Schedule of The First Half of The Course (Hasegawa)Lecture Slides (PDF files)

http://www-surface.phys.s.u-tokyo.ac.jp/KougiOHP/

１．Nanoscience and Surface Physics ナノサイエンスと表面物理Nanoscience in Nobel Prize

２．Atomic Arrangements at Surfaces 表面原子配列構造Scanning Tunneling Microscopy, Electron Diffraction走査トンネル顕微鏡、電子回折

３．Surface Electronic States 表面電子状態Surface states 表面状態、 Rashba Effect ラシュバ効果Topological Surface States トポロジカル表面状態、Band Bending バンド湾曲

４．Surface Electronic Transport 表面電気伝導Space-Charge-Layer Transport and Surface-State Transport空間電荷層伝導と表面状態伝導

2D Materials ２次元物質Atomic-Layer Superconductivity 原子層超伝導

Surface States and Space-Charge Layer (Band bending)

S. Hasegawa & F. Grey,Surface Science 500 (2002) 84–104

2DEG: Two-dimensional Electron Gas

Three Channels for Electrical ConductionS. Hasegawa & F. Grey,Surface Science 500 (2002) 84–104

1. Surface-State Conduction2. Space-Charge-Layer Conduction3. Bulk Conduction

Bscss Measured conductivity

電界効果トランジスタ Field-Effect Transistor FET

Gate-Controlling Bending of Bulk Bands near Surface

量子ホール効果 Quantum Hall Effect

*

22

2mkE

21nE c ...)3,2,1,0( n

2DEG

*meB

c

Landau levels

Cyclotron freq.H

all R

esist

ance

RH

(kΩ

)

Long

itudi

nal R

esist

ivity

ρxx

(kΩ

)

・Hall resistance is quantized.Klitzing constant RKh/e2 = 25812.807557(18) Ω

・Longitudinal resistance is zero.edge conduction

Topology (Berry’s phase)

Nobel prizes1985 von Klitzing IQHE1998 Laughlin, Storner, Tsui FQHEOkamoto Lab.

Various Surface States

** mk

mpE

22

222

Wavenumber k

Ener

gy E

Valence Band

Cond. Band

222 )()( pcmcE

kcpcE

0m

Free-Electron-like

Massless Dirac Electrons

Mono-Layer Agon Si(111)

Au(111)Bi(111)

Graphene（Monolayer Graphite）

Topological Surface StatesBi2Se3

SpinSpin

SpinSpinSpin-Deg.Spin-Deg

Spin split Due to Rashbaeffect

Valence Band

Cond. Band

Valence Band

Cond. Band

Valence Band

Cond. Band

Relativistic

(Non-relativistic)

2D Metal(Monatomic-Layer Metal)

-Inert and atomically flat surface-Free-electron-like surface state

Mono-Layer Ag on Si : Si (111)-√3×√3-Ag Surface

**////

mk

mp

E22

222

Standing Waves on Si(111)-√3×√3-Ag Surface at 65K

STM Images dI/dV Images

-0.9 V -0.9 V

-0.8 V

-0.7 V

Carrier Doping Into Surface States to Change Electrical Conductivity

Au Adsorption on Si(111)-√3×√3-Ag 0.02 ML Au

RT 65 K

0.01 ML Au 0.02 ML Au 0.03 ML

RT

135 K

1. Carrier doping in the surface-state band⇒ Increase in band occupation

2. Hybridization of the localized state and surface-state band⇒ Band splitting

C. L

iu, I

. Mat

suda

, R. H

obar

a, a

nd S

. Has

egaw

a,

Phys

. Rev

. Let

t. 96

, 036

803

( 200

6).

ne

Macro-Four-Terminal Measurements in UHV

S. Hasegawa, et al., Phys. Rev. Lett. 68, 1192 (1992)

Carrier Doping into Surface-State Band by Adatoms

6K

70K

RT

Res

ista

nce

(kΩ

)

2D Gas Phase

Nucleation

Y. Nakajima, et al., PRB 54, 14 134(1996); 56, 6782 (1997).

N. Sato, et al., PRB 60, 16 083(1999).

Ag Adatoms on Si(111)-√3×√3-Ag Surface

neR 1

Drude Theory

Crystal Structure of Bi2Se3 : Topological Insulator

H. Zhang, et al., Nature Physics (May 2009)

Crystal Structure of Bi2Se3 (Bi2Te3)H. Zhang, et al., Nature Physics (2009) S. Borisova, et al.,

Cryst. Growth Des. 12, 6098 (2012)

