Post on 13-Jan-2016
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초전도의 짝짖기 대칭성과 불순물 효과
초전도의 짝짖기 대칭성과 불순물 효과
숭실대학교 물리학과김 희 상
OutlineOutline
• Introduction service
• basics on SC
What is a superconductor? / G-L theory, type I, type II / Cooper pair, BCS theory / What kinds of SC?
• order parameter symmetry•Unconventional SC
•Exotic s-wave SC
•impurity scattering
• summary
• Introduction service
• basics on SC
What is a superconductor? / G-L theory, type I, type II / Cooper pair, BCS theory / What kinds of SC?
• order parameter symmetry•Unconventional SC
•Exotic s-wave SC
•impurity scattering
• summary
초전도가 할 수 있는 것초전도가 할 수 있는 것
From “The hunt for Red October”
<= 가속기
초고속 컴퓨터 =>
<= MRI 의료기기
대표적인 광고Diagram forpoliticians
대표적인 광고Diagram forpoliticians
하지만……
지구를 영하 200 도까지 냉각 시켜야 된다는 거… .
하지만……
지구를 영하 200 도까지 냉각 시켜야 된다는 거… .
OutlineOutline
• Introduction service
• basics on SC
What is a superconductor? / Perfect conductor vs. Superconductor / G-L theory, type I, type II / Cooper pair, BCS theory / What kinds of SC?
• order parameter symmetry•Unconventional SC / Exotic s-wave SC / impurity scattering
• summary
• Introduction service
• basics on SC
What is a superconductor? / Perfect conductor vs. Superconductor / G-L theory, type I, type II / Cooper pair, BCS theory / What kinds of SC?
• order parameter symmetry•Unconventional SC / Exotic s-wave SC / impurity scattering
• summary
초전도체의 정의초전도체의 정의
1. Perfect conductivity1. Perfect conductivity
• 1908 – H. Kermerlingh Onnes ( 네덜란드 ) – Helium 의 액화 성공• 1908 – H. Kermerlingh Onnes ( 네덜란드 ) – Helium 의 액화 성공
• 1911 – 4.2 K, 수은 (Hg) 의 초전도 발견• 1911 – 4.2 K, 수은 (Hg) 의 초전도 발견
H. Kermerlingh OnnesH. Kermerlingh Onnes
H. K. Onnes, Commun. Phys. Lab.12,120, (1911)
2. Perfect diamagnetism2. Perfect diamagnetism
• 1933 – Meissner & Oschenfeld – not only perfect conductor but also perfect diamagnetism• 1933 – Meissner & Oschenfeld – not only perfect conductor but also perfect diamagnetism
Perfect conductor 와 superconductor 의 차이는 ?Perfect conductor 와 superconductor 의 차이는 ?
Perfect conductor below TcPerfect conductor below Tc
Apply B fieldApply B field
Lenz 의 법칙 -mag flux 유지Lenz 의 법칙 -mag flux 유지
• cooling 1st & field next• cooling 1st & field next
1st cooling1st cooling
Becomes p.c.Becomes p.c.
Remove B fieldRemove B field
Lenz 의 법칙 -mag flux 유지Lenz 의 법칙 -mag flux 유지
Perfect conductor below TcPerfect conductor below Tc
Apply B fieldApply B field
Lenz 의 법칙 -mag flux 유지Lenz 의 법칙 -mag flux 유지
Current dissipationCurrent dissipation
Field penetratesField penetrates
• Field 1st & cooling next• Field 1st & cooling next
Now coolingNow cooling Becomes p.c.Becomes p.c.
Remove B fieldRemove B field
Lenz 의 법칙 -mag flux 유지Lenz 의 법칙 -mag flux 유지
BUT SCs always expel the B fieldbelow Tc, no matter what.
BUT SCs always expel the B fieldbelow Tc, no matter what.
