95 Å c a b 4. 545 Å = 57. 23˚ A Rhombohedral lattice Stacking in [111] direction C B

[111] Covalent bond Bi(111) bilayer: a 2 D Spin Hall Insulator } c a

[111] Covalent bond Bi(111) bilayer: a 2 D Spin Hall Insulator } c a 2 D bandgap 0. 2 e. V 1 Kramers pair of edge states b Honeycomb bilayer Spin Hall Conductivity: (Murakami, PRL 97, 236805; Liu et al. , PRB 76, 121301)

Spin accumulation at edges of Bi(111) bilayer K Γ With SOC M When EF

Spin accumulation at edges of Bi(111) bilayer K Γ With SOC M When EF in middle of Eg Sz + SOC of Bi(111) surface states Splitting ~ 0. 1 -0. 2 e. V Sz No charge current (Koroteev et al. , PRL 93, 046403; Liu et al. , PRB 76, 121301)

Quantum spin Hall Effect in 3 D E Conduction band Valence band 2 D

Quantum spin Hall Effect in 3 D E Conduction band Valence band 2 D Kramers pair Edge states 3 D Surface states k Number of Kramers pairs at each edge/surface must be odd (non-zero Z 2 invariant): Strong Topological Insulator (Weak topological insulator: with even number of edge-state pairs) (Kane & Mele, PRL 95, 146802; Fu & Kane, PRB 76, 045302)

Strong Topological Insulator Metallic edge/surface states linear in k meet at an odd number

Strong Topological Insulator Metallic edge/surface states linear in k meet at an odd number of points in k-space Robust against perturbation (S-c Zhang, APS Physics 1, 6 (2008))

Lattice Structure of Sb & Bi Covalent bond Honeycomb bilayer Sb: 3. 76 Å

Lattice Structure of Sb & Bi Covalent bond Honeycomb bilayer Sb: 3. 76 Å Bi: 3. 95 Å c a Sb: 4. 31 Å b Bi: 4. 545 Å = 57. 1 (Sb) = 57. 23° (Bi) Rhombohedral lattice: A distorted simple cubic (SC) or FCC lattice A C B

Electronic Structure of Bi & Sb Ls L Band overlap 38 me. V T

Electronic Structure of Bi & Sb Ls L Band overlap 38 me. V T 13. 8 me. V La EF= 26. 7 me. V (for Sb: at H, 177 me. V overlap with inverted La) Semimetal Low carrier density (~1017 cm-3) Small effective mass High carrier mobility (~ 105 cm 2/Vs) Long F, ~ 120 Å

Energy Bands of Bi 1 -x. Sbx E H T Ls La La La

Energy Bands of Bi 1 -x. Sbx E H T Ls La La La 30 me. V Inversion of L bands Ls T 0 4 Ls H 7 9 17 22 Semiconductor or Topological Insulator @ x ~ 4%: Dirac Fermions in 3+1 D x (%)

Bi 1 -x. Sbx: Topological Insulator (x ~ 7 -10%) m* ~ 0. 002

Bi 1 -x. Sbx: Topological Insulator (x ~ 7 -10%) m* ~ 0. 002 me 2 D quantum spin Hall phase 1 D edge states 3 D quantum spin Hall phase 2 D surface states (Hsieh et al. , Nature 452, 970; Teo et al. , PRB 78, 045426)

Effect of SOC on Bi bulk band near EF = 13. 7 me. V

Effect of SOC on Bi bulk band near EF = 13. 7 me. V 3 D Dirac point at L (Hsieh et al. , Nature 452, 970 (Suppl. Info. ))

Surface States on Different Bi 1 -x. Sbx Surfaces “Strong” Topological Insulator Surface Fermi

Surface States on Different Bi 1 -x. Sbx Surfaces “Strong” Topological Insulator Surface Fermi arc encloses 1 or 3 Dirac points on all surfaces (111) & (110) surfaces commonly observable Surface time-reversal-invariant momentum (TRIM) enclosed by an odd number of electron or hole pockets (from Teo, Fu & Kane, PRB 78, 045426)

