超伝導の基礎 I
有本靖
高エネルギー加速器研究機構
2022-09-06 OHO’22 加速器セミナー

目次
• 導入
• 完全電気伝導と超伝導• ロンドン方程式• ピッパード方程式• 熱力学• Ginzburg—Landau理論

超伝導の発見• K. Onnes- ヘリウムの液化に成功 (1908年)

予想- 低温での物質の抵抗を調べていた.
- 高純度が得られる水銀(Hg)を使用• Onnesの予想

抵抗- 温度を下げると抵抗は小さくなるが,- 絶対温度になると絶縁体になる →抵抗が無限大
温度

超伝導の発見• K. Onnes

抵抗- ヘリウムの液化に成功 (1908年)- 低温での物質の抵抗を調べていた.
- 高純度が得られる水銀(Hg)を使用• Onnesの予想- 温度を下げると抵抗は小さくなるが,- 絶対温度になると絶縁体になる →抵抗が無限大• 実際の測定- 抵抗が10-5 Ω以下に減少 (1911年)

温度
K. Onnes, in Procs. of koninklijke akademie
van wetenschappen, Vol. 14 (1911)

マイスナー効果

超伝導の特徴• 電気抵抗ゼロ• 完全反磁性- Meissner-Ochsenfeld 効果 (マイスナー効果)• ピン止めホバーボード by Lexus@TOYOTA- 第二種超伝導体

電流密度• 超伝導相の安定領域を決める三つの状態変数- 臨界温度- 臨界電流- 臨界磁場温度

磁場
参照: 超伝導・低温工学ハンドブック

超伝導状態になる元素

超伝導元素

アモルファス状態または高圧下でのみ超伝導状態となる元素

H

He

Li

Be

B

C

N

O

F

Ne

Na

Mg

Al

Si

P

S

Cl

Ar

K

Ca

Sc

Ti

V

Cr

Mn

Fe

Co

Ni

Cu

Zn

Ga

Ge

As

Se

Br

Kr

Rb

Sr

Y

Zr

Nb

Mo

Tc

Ru

Rh

Pd

Ag

Cd

In

Sn

Sb

Te

I

Xe

Cs

Ba

La

Hf

Ta

W

Re

Os

Ir

Pt

Au

Hg

Tl

Pb

Bi

Po

At

Rn

Fr

Ra

Ac

La

Ce

Pr

Nd

Pm

Sm

Eu

Gd

Tb

Dy

Ho

Er

Tm

Yb

Lu

Ac

Th

Pa

U

Np

Pu

Am

Cm

Bk

Cf

Es

Fm

Md

No

Lr

1

参照: 超伝導・低温工学ハンドブック
超伝導 / 家康弘

超伝導状態になる元素

超伝導元素
H

アモルファス状態または高圧下でのみ超伝導状態となる元素

He

良導体の銅, 銀, 金は超伝導状態に転移しない.

Li

Be

B

C

N

O

F

Ne

Na

Mg

Al

Si

P

S

Cl

Ar

K

Ca

Sc

Ti

V

Cr

Mn

Fe

Co

Ni

Cu

Zn

Ga

Ge

As

Se

Br

Kr

Rb

Sr

Y

Zr

Nb

Mo

Tc

Ru

Rh

Pd

Ag

Cd

In

Sn

Sb

Te

I

Xe

Cs

Ba

La

Hf

Ta

W

Re

Os

Ir

Pt

Au

Hg

Tl

Pb

Bi

Po

At

Rn

Fr

Ra

Ac

La

Ce

Pr

Nd

Pm

Sm

Eu

Gd

Tb

Dy

Ho

Er

Tm

Yb

Lu

Ac

Th

Pa

U

Np

Pu

Am

Cm

Bk

Cf

Es

Fm

Md

No

Lr

1

参照: 超伝導・低温工学ハンドブック
超伝導 / 家康弘

臨界磁場と臨界温度

臨界温度 Tc (K)臨界磁場 Bc (T)

第I種

第II種

100

100

10

10

1

1

Tc
Bc

0.1

0.1

0.01

0.01

0.001

0.001
Nb3Al

Ti

Al

Hg

Sn

Pb

Nb

NbTi

Nb3Sn

参照: 超伝導・低温工学ハンドブック

本

1960
1970
1980
1990

発

2000
2010

超伝導の発見は量子論の黎明期であり，発現機構(BCS理論)の解明に46年を要した.
EK
B,

K

er

K
EK

本

(日

)

