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초전도의 짝짖기 대칭성과 불순물 효과. 숭실대학교 물리학과 김 희 상. Outline. 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.

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slide1

초전도의 짝짖기 대칭성과 불순물 효과

숭실대학교 물리학과

김 희 상

outline
Outline
  • 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
slide7
<= 가속기

초고속 컴퓨터 =>

slide9
대표적인 광고

Diagram for

politicians

하지만……

지구를 영하 200도

까지 냉각 시켜야 된다는 거….

outline1
Outline
  • 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
slide14
1. Perfect conductivity
  • 1908 – H. Kermerlingh Onnes (네덜란드) – Helium의 액화 성공
  • 1911 – 4.2 K, 수은(Hg)의 초전도 발견

H. Kermerlingh Onnes

H. K. Onnes, Commun. Phys. Lab.12,120, (1911)

초전도체의 정의

slide15
2. Perfect diamagnetism
  • 1933 – Meissner & Oschenfeld –not only perfect conductor
  • but also perfect diamagnetism

Perfect conductor와 superconductor의 차이는?

slide16
1st cooling

Apply B field

Becomes p.c.

Lenz 의 법칙-mag flux 유지

Remove B field

Lenz 의 법칙-mag flux 유지

Perfect conductor below Tc

  • cooling 1st & field next
slide17
Apply B field

Current dissipation

Field penetrates

Lenz 의 법칙-mag flux 유지

Now cooling

Becomes p.c.

Remove B field

Lenz 의 법칙-mag flux 유지

Perfect conductor below Tc

  • Field 1st & cooling next

BUT SCs always expel the B field

below Tc, no matter what.

slide18
B field

Superconductor

London penetration depth

  • 1935 – London brothers – two fluid model => penetration depth

Magnetic length scale

slide20
Where is a complex order parameter,

and is to represent local density of sc electrons, .

Take the variation w.r.t. and .

There exists sc coherence length.

There exists flux quantum.

Flux quantization.

  • 1950 – Ginzburg-Landau theory => free energy expansion
slide21
Vortex state

Flux quantum

  • 1957 –Abrikosov-predict type II SC
slide22
How to understand type I, II ?

Introduce a vortex in SC

이득 :

자기장을 상쇄시키지 않아도 됨

손실 :

응축에너지의 이득을 못 봄

slide25
1957 – BCS theory –초전도 현상을 설명

John Robert Schrieffer

John Bardeen

Leon Neil Cooper

slide26
e

e

Fermi Sea

and

for

otherwise zero!

Cooper pair problem

  • fully filled F.S. + two interacting electrons
  • two electrons interact with F.S.
  • only through Pauli exclusion principle.
slide27
Conclusion
  • F.S. becomes unstable for arbitrarily small attractive interaction.
  • electrons are bounded, i.e., get paired.
  • Bound energy is not analytic in v. => pertubation is not possible

Cooper’s results

Let and, then,

Size of the bound state

slide28
=> Ion plays a role

=> lattice vibration, i.e., phonon

Where could the attractive interaction come from?

Isotope effect

slide29
The pairs are heavily entangled!!

Indirect interaction through phonon

slide31
BCS theory

Hamiltonian

Order parameter

BCS ground state wave function

<= trial wave function

Quasiparticle’s

Excitation energy

Variational Method

slide33
초전도의 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
slide34
CeCu2Si2 - heavy effective mass ~ 200me

UBe13– rich phase diagram

UPt3– possible spin triplet

  • 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS
  • 1979 – Steglich Heavy fermion superconductor
  • 1986 – Bednorz, Muller - High Tc superconductor
slide38
antisymmetric

Spin part

Spatial part

Singlet pairing

antisymm.

Spherical symm.있는 경우

Triplet pairing

symm.

  • Spherical harmonics

s, d, g, … symm. Singlet pairing

p, f, … antisymm. Triplet pairing

Order parameter in SC

Two particle func.

slide39
using the generalized BCS

Therefore, OP symm. has info. of the interaction, i.e. the mechanism.

The solution has

the following form.

slide40
Tetragonal symm. group; D4

YBCO

Irreducible rep.

dimension

Base func

Etc.