Superconductor
B field
London penetration depthLondon penetration depth
• 1935 – London brothers – two fluid model => penetration depth• 1935 – London brothers – two fluid model => penetration depth
2
2
4 en
mc
s
Magnetic length scaleMagnetic length scale
/~ xe
• 1950 – Ginzburg-Landau theory => free energy expansion• 1950 – Ginzburg-Landau theory => free energy expansion
• 1950 – Ginzburg-Landau theory => free energy expansion• 1950 – Ginzburg-Landau theory => free energy expansion
8
2||
2242
0
hA
c
eiff ns
Where is a complex order parameter,
and is to represent local density of sc electrons, .
Where is a complex order parameter,
and is to represent local density of sc electrons, .
2)(r
)(r
)(rns
Take the variation w.r.t. and .Take the variation w.r.t. and .)(r A
There exists sc coherence length.There exists sc coherence length.
)(T
There exists flux quantum.There exists flux quantum.
e
hc
20 Flux quantization.Flux quantization. Ntotal 0
• 1957 –Abrikosov-predict type II SC• 1957 –Abrikosov-predict type II SC
Vortex state
Flux quantumFlux quantum
How to understand type I, II ?How to understand type I, II ?
Introduce a vortex in SCIntroduce a vortex in SC 이득 : 자기장을 상쇄시키지 않아도 됨
손실 :응축에너지의 이득을 못 봄
8~
22 hLE
4
~2
2 LE
Physics Letters, 24A, 526(1967) PRL, 62, 214 (1989)
• 1957 – BCS theory – 초전도 현상을 설명• 1957 – BCS theory – 초전도 현상을 설명
John Bardeen Leon Neil Cooper
John Robert Schrieffer
Cooper pair problemCooper pair problem
Fermi Sea
e e
• fully filled F.S. + two interacting electrons• fully filled F.S. + two interacting electrons
• two electrons interact with F.S. only through Pauli exclusion principle.• two electrons interact with F.S. only through Pauli exclusion principle.
),(),()(22 212121
22
21 rrErrrrV
mm
Fkk
rrikekrr )(21
21)()(
and
3/)( LvpkV for 0, kkpkk FF otherwise zero!
Cooper’s resultsCooper’s results
Let and, then, vN
B eE )0(/202|| ||2 BF EEE
• F.S. becomes unstable for arbitrarily smallarbitrarily small attractive interaction.
ConclusionConclusion
• Bound energy is not analyticnot analytic in v. => pertubation is not possible
• electrons are bounded, i.e., get paired.
Size of the bound state ||/~ BF Ev
Where could the attractive interaction come from?Where could the attractive interaction come from?
Isotope effectIsotope effect
ionc MT /1 => Ion plays a role=> Ion plays a role
=> lattice vibration, i.e., phonon => lattice vibration, i.e., phonon
Indirect interaction through phononIndirect interaction through phonon
The pairs are heavily entangled!!The pairs are heavily entangled!!
BCS theoryBCS theory
HamiltonianHamiltonian
llkk
klkl
kkk ccccVnH **
0**
,...,1
mkkk
kkkkG ccvu
BCS ground state wave functionBCS ground state wave function
<= trial wave function<= trial wave function
0 GG NH
Variational MethodVariational Method
VNcc eT )0(/113.1
22kFkkE Quasiparticle’s
Excitation energy
Order parameterOrder parameter
BCS explains exp. dataBCS explains exp. data
초전도의 분류초전도의 분류
• type I, type II - magnetic property
• BCS type SC • He3 • heavy fermion SC • high Tc cuprates• Fullerine C60• organic SC• MgB2 금속화합물• and many more ……
• conventional, unconventional – OP symmetry
• 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS• 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS
• 1979 – Steglich Heavy fermion superconductor• 1979 – Steglich Heavy fermion superconductor
• 1986 – Bednorz, Muller - High Tc superconductor• 1986 – Bednorz, Muller - High Tc superconductor
CeCu2Si2 - heavy effective mass ~ 200me
UBe13 – rich phase diagramUPt3 – possible spin triplet
High Tc SC; copper oxides; CupratesHigh Tc SC; copper oxides; Cuprates
We are interested in the order parameter symmetry!!!
