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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.