1940

Su
p

見
系
(秋
LH 超電
光
C 導
)
,C 体
ER の
N 発
(欧 見
州 (細
) 野
)

1930

鉄

1920

2 の

1910

K
E
RH KB
,
第 IC KE,
II B K
種 NL (日
超 ( 本
伝米 )
導国
体)
:M
gB

)

1900

銅
A 酸
B 化
Te 効 物va 果 高tr の実 温超on,F 証 伝er (外 導m 村 体ila ) のb /ト 発(米 リ 見
H
ER
国 ス
A
) タ
,D
ン
ES
,K
Y
EK
(独
(日
)

自
発
Jo 的
s
第 ep 対II hs 称性
種 o の
SQ 超 n 効 破U 伝導 果の れID
体 予 (南:N 言 部
の
発
)
bT
明
i
/電 の
弱 出現
統
一
理
論

見
電
磁

言

力
G
学
in
の
zb
確
ur
立
gLa
Pi
p
nd
第 par
au
II d 方
理
種 程
論
超 式
伝
導
BC
体
S
:N
理
b
論
A
3S
ha
n
ro
の
no
出
v現
Bo
hm
(A
B)
効
果
の
予

量
子

Pa
u
H li のe
Sc isen 排他
hr b 原öd erg 理
in ら
ge に
rの よ
波 る行
動 列
方 力
程 学
式
M
ei
ss
ne
第
rO
II
ch
種
se
Lo 超
nd 伝導 nfeon
体 ld 効
の
方
果
発
程
の
見
式
発
の
見
提
唱
,超
流
動
の
発

よ
O
る
nn
ヘ
リ
es
ウ
Bo に
ム
よ
hr
の
る
液
の
超
化
原
伝
子
導
模
型 の発
見

に

O
nn
es

則

法

の

k

nc

Pl
a

超伝導科学技術年表

1950
1960

2020

超伝導体と完全導体

Perfect conductor

完全伝導体 (ρ=0)

T > Tc
H=0

T > TcH≠0(a) Tc以上の温度で外部磁場ゼロ
T ≤ Tc
H=0

1. Tc 以下まで冷却
2. 外部磁場を印加. レンツの法則により

T ≤ TcH≠0

導体内の磁場はゼロに保持
3. 外部磁場をゼロに
4. 導体内の磁場もゼロに

T ≤ TcH≠0j(b)Tc以上の温度で磁場を印加
1. Tc 以下まで冷却T ≤ TcH=02. 磁場をゼロに.

jT ≤ Tc
H=0

3. レンツの法則により導体内の磁場は有限値に保持.

(a)(b)

最初に磁場を印加するかどうかによって導体内の状態が異なるPerfect conductor
超伝導体(ρ=0)

Superconductor(i)

T > Tc
H=0

T > TcH≠0

T > Tc
H=0

T ≤ Tc2. 磁場を印加．
マイスナー効果により
H=0

T ≤ TcH=0(c) Tc以上の温度で磁場ゼロ

T > TcH≠0

1. Tc 以下まで冷却(ii)

導体内の磁場はゼロ.
T ≤ TcH≠03. 磁場をゼロに
4. 導体内の磁場もゼロに(d)jT ≤ TcTc以上の温度で磁場を印加
H≠0
j

j

T ≤ TcH≠0

T ≤ TcH≠0

1. Tc 以下まで冷却
2. 磁場をゼロに(iii)

T ≤ TcT ≤ Tc3. マイスナー効果により導体内の磁場
H=0

はゼロ.

j

T ≤ Tc
H=0

H=04. 導体内の磁場もゼロに
(a)

(b)

(c)

T ≤ TcH=0(d)