We are interested in the order parameter symmetry!!!
Order parameter in SCOrder parameter in SC
)2,1(, 21 rr antisymmetric
Spin partSpin part
2/1
2/1 Singlet pairingantisymm.
Triplet pairingsymm.
Two particle func.
21, rr
rR,
kR,
Spatial partSpatial part
k Spherical harmonics
s, d, g, … symm. Singlet pairingp, f, … antisymm. Triplet pairing
Spherical symm. 있는 경우
using the generalized BCS
The solution has the following form.
Therefore, OP symm. has info. of the interaction, i.e. the mechanism.
Therefore, OP symm. has info. of the interaction, i.e. the mechanism.
(xz,yz)2E
xy1B2
d-wave1B1
1A2
s-wave1A1
Etc.Base funcdimension
Irreducible rep.
Tetragonal symm. group; D4
222 , zyx
22 yx
YBCO
Unconventional SC(USC)Unconventional SC(USC)
Definition – order parameter(spatial part) has less rotational symmetry than the host lattice
Definition – order parameter(spatial part) has less rotational symmetry than the host lattice
k
(xz,yz,zx)3T2
(x,y,z)3T1
2E
1A2
s-wave1A1
Etc.Base funcdimension
Irreducible rep.
Cubic symm. group; Oh
222 zyx
Heavy fermion SCHeavy fermion SC
Structure of SC OP could be very complicated !!!Structure of SC OP could be very complicated !!!Conventional SC
• s-wave
• extended s-wave (sign change)
Unconventional SC
• d-wave(spin singlet)
• p-wave(spin triplet)
• and more ……
1.Zero average of OP on F.S.
2.Nodes exist.
gapless, power law behavior
Sensitive to imp. scattering
Non-zero ave. on F.S.No nodeGap-yesExponential behaviorIgnore imp. scattering
1.Zero average of OP on F.S.
2.Nodes exist.
=> structure of nodes (point node, line node, etc.) determines SC property
gapless, power law behavior
sensitive to impurity scattering
1. Line node : d-wave
2. Extended s-wave, d+s wave, ellipsoid
3. Point node
4. Nodeless UOP
1. Line node : d-wave
2. Extended s-wave, d+s wave, ellipsoid
3. Point node
4. Nodeless UOP
Eqs. to solve self-consistentlyEqs. to solve self-consistently
parameters describing impurity parameters describing impurity
Scattering rate
Scattering cross section(normalized by strong limit)
Line node (d-wave)Line node (d-wave)
Striking difference
Finite DOS at FS
Sensitive to imp scatteringSensitive to imp scattering
Extended s-wave, d+s waveExtended s-wave, d+s wave
Exotic s-wave SCsExotic s-wave SCs
• Two-gap like feature• critical value of imp. exists• Impurity-induced gap
Single peak
Two gap like feature
EllipsoidEllipsoid ~ D(1 + a cos(theta))
Maki (2002)
Exotic s-wave SCsExotic s-wave SCs
Gap amp. is not sensitive to impurity
Point nodePoint node
Notice : the difference
A-phase of SF He3
Zero FS average (USC)
Notice : the difference
A-phase of SF He3
Zero FS average (USC)
Exotic s-wave SCsExotic s-wave SCs
Gap opens with impurity scatteringGap opens with impurity scattering
T^3 behavior (w/o imp)
T^3 behavior (w/o imp)
Exponential behavior
(w/ imp.)
Exponential behavior
(w/ imp.)
Tc is not sensitive to imp.
All agree with borocarbides data.All agree with borocarbides data.
Summing up ……
• basics on SC (from def. to BCS)• why order parameter symmetry?• unconventional order parameter• exotic s-wave order parameters
•Extended s-wave, d+s wave•Point node SC – special atten. w/ borocarbides
• Imp. effect plays a key role in detecting OP symm.