XTEM

van der Waals gap

van der Waals gap

van der Waals gap

Electronic States of Bi2Se3 (Theory)

H. Zhang, et al., Nature Physics (May 2009)

Isolated Atom（Atomic Orbitals）

Atomic Bondings

Split due to Crystal filed

Spin-Orbit Intercation

Conduction Band

Valence Band

SSDirac Cone

Dirac Cones of Topological Insulators

Bi2Se3 Bi2Te3

Hole‐doping by Pb alloying in Bi2Te3

Formation of stoichiometric PbBi4Te7, Bi2Te3(PbTe)0.5 orTe‐Bi‐Te‐Pb‐Te‐Bi‐Te?  

Fermi Level

Dirac Point

Band Dispersion Truly bulk insulator

M. Aitani, et al., Jap. J. Appl. Phys.52 (2013) 110112

Conductivity of a single Dirac-cone surface state

heSSS

2

5.020

Conductivity of Single (Spin-split) Dirac Cone

Drude Model ne 12104n cm-2Carrier Density

⇒ Mobility 30 cm2/Vs

Not high mobility!

Bulk carrier

SS carrier

2D Conductivity

M. Aitani, et al., Jpn. J. Appl. Phys. 52, 110112 ( 2013)

Current I

Electrical Resistance

R = VI ・C C: Correction Factor

Voltage Drop V

Bulk-Sensitive(Surface -Insensitive)

Macro-4-Point ProbeSurface -Sensitive

Micro-4-Point Probe

- Contact Resistance- Three Parallel Conduction Channels- Surface Sensitivity- Local Conductivity

σmeas=σSS＋σSC＋σB

Four-Point Probe Method for Transport Measurements

σSS

σSC

σB

Temperature-Variable Monolithic Micro-Four-Point Probe

Contacting to Si(111) sample surface in SEM

Developed at Denmark Technical UniversityCommercially available; http://www.capres.com

Si(111) Crystal

I. Shiraki, et al., Surf. Rev. Lett. 7 (2000) 533.C. L. Peteresen, et al., Appl. Phys. Lett. 77 (2000) 3782.S. Hasegawa, et al., J. Phys: Cond. Matters 14 (2002) 8379.T. Tanikawa, et al., e-J. Surf. Sci. Nanotech. 1 (2003) 50.

1D, 2D, and 3D conduction

d: probe distance(length of measured

area of sample)

1mm

1mm

200μm

5μm

SEM Images of Independently Driven Four W-Tips in UHV

I. Shiraki, et al., Surf. Sci. 493 (2001) 633.S. Hasegawa, et al., Current Appl. Phys. 2 (2002) 465.

Square 4PP正方４端子プローブ法

Linear 4PP線形４端子プローブ法

Four-Tip STM as Micro-Four-Point Probes142

Surface-Dominated Transport on a Bulk Topological Insulator Bi2Te2Se L. Barreto, et al.,

Nano Letters 14, 3755 (2014)

⇒ Mobility 390 cm2/Vs

2D transport

3D transport

LT: Bulk carriers are frozen out.⇒ SS transport only

Fairly high mobility!

Probe Spacing d (m)

SRR 22ln

dR

2

2D transport

3D transport

SRIVR

22ln

dIVR

2

Current Distribution vs. Probe-Spacing Dependence of Resistance

SR : Sheet Resistivity (Ω)

: 3D Resistivity (Ωcm

Four-Point Probe Resistance for a 3D sample 152 Four-Point Probe Resistance for a 2D sample153

Intrinsic conduction through topological surface states of insulating Bi2Te3 epitaxial thin films on BaF2 (111)

K. Hoefer, et al., PNAS 111, 14979 (2014)

⇒ Mobility 600,4 cm2/Vs Very high mobility!

Four-Tip STM with 20 nm Tip Spacing

S. Yoshimoto, et al., Nano Letters 7, 956 (May, 2007)

209

Electrical Resistance due to an Atomic Step

Standing Waves on Si(111)-√3×√3-Ag Surface at 65K

STM Images dI/dV Images

-0.9 V -0.9 V

-0.8 V

-0.7 V

166

Resistance Measurements Across a Step Bunch or On a Terrace

VOn Terrace Across Step Bunch

Step BunchTerrace

10μm

10μm

Step BunchTerrace

TerraceStep Bunch

Monatomic Steps decorated by a tiny amount of Ag adsorption

161Line Profile of Resistance measured across Step Bunches at RT in UHV

Si(111)-7×7 Clean Surface Si(111)-√3×3-Ag Surface

162

Line Profile of Resistance measured through Step Bunches at RT in UHV

Si(111)-√3×3-Ag Surface

R= 800Ω/300 steps ～3Ω

800Ω

Resistance of a single step(Experiment)