A1

1

s-wave

A2

1

B1

1

d-wave

B2

1

xy

E

2

(xz,yz)

Unconventional SC(USC)

Definition –

order parameter(spatial part) has less rotational symmetry than the host lattice

slide41
Cubic symm. group; Oh

Irreducible rep.

dimension

Base func

Etc.

A1

1

s-wave

A2

1

E

2

T1

3

(x,y,z)

T2

3

(xz,yz,zx)

Heavy fermion SC

slide42
Structure of SC OP could be very complicated !!!
  • Conventional SC
  • s-wave
  • extended s-wave (sign change)

Non-zero ave. on F.S.

No node

Gap-yes

Exponential behavior

Ignore imp. scattering

  • 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

slide43
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
  • Line node : d-wave
  • Extended s-wave, d+s wave, ellipsoid
  • Point node
  • Nodeless UOP
slide45
parameters describing impurity

Scattering cross section

(normalized by strong limit)

Scattering rate

slide46
Line node (d-wave)

Striking difference

slide48
Exotic s-wave SCs

Extended s-wave, d+s wave

slide49
Two-gap like feature
  • critical value of imp. exists
  • Impurity-induced gap
slide50
Ellipsoid

~ D(1 + a cos(theta))

Single peak

Exotic s-wave SCs

Two gap like feature

Maki (2002)

slide52
Exotic s-wave SCs

Point node

Notice : the difference

A-phase of SF He3

Zero FS average (USC)

slide55
T^3 behavior

(w/o imp)

Exponential behavior

(w/ imp.)

slide56
Tc is not sensitive to imp.

All agree with borocarbides data.

slide57
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.
slide58
1913

2003

1972

2003

1973

1996

2003

1987

오늘 우리가 이야기한 것들……

  • 1908 – H. Kermerlingh Onnes (네덜란드) – Helium의 액화 성공
  • 1911 – 4.2 K, 수은(Hg), perfect conductivity
  • 1933 – Meissner & Oschenfeld – perfect diamagnetism
  • 1935 – London brothers –현상론 => penetration depth
  • 1950 – Ginzburg-Landau theory => free energy expansion
  • 1957 – BCS theory –초전도 현상을 설명; Abrikosov-predict type II SC
  • 1962 – Josephson effect
  • 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS
  • 1979 – Heavy fermion superconductor
  • 1986 – Bednorz, Muller - High Tc superconductor
  • 2001 – MgB2 - 39K - 금속화합물
  • 초전도문제는 어렵지만, 재미있고 방대한 구조를 가지고 있다.
  • 아직도 중요한 open problems가 널려있다.
  • 가장 rewarding한 분야이다.
  • 그리고……고도의 복지사회로 인도하는……
slide62
초전도의 주요 역사
  • 1908 – H. Kermerlingh Onnes (네덜란드) – Helium의 액화 성공

1913

  • 1911 – 4.2 K, 수은(Hg), perfect conductivity
  • 1933 – Meissner & Oschenfeld – perfect diamagnetism
  • 1935 – London brothers –현상론 => penetration depth

2003

  • 1950 – Ginzburg-Landau theory => free energy expansion

1972

2003

  • 1957 – BCS theory –초전도 현상을 설명; Abrikosov-predict type II SC

1973

  • 1962 – Josephson effect

1996

2003

  • 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS
  • 1979 – Heavy fermion superconductor

1987

  • 1986 – Bednorz, Muller - High Tc superconductor

마침내…종착역!!!