Summing up ……
• basics on SC (from def. to BCS)• why order parameter symmetry?• unconventional order parameter• exotic s-wave order parameters
•Extended s-wave, d+s wave•Point node SC – special atten. w/ borocarbides
• Imp. effect plays a key role in detecting OP symm.
오늘 우리가 이야기한 것들……오늘 우리가 이야기한 것들……
• 1908 – H. Kermerlingh Onnes ( 네덜란드 ) – Helium 의 액화 성공• 1908 – H. Kermerlingh Onnes ( 네덜란드 ) – Helium 의 액화 성공
• 1911 – 4.2 K, 수은 (Hg), perfect conductivity• 1911 – 4.2 K, 수은 (Hg), perfect conductivity
• 1935 – London brothers – 현상론 => penetration depth• 1935 – London brothers – 현상론 => penetration depth
• 1933 – Meissner & Oschenfeld – perfect diamagnetism• 1933 – Meissner & Oschenfeld – perfect diamagnetism
• 1950 – Ginzburg-Landau theory => free energy expansion• 1950 – Ginzburg-Landau theory => free energy expansion
• 1957 – BCS theory – 초전도 현상을 설명 ; Abrikosov-predict type II SC• 1957 – BCS theory – 초전도 현상을 설명 ; Abrikosov-predict type II SC
• 1962 – Josephson effect • 1962 – Josephson effect
• 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS• 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS
• 1979 – Heavy fermion superconductor• 1979 – Heavy fermion superconductor
• 1986 – Bednorz, Muller - High Tc superconductor• 1986 – Bednorz, Muller - High Tc superconductor
• 2001 – MgB2 - 39K - 금속화합물• 2001 – MgB2 - 39K - 금속화합물
19131913
2003
2003
2003200319721972
19731973
19961996 20032003
19871987
• 초전도문제는 어렵지만 , 재미있고 방대한 구조를 가지고 있다 .• 아직도 중요한 open problems 가 널려있다 .• 가장 rewarding 한 분야이다 .• 그리고…… 고도의 복지사회로 인도하는……
초전도의 주요 역사초전도의 주요 역사
• 1908 – H. Kermerlingh Onnes ( 네덜란드 ) – Helium 의 액화 성공• 1908 – H. Kermerlingh Onnes ( 네덜란드 ) – Helium 의 액화 성공
• 1911 – 4.2 K, 수은 (Hg), perfect conductivity• 1911 – 4.2 K, 수은 (Hg), perfect conductivity
• 1935 – London brothers – 현상론 => penetration depth• 1935 – London brothers – 현상론 => penetration depth
• 1933 – Meissner & Oschenfeld – perfect diamagnetism• 1933 – Meissner & Oschenfeld – perfect diamagnetism
• 1950 – Ginzburg-Landau theory => free energy expansion• 1950 – Ginzburg-Landau theory => free energy expansion
• 1957 – BCS theory – 초전도 현상을 설명 ; Abrikosov-predict type II SC• 1957 – BCS theory – 초전도 현상을 설명 ; Abrikosov-predict type II SC
• 1962 – Josephson effect • 1962 – Josephson effect
• 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS• 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS
• 1979 – Heavy fermion superconductor• 1979 – Heavy fermion superconductor
• 1986 – Bednorz, Muller - High Tc superconductor• 1986 – Bednorz, Muller - High Tc superconductor
• 2001 – MgB2 - 39K - 금속화합물• 2001 – MgB2 - 39K - 금속화합물
19131913
2003
2003
2003200319721972
19731973
19961996 20032003
19871987
마침내… 종착역 !!!
• 2001 – MgB2 - 39K• 2001 – MgB2 - 39K
• 금속화합물 (cuprates are seramic)
• 포항공대 초전도 연구실이 선두 group 의 하나• 음……… 그정도 !