Bi(111) Surface ARPES measurement of surface states EF mapping (Hofmann, Prog. Surf. Sci. 81,

Bi(111) Surface ARPES measurement of surface states EF mapping (Hofmann, Prog. Surf. Sci. 81, 191; Ast & Hochst, PRL 87, 177602) Spin direction of states at EF

Bi(110) Surfaces ARPES & computed of surface states EF mapping & spin directions (Hofmann,

Bi(110) Surfaces ARPES & computed of surface states EF mapping & spin directions (Hofmann, Prog. Surf. Sci. 81, 191; Pascual et al. , PRL 93, 196802)

Bi & Sb Nanostructures Grown on Inert Substrates Ø HOPG or Mo. S 2

Bi & Sb Nanostructures Grown on Inert Substrates Ø HOPG or Mo. S 2 cleaved in air, ~ 5 hours degas at 300550 C in UHV Ø Sb & Bi from thermal evaporators Ø Nearly free-standing structures grow on aninert surface Ø STM imaging at RT UHV STM system

3 D, 2 D & 1 D Sb Nanostructures on HOPG 1 D, h

3 D, 2 D & 1 D Sb Nanostructures on HOPG 1 D, h ~ 23 nm 3 D, h ~ 60 nm 2 D, h ~ 3. 5 nm (100 nm)2 (111)-oriented 2 D islands (1000 nm)2 Lateral period: Sb 4, F = 4 Å/min, 12 Å deposited at RT. 3 D, 2 D & 1 D islands formed at early stage a = 4. 17 0. 12 Å (10 nm)2 Bulk Sb: a = 4. 31 Å

1 D & 2 D Bi Nanostructures on HOPG (0. 6 m)2 1 D

1 D & 2 D Bi Nanostructures on HOPG (0. 6 m)2 1 D nanobelts (1 m)2 2 D islands, height ~ 1 nm (111) oriented Bi(111) bilayer spacing: 3. 95 Å

Bi Nanobelts: (110) oriented (200 nm)2 Narrow belts on top of wide belt Narrow

Bi Nanobelts: (110) oriented (200 nm)2 Narrow belts on top of wide belt Narrow belt h ~ 8 Å (2 m)2 Height ~ 1 -10 nm Width ~ 25 -70 nm Belt surface with rectangular lattice: 4. 34 Å × 4. 67 Å Bulk Bi(110): 4. 55 Å × 4. 75 Å Layer spacing: 3. 28 Å (9 nm)2

Aligned Bi Nanobelt on Low-symmetry Surface Bi(110) nanobelts on Bi/Ag(111) Bi wetting layer on

Aligned Bi Nanobelt on Low-symmetry Surface Bi(110) nanobelts on Bi/Ag(111) Bi wetting layer on Ag(111): with a 2 D rectangular lattice Aligned Bi nanobelts on Si(111)4 1: In single-domain terrace observed in Surface Physics Lab, Inst. of Physics, CAS, Beijing (300 nm)2

Self-Assembly of Sb & Bi Nanobelts Deposited atoms Growth direction (111) top surface of

Self-Assembly of Sb & Bi Nanobelts Deposited atoms Growth direction (111) top surface of Bi nanobelt Inert sidewall Dangling bonds Removal of dangling bonds on Bi(110) by “puckered-layer” atomic reconfiguration (Nagao et al. PRL 2004)

Transformation of Bi(110) to Bi(111) (1 m)2 After 10 min 100 C anneal h

Transformation of Bi(110) to Bi(111) (1 m)2 After 10 min 100 C anneal h ~ 5 – 9 nm After 10 min 130 C anneal h ~ 5 – 10 nm

Topological Insulators at Room Temperature Surface states on (111) Bi 2 Se 3: Eg

Topological Insulators at Room Temperature Surface states on (111) Bi 2 Se 3: Eg 0. 3 e. V Sb 2 Te 3: Eg 0. 1 e. V (H. Zhang et al. , Nature Physics 5 (2009) 438)

