초전도의 짝짖기 대칭성과
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초전도의 짝짖기 대칭성과 불순물 효과 PowerPoint PPT Presentation


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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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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


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초전도가 할 수 있는 것


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From “The hunt for Red October”


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<= 가속기

초고속 컴퓨터 =>


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<= MRI 의료기기


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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


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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


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2. Perfect diamagnetism

  • 1933 – Meissner & Oschenfeld –not only perfect conductor

  • but also perfect diamagnetism

Perfect conductor와 superconductor의 차이는?


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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


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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.


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B field

Superconductor

London penetration depth

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

Magnetic length scale


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


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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


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Vortex state

Flux quantum

  • 1957 –Abrikosov-predict type II SC


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How to understand type I, II ?

Introduce a vortex in SC

이득 :

자기장을 상쇄시키지 않아도 됨

손실 :

응축에너지의 이득을 못 봄


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Physics Letters, 24A, 526(1967)

PRL, 62, 214 (1989)


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  • 1957 – BCS theory –초전도 현상을 설명

John Robert Schrieffer

John Bardeen

Leon Neil Cooper


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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.


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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


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=> Ion plays a role

=> lattice vibration, i.e., phonon

Where could the attractive interaction come from?

Isotope effect


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The pairs are heavily entangled!!

Indirect interaction through phonon


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BCS theory

Hamiltonian

Order parameter

BCS ground state wave function

<= trial wave function

Quasiparticle’s

Excitation energy

Variational Method


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BCS explains exp. data


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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


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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


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High Tc SC; copper oxides; Cuprates


We are interested in the order parameter symmetry

We are interested in the order parameter symmetry!!!


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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.


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using the generalized BCS

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

The solution has

the following form.


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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


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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


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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


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  • 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


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Eqs. to solve self-consistently


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parameters describing impurity

Scattering cross section

(normalized by strong limit)

Scattering rate


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Line node (d-wave)

Striking difference


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Sensitive to imp scattering

Finite DOS at FS


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Exotic s-wave SCs

Extended s-wave, d+s wave


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  • Two-gap like feature

  • critical value of imp. exists

  • Impurity-induced gap


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Ellipsoid

~ D(1 + a cos(theta))

Single peak

Exotic s-wave SCs

Two gap like feature

Maki (2002)


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Gap amp. is not sensitive to impurity


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Exotic s-wave SCs

Point node

Notice : the difference

A-phase of SF He3

Zero FS average (USC)


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Gap opens with impurity scattering


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T^3 behavior

(w/o imp)

Exponential behavior

(w/ imp.)


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Tc is not sensitive to imp.

All agree with borocarbides data.


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  • 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.


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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……


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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


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  • 2001 – MgB2 - 39K

  • 금속화합물 (cuprates are seramic)

  • 포항공대 초전도 연구실이 선두 group의 하나

  • 음………그정도!


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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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  • 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……


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Josephson tunneling

Tunneling in QM

tunneling

eV

sc1

sc2

  • 1962 – Josephson effect

Zero bias voltage,

cooper pair tunneling


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  • 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


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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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Type I


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Type II

Among conventional sc

Basically all the compound SC


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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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