London方程式

London 方程式 I
電場 E 内での超伝導電子のNewton の運動方程式 (摩擦無し)<latexit sha1_base64="Y+HQ1/UuSg9wU/zzZKVpqPjnciI=">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</latexit>

m

加速器の電子の運動と同じ

vS
⇤ @~
@t

⇤~

=e E

m* : 超伝導電子の質量vs : 超伝導電子の速度
e* : 超伝導電子の電荷

超伝導電子電流密度: js~js = e nS~vS<latexit sha1_base64="VPOpdg9fcqWKm9htr88yBUY1e1Y=">AAAGcHicnVRLb9NAEJ4WGkp4tIULEgcMFRKqSjOpKkBIoIoixAFEKvpCTSmOs0ndOLaxN1GiqBzgwAG48Bv4NVzhwj/gCr+AbycOfYQ4qF7Znv32m8fOzG4p9NxYM/8YGT1xcixzavx09szZc+cnJqcurMVBI3LUqhN4QbRRsmPlub5a1a721EYYKbte8tR6qbZk1tebKordwF/R7VBt1e2q71Zcx9aAtifvW8WnheZubN2z1MuiHWvL3y7qln5uFZv2TKe5150VPbukvI56fbesKnEjVJHTiKK97PbkNM+xPFa/kE+EaUqeQjA1+omKVKaAHGpQnRT5pCF7ZFOMsUl5YgqBbVEHWATJlXVFe5SFbgMsBYYNtIZvFbPNBPUxNzZj0XbgxcMbQdOi6wmnDLkiaPdv/FsHuFkw/+2lI9ZNlG38S4nVOlBNO0CHa/a4/6+5SU3JQlV2pKn1N+ZY8jHYY896iNHL3mB2eCzLGnIrpS4deK7DahlyBNtpTAfjYAQmQ9YR1OLPy4o/8gfe4RHMXeCzSfVifsXLvMHveJef8Qtuc4X9t7/Ue35CS2LBQQwKdhTXwHGwvs5v+BH7XPV+2hMp3aWAe7KHm9iLC9SVeExN9tea2Gtaj66gt41Gbz9KYkrLieG05HwEsB0OOQEalu+IB5OXUJDhPg535mxfjw/WDMFvSxWcoT3Tn6XBHZ++k/2TXBGbFtYC+bbBVJBMhUylHWAe0C5iS/3d5D4xPbMjJ8sWnoksTtlrjlYFN6yc6LnS2cZ3jh4euc8Mpyy2K5jlaB6DaQHdE8Cr0ahLtAd9ICe4TfNH785+YW1+Ln9rbmF5YXrxQXKvjtNlukY30F+3aZEeUwHROvSFvtI3+j72O3MpcyVztUsdHUl0LtKhJzPzBzDSVzE=</latexit>⇤

ns : 超伝導電子の数密度<latexit sha1_base64="Hsm7lrbOnBhfQLRuWb0+zEJy8dA=">AAAGr3icnVRLb9NAEJ4UCG149HXkYlFRIVSaTVUBQkKqKCAORbSibYpq2m42m3Rbv2o7ViLLHODAAbjw7zhz4co/4NuNQx8hCcKrOONvv/lmdnZ2a4Gjopix74WxS5evFK+OT5SuXb9xc3JqemY78luhkFvCd/xwp8Yj6ShPbsUqduROEEru1hxZrR2v6vlqIsNI+d5m3AnkO5c3PdVQgseA9qcyyw7qSWq/Wk+OoiyNM2v+ScmyGyEXaSVL7TVI1XlmJ/xe+jyzHV6TTipPHnMhpCNDo5It2DZ8ulRr3pYnLZXkGu6ezaM4S719O27Hbyy5l2rAWsqsrFTan5pji8w8Vr9RyY05yp91f3rsK9lUJ58EtcglSR7FsB3iFGHsUoUYBcDeUQoshKXMvKSMSvBtgSXB4ECP8W7iazdHPXxrzch4C0Rx8AvhadGdnFOH3TBo91/Ht85wS2D+PUpq1HWWHfzXclUXaEyHQEd79rj/7rlLialC06wopvafnCNTj8ERe+oBRq96g9nBfynHsNtD9iVFZBeqddghtIcxBcbZDHSFrAuoxb5tSPaFfWaHrIBvBXwh372IHbANtsM+siP2mr1lHdZg3odf8hNbo1WjIJCDhI5kx+AIzFfZe/aCeazp/OSTQ7pLAnfMGu5jLQqoMvnoPTmdS7DWYT26id7WHr31SJPTsJpoTtucDx/awYgTEEP5kYmg6xIYZHSM85250Nfjgz0D8DtmF8TInumv0uCOH76S05PcMJoW5nzz7oApYekd0jstgDlAuwg3+6/y+0T3zKE5WdzwdGbRkLWWacvgmlU2fsp0to5dpmcX7jPNqRvtBr7KtITBaBnd4yOq9nBNtmdjoCa4TSsX785+Y3tpsfJgcXljeW7laX6vjtMtuk130V8PaYVe0jqyFfSjMFGYKcwWK8Vqca940KWOFXKfWTr3FNVvSA1sDg==</latexit>