Magneto-Electric Effects in Topological Insulators Normal insulator: Additional action term: where All time reversal

Magneto-Electric Effects in Topological Insulators Normal insulator: Additional action term: where All time reversal invariant insulators can be divided into two classes: Normal insulator: θ = 0; Topological insulator: θ = π (Qi, Hughes and Zhang, PRB 78, 195424)

Topological Magneto-Electric (TME) Effect P 3 = θ/2π A charge near TI induces an

Topological Magneto-Electric (TME) Effect P 3 = θ/2π A charge near TI induces an image magnetic monopole: g (Qi, Hughes and Zhang, PRB 78, 195424; Qi et al, ar. Xiv: 0811. 1303)

Summary Ø Topological insulators possess novel properties with potential spintronic applications due to QSHE

Summary Ø Topological insulators possess novel properties with potential spintronic applications due to QSHE Ø Hg. Te QW, Bi(111) monolayer, Bi 1 -x. Sbx alloy, Bi 2 Se 3 and Sb 2 Te 3 are possible topological insulators Ø Bi(111) bilayer/film similar to graphene/graphite Ø Ultrathin (2 -6 bilayers) Bi(111) and Bi(110) nanobelts can be obtained on inert substrates (e. g. graphite and Mo. S 2) Ø Bi & Sb nanostructures can be fabricated at much less demanding conditions than for graphene. Certain growth controls have been accomplished

Further Studies Ø Fabrication of Bi 1 -x. Sbx (x ~ 10%) thin films

Further Studies Ø Fabrication of Bi 1 -x. Sbx (x ~ 10%) thin films and nanostructures, effect of inhomogeneity Ø Electronic & spintronic transport measurements, TME effect: contact, patterning and processing Ø Controlled growth of Bi & Bi. Sb structures on Si-based substrates Ø Other topological materials, e. g. Bi 2 Se 3, Sb 2 Te 3

Universal Intrinsic Spin Hall Effect in 2 DEG Spin current is polarized in z

Universal Intrinsic Spin Hall Effect in 2 DEG Spin current is polarized in z direction, with spin Hall conductivity Still need charge current (Sinova et al. , PRL 92, 126603) s p

Phases of Honeycomb Lattice with Repulsive Interactions V 1 V 2 U QSE phase

Phases of Honeycomb Lattice with Repulsive Interactions V 1 V 2 U QSE phase more likely in bilayer lattice of dipolar atoms with V 2 > U, V 1 (Raghu et al. , PRL 100, 156401)

Lattice distortion across 90 -elbow of Bi nanobelt y Variation of X-period D D:

Lattice distortion across 90 -elbow of Bi nanobelt y Variation of X-period D D: ax = 4. 88 Å C: ax = 4. 73 Å C B: ax = 4. 49 Å B x A: ax = 4. 47 Å Reverse variation of Y-period A On bulk Bi(110): 4. 55 Å × 4. 75 Å

2 bilayer (~ 6. 6 Å) Bi(110) growth On Ag(111) with a Bi wetting

2 bilayer (~ 6. 6 Å) Bi(110) growth On Ag(111) with a Bi wetting layer

Semimetal-to-Semiconductor transition in Bi nanowires (Lin et al. , PRB 62, 4610)

Semimetal-to-Semiconductor transition in Bi nanowires (Lin et al. , PRB 62, 4610)

Bi(111) Ultrathin Films 1 bilayer: Semiconducting 2 – 3 bilayer films: Semimetallic electron hole

Bi(111) Ultrathin Films 1 bilayer: Semiconducting 2 – 3 bilayer films: Semimetallic electron hole (Koroteev et al. , PRB 77, 045428) With SOC

Bi(110): bilayer pairing Remove dangling bonds on Bi(011) by “puckered-layer” pairing reconfiguration (Nagao et

Bi(110): bilayer pairing Remove dangling bonds on Bi(011) by “puckered-layer” pairing reconfiguration (Nagao et al. PRL 2004) >10% in vacuum (Koroteev et al. , PRB 77, 045428)