초전도의 주요 역사초전도의 주요 역사
• 1908 – H. Kermerlingh Onnes ( 네덜란드 ) – Helium 의 액화 성공• 1908 – H. Kermerlingh Onnes ( 네덜란드 ) – Helium 의 액화 성공
• 1911 – 4.2 K, 수은 (Hg), perfect conductivity• 1911 – 4.2 K, 수은 (Hg), perfect conductivity
• 1935 – London brothers – 현상론 => penetration depth• 1935 – London brothers – 현상론 => penetration depth
• 1933 – Meissner & Oschenfeld – perfect diamagnetism• 1933 – Meissner & Oschenfeld – perfect diamagnetism
• 1950 – Ginzburg-Landau theory => free energy expansion• 1950 – Ginzburg-Landau theory => free energy expansion
• 1957 – BCS theory – 초전도 현상을 설명 ; Abrikosov-predict type II SC• 1957 – BCS theory – 초전도 현상을 설명 ; Abrikosov-predict type II SC
• 1962 – Josephson effect • 1962 – Josephson effect
• 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS• 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS
• 1979 – Heavy fermion superconductor• 1979 – Heavy fermion superconductor
• 1986 – Bednorz, Muller - High Tc superconductor• 1986 – Bednorz, Muller - High Tc superconductor
• 2001 – MgB2 - 39K - 금속화합물• 2001 – MgB2 - 39K - 금속화합물
19131913
2003
2003
2003200319721972
19731973
19961996 20032003
19871987
오늘 우리가 이야기한 것들……오늘 우리가 이야기한 것들……
• 1908 – H. Kermerlingh Onnes ( 네덜란드 ) – Helium 의 액화 성공• 1908 – H. Kermerlingh Onnes ( 네덜란드 ) – Helium 의 액화 성공
• 1911 – 4.2 K, 수은 (Hg), perfect conductivity• 1911 – 4.2 K, 수은 (Hg), perfect conductivity
• 1935 – London brothers – 현상론 => penetration depth• 1935 – London brothers – 현상론 => penetration depth
• 1933 – Meissner & Oschenfeld – perfect diamagnetism• 1933 – Meissner & Oschenfeld – perfect diamagnetism
• 1950 – Ginzburg-Landau theory => free energy expansion• 1950 – Ginzburg-Landau theory => free energy expansion
• 1957 – BCS theory – 초전도 현상을 설명 ; Abrikosov-predict type II SC• 1957 – BCS theory – 초전도 현상을 설명 ; Abrikosov-predict type II SC
• 1962 – Josephson effect • 1962 – Josephson effect
• 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS• 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS
• 1979 – Heavy fermion superconductor• 1979 – Heavy fermion superconductor
• 1986 – Bednorz, Muller - High Tc superconductor• 1986 – Bednorz, Muller - High Tc superconductor
• 2001 – MgB2 - 39K - 금속화합물• 2001 – MgB2 - 39K - 금속화합물
19131913
2003
2003
2003200319721972
19731973
19961996 20032003
19871987
• 초전도문제는 어렵지만 , 재미있고 방대한 구조를 가지고 있다 .• 아직도 중요한 open problems 가 널려있다 .• 가장 rewarding 한 분야이다 .• 그리고…… 고도의 복지사회로 인도하는……
eV
tunneling
Tunneling in QMTunneling in QM
Josephson tunnelingJosephson tunneling
210 SinJJ
111
ie 222
ie
sc2sc1
Zero bias voltage,
cooper pair tunneling
Zero bias voltage,
cooper pair tunneling
• 1962 – Josephson effect • 1962 – Josephson effect
초전도의 주요 역사초전도의 주요 역사
• 1908 – H. Kermerlingh Onnes ( 네덜란드 ) – Helium 의 액화 성공• 1908 – H. Kermerlingh Onnes ( 네덜란드 ) – Helium 의 액화 성공
• 1911 – 4.2 K, 수은 (Hg), perfect conductivity• 1911 – 4.2 K, 수은 (Hg), perfect conductivity
• 1935 – London brothers – 현상론 => penetration depth• 1935 – London brothers – 현상론 => penetration depth
• 1933 – Meissner & Oschenfeld – perfect diamagnetism• 1933 – Meissner & Oschenfeld – perfect diamagnetism