@~js
1~
= E,
@t
⇤
⇤
m
⇤⌘
nS e⇤2加速方程式と呼ぶ

London 方程式 II~r⇥<latexit sha1_base64="PuFH1njoiQpwfhyihTykpdIM7VA=">AAAGQ3icnVRLbxJRFD5U0YqPgi7dEImJMRUODVGXjTXGhYltUkoNNHUYLjAyr8xMEULqQhcu1I17t/pL/BH+AxNXGrcmfvd0sBRkMM7NzJz73e887jnn3qZvW2HE/CW1dOp0+szZ5XOZ8xcuXlrJ5i7vhN5BYKqq6dlesNs0QmVbrqpGVmSrXT9QhtO0Va3Z29Drtb4KQstzt6Ohr/Yco+Nabcs0IkD72Vyjb9wcNTqB0TpsmIEXhvvZAhdZnvysUI6FAsXPppdbekcNapFHJh2QQ4pciiDbZFCIUacyMfnA9mgELIBkybqiQ8pA9wAsBYYBtIdvB7N6jLqYa5uhaJvwYuMNoJmn6zGnBbkt6NFf+89PcDNg/t3LSKzrKIf4N2OrDtCIukAXa465/65Zp75koSM7imjwJ+ZQ8jHf49i6jzHO3ny2/1+WI8iDhLqM4NmB1RbkALaTmCbGZAQ6Q/kpNM/vtxS/5Tfc5RTmFvDVuHohP+Ut3uVX/Iwf8xMecpvdl9/Va35EG2LBRAwKdhT3wDGxXuMX/IBd7thfjZWE7lLAbdnDLezFAmpJPLomx2t97DWpR7fR21pjvB8lMSXlRHMGcj482PYXnIAIlu+KB50XX5DFPk525upMj8/X9MEfShXMhT0zm6X5HZ+8k+OT3Babeax58h2CqSDpCulKm8BsoEeIIfW34vtE90xXTpYhPB1ZmLDXElUF16yS6FnS2dp3ie5P3Wea0xLbbcxKtIbBVEH3ePCqNRyJdtIHcoLbtDx9d84KO2vF8u1iZatSWL8X36vLdJWu0Q301x1ap4e0iWhNek4f6CN9Sn9Of0v/SP88oi6lYp0rdOJJ//oNBwRJEw==</latexit><latexit sha1_base64="Hsm7lrbOnBhfQLRuWb0+zEJy8dA=">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</latexit>

@~js
1~
= E,
@t
⇤
m⇤
⇤⌘
nS e⇤2

Maxwell 方程式

~js
@
1
~ ⇥
~ ⇥ ~Er= r@t⇤<latexit sha1_base64="3uOzIJBvqc/ddgM1KlyaPmeMVJo=">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</latexit>~@B~ ⇥ ~E = r@t<latexit sha1_base64="xds0yBUCtGXh4eaDKaIQxO+CRBU=">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</latexit>の右辺を上式の右辺に代入

~js
~
@
1
@
B
~ ⇥
r
=@t
⇤ @t
<latexit sha1_base64="CgUUVkaox0aDtxY5X0s+fBgmgM0=">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</latexit><latexit sha1_base64="xaZ1nzJUb1q/PBhkY2TkA/jov2c=">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</latexit>

⇣
@

@t

⌘

~ =0
~ ⇥ ~js + B⇤r

ここまでは古典電磁気学の範囲

London 方程式 III<latexit sha1_base64="xaZ1nzJUb1q/PBhkY2TkA/jov2c=">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</latexit>

⇣
@

@t

⌘

~ =0
~ ⇥ ~js + B⇤r

ここでLondon 兄弟はマイスナー効果が表われるために,( )内の定数を0とおいた.