R=1/G～5ΩResistance of a single step

(Friedel振動から)

Good Match

S. Hasegawa et al.,J. Phys.: Cond. Matter 14, 8379 (2002).

168Tunneling Transport Landauer Formula (Tsu-Esaki)

１D: G = ・T(μ) [Ω-1]h2e2

2D: g = ・T(μ) [Ω-1m-1]h2e2

πkF

3D: g = ・T(μ) [Ω-1m-2]h2e2

4πkF2

T(μ): Transmission Probability througha potential barrier/a inlet・exit

I. Matsuda, et al., Physical Review Letters 93, 236801 (Dec, 2004)

ナノワイヤにおける電気伝導 Electrical Conduction through a nano-wire

谷城（東工大）

⇒ Ohm’s Law 𝐺 ∝ 𝑤ρ · ℓ

⇒ independent of Length ℓ ConductanceQuantization

𝝀𝒇： Fermi wave length , n: number of modes

ℓ𝒎𝒇𝒑： Mean free path, 平均自由工程2次元 ブロッホ波

入射波 Ψi=exp[i(kx・x+ky・y)]・u(x, y)E=E0+ (kx2+ky2)2m*

h2

u(x,y)= cell function

反射波 Ψr=R・exp[i(-kx・x+ky・y)]・u(x, y)R=|R|・exp[iη]

η：反射位相シフト

ポテンシャル障壁ステップドメイン境界

ρ(E, x)（局所状態密度）∝|Ψi+Ψr|2∝{1+|R|2+2|R|cos(2kx・x-η)}・|u(x,y)|2

定在波原子像

定在波の波長λ＝kxπ

電子定在波 108

Phase Shift in Reflection at a Step Edge

Phase shifts at a step edge, : - 0.8

Ψi ∝ exp{-ikx}

Ψr ∝ exp{i(kx-η)}

∝ | Ψi + Ψr |2

I. Matsuda, et al., Physical Review Letters 93, 236801 (Dec, 2004)

Phase Shift, Transmission Coefficient, and Conductance

1+tan2 (η+π)1Transmission Prob. T=1-

η= - 0.8π ⇒ T = 0.3 ～ 0.4

Transmission through δ- potentialL. Buergi, et al. Phys. Rev. Lett. 81, 5370 (1998)

g = ・T(μ) [Ω-1m-1]h2e2

πkF

2D Landauer Formula

3d

Measured Conductance G ～ g・3d

kF= 0.1Å-1d = 8μm (Probe Spacing)

R=1/G～5ΩResistance of a single step

=5×103 [Ω-1m-1]

173

Atomic-Layer Superconductivity Surface-State Superconductivity

Resistance of Bilayer Graphene w/wo Ca/LiS. Ichinokura, K. Sugawara, A. Takayama, T. Takahashi, and S. Hasegawa:“Superconducting Calcium‐Intercalated Bilayer Graphene” , ACS Nano 10, 2761‐2765 (Jan, 2016)

Tconset=4 K

Intercalation in GraphiteBulk Ca‐GIC

Stage1  Stage2  Stage3  TC=11.5K  non‐SC    non‐SC

Weak Localization

S. L. Surnev, et. al. A. A. Sarranin, et. al. S. Takeda, et al.

Indium-adsorbed Silicon (111) Surface

√7×√3

Insulator 2D MetalQuasi-1D Metal４×１√3×√3

RT(metallic)Plan View 60 K (CDW)H. Y. Yeom, et al., PRL 82, 4898 (1999)

Electrical Resistance of (Sub)Monolayer In-adsorbed Si

Semicond.

Quasi-1D metal

2D Metal

S. Yamazaki, et. al., Phys. Rev. Lett., 106, 116802 (2011).

(Ω)

Si(111)

λ=1.1Shee

t Res

istiv

ity

Temperature Ｔ（Ｋ）

（ＣＤＷ）

In Atoms

・e-Ph coupling constant （PES）（LBI USA 2003）・Energy gap （STS）（Tsinghua Univ. China 2010）

√7×√3: Suggestions of Superconductivity

In Atoms

Eli. Rotenberg, et. al.,Phys. Rev. Lett. 91 246404 (2003)