• 1950 – Ginzburg-Landau theory => free energy expansion• 1950 – Ginzburg-Landau theory => free energy expansion
• 1957 – BCS theory – 초전도 현상을 설명 ; Abrikosov-predict type II SC• 1957 – BCS theory – 초전도 현상을 설명 ; Abrikosov-predict type II SC
• 1962 – Josephson effect • 1962 – Josephson effect
• 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS• 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS
• 1979 – Heavy fermion superconductor• 1979 – Heavy fermion superconductor
• 1986 – Bednorz, Muller - High Tc superconductor• 1986 – Bednorz, Muller - High Tc superconductor
• 2001 – MgB2 - 39K - 금속화합물• 2001 – MgB2 - 39K - 금속화합물
19131913
19721972
19731973
19871987
19961996
2003
2003
20032003
20032003
초전도의 주요 역사초전도의 주요 역사
• 1908 – H. Kermerlingh Onnes ( 네덜란드 ) – Helium 의 액화 성공• 1908 – H. Kermerlingh Onnes ( 네덜란드 ) – Helium 의 액화 성공
• 1911 – 4.2 K, 수은 (Hg), perfect conductivity• 1911 – 4.2 K, 수은 (Hg), perfect conductivity
• 1935 – London brothers – 현상론 => penetration depth• 1935 – London brothers – 현상론 => penetration depth
• 1933 – Meissner & Oschenfeld – perfect diamagnetism• 1933 – Meissner & Oschenfeld – perfect diamagnetism
• 1950 – Ginzburg-Landau theory => free energy expansion• 1950 – Ginzburg-Landau theory => free energy expansion
• 1957 – BCS theory – 초전도 현상을 설명 ; Abrikosov-predict type II SC• 1957 – BCS theory – 초전도 현상을 설명 ; Abrikosov-predict type II SC
• 1962 – Josephson effect • 1962 – Josephson effect
• 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS• 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS
• 1979 – Heavy fermion superconductor• 1979 – Heavy fermion superconductor
• 1986 – Bednorz, Muller - High Tc superconductor• 1986 – Bednorz, Muller - High Tc superconductor
• 2001 – MgB2 - 39K - 금속화합물• 2001 – MgB2 - 39K - 금속화합물
19131913
2003
2003
2003200319721972
19731973
19961996 20032003
19871987
Type IType I
Type IIType II
Among conventional scAmong conventional sc
Basically all the compound SC
Basically all the compound SC
초전도의 주요 역사초전도의 주요 역사
• 1908 – H. Kermerlingh Onnes ( 네덜란드 ) – Helium 의 액화 성공• 1908 – H. Kermerlingh Onnes ( 네덜란드 ) – Helium 의 액화 성공
• 1911 – 4.2 K, 수은 (Hg), perfect conductivity• 1911 – 4.2 K, 수은 (Hg), perfect conductivity
• 1935 – London brothers – 현상론 => penetration depth• 1935 – London brothers – 현상론 => penetration depth
• 1933 – Meissner & Oschenfeld – perfect diamagnetism• 1933 – Meissner & Oschenfeld – perfect diamagnetism
• 1950 – Ginzburg-Landau theory => free energy expansion• 1950 – Ginzburg-Landau theory => free energy expansion
• 1957 – BCS theory – 초전도 현상을 설명 ; Abrikosov-predict type II SC• 1957 – BCS theory – 초전도 현상을 설명 ; Abrikosov-predict type II SC
• 1962 – Josephson effect • 1962 – Josephson effect
• 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS• 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS
• 1979 – Heavy fermion superconductor• 1979 – Heavy fermion superconductor
• 1986 – Bednorz, Muller - High Tc superconductor• 1986 – Bednorz, Muller - High Tc superconductor
• 2001 – MgB2 - 39K - 금속화합물• 2001 – MgB2 - 39K - 금속화합물
19131913
2003
2003
2003200319721972
19731973
19961996 20032003
19871987