  • 2001 – MgB2 - 39K - 금속화합물
slide63
2001 – MgB2 - 39K
  • 금속화합물 (cuprates are seramic)
  • 포항공대 초전도 연구실이 선두 group의 하나
  • 음………그정도!
slide64
초전도의 주요 역사
  • 1908 – H. Kermerlingh Onnes (네덜란드) – Helium의 액화 성공

1913

  • 1911 – 4.2 K, 수은(Hg), perfect conductivity
  • 1933 – Meissner & Oschenfeld – perfect diamagnetism
  • 1935 – London brothers –현상론 => penetration depth

2003

  • 1950 – Ginzburg-Landau theory => free energy expansion

1972

2003

  • 1957 – BCS theory –초전도 현상을 설명; Abrikosov-predict type II SC

1973

  • 1962 – Josephson effect

1996

2003

  • 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS
  • 1979 – Heavy fermion superconductor

1987

  • 1986 – Bednorz, Muller - High Tc superconductor
  • 2001 – MgB2 - 39K - 금속화합물
slide65
1908 – H. Kermerlingh Onnes (네덜란드) – Helium의 액화 성공

1913

  • 1911 – 4.2 K, 수은(Hg), perfect conductivity
  • 1933 – Meissner & Oschenfeld – perfect diamagnetism
  • 1935 – London brothers –현상론 => penetration depth

2003

  • 1950 – Ginzburg-Landau theory => free energy expansion

1972

2003

  • 1957 – BCS theory –초전도 현상을 설명; Abrikosov-predict type II SC

1973

  • 1962 – Josephson effect

1996

2003

  • 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS
  • 1979 – Heavy fermion superconductor

1987

  • 1986 – Bednorz, Muller - High Tc superconductor
  • 2001 – MgB2 - 39K - 금속화합물

오늘 우리가 이야기한 것들……

  • 초전도문제는 어렵지만, 재미있고 방대한 구조를 가지고 있다.
  • 아직도 중요한 open problems가 널려있다.
  • 가장 rewarding한 분야이다.
  • 그리고……고도의 복지사회로 인도하는……
slide66
Josephson tunneling

Tunneling in QM

tunneling

eV

sc1

sc2

  • 1962 – Josephson effect

Zero bias voltage,

cooper pair tunneling

slide67
1908 – H. Kermerlingh Onnes (네덜란드) – Helium의 액화 성공
  • 1911 – 4.2 K, 수은(Hg), perfect conductivity
  • 1933 – Meissner & Oschenfeld – perfect diamagnetism
  • 1935 – London brothers –현상론 => penetration depth

2003

2003

2003

초전도의 주요 역사

1913

  • 1950 – Ginzburg-Landau theory => free energy expansion

1972

  • 1957 – BCS theory –초전도 현상을 설명; Abrikosov-predict type II SC

1973

  • 1962 – Josephson effect

1996

  • 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS
  • 1979 – Heavy fermion superconductor

1987

  • 1986 – Bednorz, Muller - High Tc superconductor
  • 2001 – MgB2 - 39K - 금속화합물
slide68
초전도의 주요 역사
  • 1908 – H. Kermerlingh Onnes (네덜란드) – Helium의 액화 성공

1913

  • 1911 – 4.2 K, 수은(Hg), perfect conductivity
  • 1933 – Meissner & Oschenfeld – perfect diamagnetism
  • 1935 – London brothers –현상론 => penetration depth

2003

  • 1950 – Ginzburg-Landau theory => free energy expansion

1972

2003

  • 1957 – BCS theory –초전도 현상을 설명; Abrikosov-predict type II SC

1973

  • 1962 – Josephson effect

1996

2003

  • 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS
  • 1979 – Heavy fermion superconductor

1987

  • 1986 – Bednorz, Muller - High Tc superconductor
  • 2001 – MgB2 - 39K - 금속화합물
slide71
Type II

Among conventional sc

Basically all the compound SC

slide72
초전도의 주요 역사
  • 1908 – H. Kermerlingh Onnes (네덜란드) – Helium의 액화 성공

1913

  • 1911 – 4.2 K, 수은(Hg), perfect conductivity
  • 1933 – Meissner & Oschenfeld – perfect diamagnetism
  • 1935 – London brothers –현상론 => penetration depth

2003

  • 1950 – Ginzburg-Landau theory => free energy expansion

1972

2003

  • 1957 – BCS theory –초전도 현상을 설명; Abrikosov-predict type II SC

1973

  • 1962 – Josephson effect

1996

2003

  • 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS
  • 1979 – Heavy fermion superconductor

1987

  • 1986 – Bednorz, Muller - High Tc superconductor
  • 2001 – MgB2 - 39K - 금속화합물
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