Circular Fermi surface

Parabolic dispersion relation

Fermi wave number

emm 1.1*

-1nm14Fk

*

22

2mkE

Effective mass

Isotropic two dimensionalnearly-free electron gas

]nm[eV6.4 212*

2

mD D

Fermi Surface

(very large)

120 Fk→metallic conduction

ARPES for Si(111)-√7×√3-In

2151013 cmn .・T-dependence of Peak width in spectra

⇒ e-Ph coupling constant λ～１ (Very large)⇒ Superconducting Band Dispersion

Unisoku Co. 2011

Sub-Kelvin μ4PP with strong B

MBE-RHEED

μ4PPSCMagnet

Sample

μ4PP

Lowest T：~800 mKMag. Field：7 T（⊥Surface）UHV (10-10Torr) in situ

M. Yamada, T. Hirahara, S. Hasegawa, T. Nagamura, e-J. Surf. Sci. Nanotech. 10, 400-405 (Jul, 2012).

0

100

200

300

400

500

600

0 1 2 3 4 5 6 7 8

Sheet Resis

tance (

/)

T (K)

Tc= 2.77K

Superconductivity at Si(111) -√7x√3-In

2D Aslamazov-Larkin (AL) termExcess conductivity by Cooper pairsgenerated by thermal fluctuation

Superconducitivy only locally

・Below TcGlobal coherent superconductivityTc=2.77 K

(Uchihashi：Tc=2.8 K)< Tc=3.18 K (from STS)< Tc=3.41 K (Bulk In)

aMTAL

R

0

1Above Tc:

Large fluctuation above TC

Si(111)-√7x√3-In : Under Magnetic Field

0

100

200

300

400

500

600

700

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Sheet Resis

tance (

/)

B (T)

BDP= 0.33T

Bc2= 0.43T

0

100

200

300

400

500

600

0 1 2 3 4 5

Sheet Resis

tance (

/)

T (K)

0T0.15T0.30T

cf. bulk In : Hc=293 Oe Strong Critical Field Hc2 (0)~5000 Oe

Very high Hc (=short ξ)

Short Coherence LengthξGL(0)~25 nm

Cooper Pairs in Free-Electron Band

kx

ky

k

E

kkkk

kkkk

Singlet

, kk , kkTriplet22

2k

mE

Fermi SurfaceBand Dispersion

Spin Split and Cooper Pairs in Free-Electron Band

kx

ky

k

E

kkkk

kkkk

Singlet

, kk , kkTriplet22

2k

mE

k

E

⊿k

20

2

)(2

kkm

E

kx

ky

kk

'' kk

Outer

Inner kkkkkkkkkk21

21

Singlet（ｓ-wave) Triplet(p-wave)

Fermi SurfaceBand Dispersion

⇒ Parity-Broken Superconductors

Si(111)–1x1-Tl

Si(111)–√3x√3-(Tl, Pb)

SiSi

Tl

Pb

√3x√3

1x1

+Pb 1/3 ML @ 300K

Mono-Layer

Tl 1ML on 7x7 @ 600K

Sample: Si(111)–√3x√3-(Tl, Pb) Surface SuperstructureD. V. Grunev, et al.; Sci. Rep. 4, 4742 (2014).

Si(111)-√3×√3-(Tl, Pb) :Rashba-type SS

ARPES+Theory⇒ Spin-Split Surface-State Bands

D. V. Gruznev, et al., Sci. Rep. 4, 4742 (2014)

STS below TC on Si(111)-√3×√3-(Tl,Pb) w/o BT. Nakamura, et al.; Phys. Rev. B 98, 134505 (Oct, 2018).

Fitting STS Spectra by Theory

s-wave (isotropic gap)(1.0 meV)

cos10 anisotropic gap

47.00 84.01

meVmeV

.const

T. Nakamura, et al.; Phys. Rev. B 98, 134505 (Oct, 2018).

Superconductivity above 100 K in single-layer FeSe films on doped SrTiO3 J-F. Ge, et al., Nature Materials 14, 285 (Mar, 2015)

Cf: Bulk FeSeTC = 9.4 K

measured in situ by μ4PP in UHVSpin Transport at Surfaces and Edges

- Storage Media記憶媒体 Magnetic Disk/Head, MRAM, …

- Energy-Saving /High-Speed Devices省エネ・高速素子

ｓｐｉｎ currentspin transistors sensors

- 量子情報処理素子Quantum Infomration Devices

Superposition of spin-up and spin-down states

Magnetic MaterialsHetero-, Wire-structuresDiluted Mag. SemiconductorsMagnetic molecuesGrapheneTopological Insulators

Utilizing Spins

Fert(France)

Gruenberg(Germany)

Miyazaki(Tohoku Univ.)

