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