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

  • 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 것


From “The hunt for Red October”


<= 가속기

초고속 컴퓨터 =>


<= MRI 의료기기


대표적인 광고

Diagram for

politicians

하지만……

지구를 영하 200도

까지 냉각 시켜야 된다는 거….


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


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


2. Perfect diamagnetism

  • 1933 – Meissner & Oschenfeld –not only perfect conductor

  • but also perfect diamagnetism

Perfect conductor와 superconductor의 차이는?


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


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.


B field

Superconductor

London penetration depth

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

Magnetic length scale


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


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


Vortex state

Flux quantum

  • 1957 –Abrikosov-predict type II SC


How to understand type I, II ?

Introduce a vortex in SC

이득 :

자기장을 상쇄시키지 않아도 됨

손실 :

응축에너지의 이득을 못 봄


Physics Letters, 24A, 526(1967)

PRL, 62, 214 (1989)


  • 1957 – BCS theory –초전도 현상을 설명

John Robert Schrieffer

John Bardeen

Leon Neil Cooper


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.


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


=> Ion plays a role

=> lattice vibration, i.e., phonon

Where could the attractive interaction come from?

Isotope effect


The pairs are heavily entangled!!

Indirect interaction through phonon


BCS theory

Hamiltonian

Order parameter

BCS ground state wave function

<= trial wave function

Quasiparticle’s

Excitation energy

Variational Method


BCS explains exp. data


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


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


High Tc SC; copper oxides; Cuprates


We are interested in the order parameter symmetry!!!


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.


using the generalized BCS

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

The solution has

the following form.


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


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


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


  • 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


Eqs. to solve self-consistently


parameters describing impurity

Scattering cross section

(normalized by strong limit)

Scattering rate


Line node (d-wave)

Striking difference


Sensitive to imp scattering

Finite DOS at FS


Exotic s-wave SCs

Extended s-wave, d+s wave


  • Two-gap like feature

  • critical value of imp. exists

  • Impurity-induced gap


Ellipsoid

~ D(1 + a cos(theta))

Single peak

Exotic s-wave SCs

Two gap like feature

Maki (2002)


Gap amp. is not sensitive to impurity


Exotic s-wave SCs

Point node

Notice : the difference

A-phase of SF He3

Zero FS average (USC)


Gap opens with impurity scattering


T^3 behavior

(w/o imp)

Exponential behavior

(w/ imp.)


Tc is not sensitive to imp.

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.


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……


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


  • 2001 – MgB2 - 39K

  • 금속화합물 (cuprates are seramic)

  • 포항공대 초전도 연구실이 선두 group의 하나

  • 음………그정도!


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


  • 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……


Josephson tunneling

Tunneling in QM

tunneling

eV

sc1

sc2

  • 1962 – Josephson effect

Zero bias voltage,

cooper pair tunneling


  • 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


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


Type I


Type II

Among conventional sc

Basically all the compound SC


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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