Discovery of Giant MagnetoResistance (GMR) Effect巨大磁気抵抗効果の発見

France Germany 南パリ大学 Julich Inst

b. 1938 b. 1939

Albert Fert Peter Grünberg

The Nobel Prize in Physics 2007

S. Yuasa, et al., Nature Materials 3, 868 (2004).

Tunnel MagnetoResistance (TMR) Effect

磁気ヘッド（ハードディスクの小型化・高密度化）Magnetic Head (HDs becomes smaller and high-density)

Fe

Fe

酸化Mg

Various Surface States

** mk

mpE

22

222

Wavenumber kEn

ergy

EValence Band

Cond. Band

222 )()( pcmcE

kcpcE

0m

Free-Electron-like

Massless Dirac Electrons

Mono-Layer Agon Si(111)

Au(111)Bi(111)

Graphene（Monolayer Graphite）

Topological Surface StatesBi2Se3

SpinSpin

SpinSpinSpin-Deg.Spin-Deg

Spin split Due to Rashbaeffect

Valence Band

Cond. Band

Valence Band

Cond. Band

Valence Band

Cond. Band

Relativistic

(Non-relativistic)

Spin-Textured Fermi Surface＋Electric Field⇒Current –Induced Spin Polarization電流誘起スピン偏極

ky

kx

M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010)

Spin-Textured Fermi Surfaceフェルミ面のスピン繊維構造

Spin Hall Effect・外因性（SOCによる非対称散乱）Extrinsic reason (asymmetric scattering due to SOC)・内因性Intrinsic （バンド構造に内在するベリー位相）

Intrinsic reason (Berry phase in band structure)

-

+E

磁場の印加が不要No external magnetic field非磁性物質（SOCが強い）Non-magnetic materials(strong SOC)

Spin Current

FxFxFxS

vnvnvnJ

2.....

pVσmcxVpmH grad)( 22 4 121スピン-軌道相互作用 (Spin-Orbit Coupling) Hamiltonian

Spin Current

Detecting Spin Hall Effect

Current Current/Voltage

Spin FlowSHE ISHE Electrical

Detection

It should be L < Ls (Spin relaxation length).

•Bi2Se3; 8QL thick•Se capping →FIB Fabrication•Heating → Remove Se Capping

Y. K. Kato, et al., Science 306, 1910 (2004)

GaAsKerr Rotation Microscopy

Up-

Spin

Dow

n-Spin

Edge Currents at Q(A)(S)HE

HgTe (QW)

QHE (chiral)2D Topol. Ins. (QSHE)

(helical)

3D Topol. Ins. 3D Mag.Topol. Ins. (chiral)

Breaking time-reversal symmetryby magnetic order Mag. proximity

3D Higher-OrderTopol. Ins.

QAHEE(+k, ↑)≠E(-k, ↓)

Need EF tuning EF should be in the gap. 

1D chiral edge state

Magnetic Topological InsulatorCr or V doped Bi1-xSbxTewithout external mag. Field

Anomalous QHE

C. Z, Chang, et al., Science 340, 167 (2013)

Quantum Hall Effect at 2DEGunder strong external mag. field

Longitudinal ResistivityVanishes

from Okamoto Lab

Hall ResistanceQuantizedin unit of h/e2

- Hall Resistance : quantized in unit of h/e2

- Longitudinal Resistance : vanishes

Hal

l Res

ista

nce

RH

(kΩ

)

Longitudinal Resistivity ρ

xx(kΩ

)

Mag. Proximity to break TRSBut, bulk doping isInhomogeneous.

Si/SiGe HeterojunctionT=40 mK

Dissipation-less currents at atomic layers/edges/hinges1. Superconducting Current

(1) UC FeSe on SrTiO3(2) Monolayer Metals, Pb, In, Ga,…(3) Metal-intercalated Graphene

2. Ballistic Current3. Edge Currents

(1) QHE(2) 2D Topological Insulators (QSHE)(3) 3D Magnetic Topological Ins.(QAHE)(4) Higher-order Topo. Ins.

4. Spin Current(1) Strong Spin-Orbit Int. Mat.(SHE)(2) Heterojunctions at Ferro/Non-mag.

Hinge statesAt higher-order Topol.

Edge states at 2D Topol. Ins.

Edge states at QHE

Rashba Superconductor

Graphene Superconductor

High-TC Superconductor

Pure Spin Current.