~ = ~0,~ ⇥ ~js + B⇤r<latexit sha1_base64="wWKlcWqbzz2cGwCLZX2pzpvhG7U=">AAAGenicnVRLb9NAEJ4WGkp4tIUjF6sVCGhJJlUECAmpahHqoYhW6gvVVXHsTerWL2w3ahSFAxw4ABd+CL+GCwc4c+XOgW+nDn2EOAivbM9++81jZ2a3FnlukjJ/HRo+d36kcGH0YvHS5StXx8Ynrq0n4UFsqzU79MJ4s2YlynMDtZa6qac2o1hZfs1TG7X9Bb2+0VRx4obBatqK1LZvNQK37tpWCmhnfNEwl8B2LLNp3W2bjdhyOmbq+ioxzGfLzb2kOC0r8x3DuPXYEJk7pmfVlNdWrx55YeCEQWemuDM+xSWWx+gVKpkwRdmzHE4MfySTHArJpgPySVFAKWSPLEowtqhCTBGwbWoDiyG5sq6oQ0XoHoClwLCA7uPbwGwrQwPMtc1EtG148fDG0DToZsZxINcFPfpr/8YJbhHMv3tpi3UdZQv/WmbVB5rSLtDBml3uv2tuUVOy0JAdpXT4J+ZE8tHfY9d6hNHNXn929F+WU8iHOXVpw7MPqw7kGLbzmDbGyQh0howzqMGfVhR/4Pe8y0OYu8Bnsuol/JJXeJPf8h4/5xfc4joHb36qd7xEC2LBRgwKdhTvg2NjfYNf81MOuOH9sMZyuksB92QP97AXF6gr8eiaHK81sde8Hl1Fb2uN7n6UxJSXE805lPMRwnY04ASksPxQPOi8RIIM9nG6M2d6ery/ZgR+S6pgD+yZ3iz17/j8nRyf5LrYNLAWyrcFpoKkK6QrbQPzgB4hltTfze4T3TO7crIs4enIkpy9lmlNcM0qi54rna19l+nJmftMcxyxXcesTLMYTFV0TwivWsOXaE/6QE5wm1bO3p29wvpsqXK/VF2pTs3NZ/fqKN2gSbqN/npAc7RIy4jWps/0hb7R95FfhcnCncL0EXV4KNO5TqeeQvU3U3tZlg==</latexit>

London 方程式

Londonの磁場侵入深さ 1
Maxwell方程式~ = µ0~js~ ⇥Br

London方程式~ = ~0,~ ⇥ ~js + B⇤r<latexit sha1_base64="p6ECItM1UhDCqnt6u5+FETJsRZo=">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</latexit><latexit sha1_base64="wWKlcWqbzz2cGwCLZX2pzpvhG7U=">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</latexit>~を消去~ ⇥ ~js + B⇤r= ~0,<latexit sha1_base64="wWKlcWqbzz2cGwCLZX2pzpvhG7U=">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</latexit><latexit sha1_base64="nIse3nPUVDF6HJKsgD+jQVPFW+s=">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</latexit>

1 ~ ~r B- 2B=02~<latexit sha1_base64="qGkPttA037VQ9CRSMMZG9T9NiE8=">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</latexit>

s

L

r

m⇤
L ⌘
µ0 nS e⇤2
r
⇤
m⇤
⌘
=
L :Londonの侵入深さµ0µ0 nS e⇤2<latexit sha1_base64="qGkPttA037VQ9CRSMMZG9T9NiE8=">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</latexit>

⇤
=
µ0 s

Londonの磁場侵入深さ 2

Vacuum<latexit sha1_base64="A+JMiH228jbF5kIlPmhPSQmWuZc=">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</latexit>2

By (x)
1
B
(x)
=
0
y
2
x2
L

y

Superconductor

B0
x

0

B=0
<latexit sha1_base64="L91KPijgrw87IU7yZ8iw7QJbi5w=">AAAGaXicnVRLb9NAEJ4WGkp4tIULgotFhMShNJOqPC6VqhQhDki0Ul+oQcVx1slSx3Ztt8SKygEOHEAcuPJruMIv4B8gceIf8O3UoWlDHIRXtme//eaxM7NbDz0dJ8zfx8bPnJ0onJs8X7xw8dLlqemZKxtxsB85at0JvCDaqtux8rSv1hOdeGorjJTdrntqs767bNY3D1QU68BfS9JQPW/bTV+72rETQDvTd6uLbNX29rpuEB1anVqkm63EjqLglVXTvpuktVqxuljdSftIi7wzXeI5lscaFCqZUKLsWQlmxj9SjRoUkEP71CZFPiWQPbIpxtimCjGFwJ5TF1gEScu6okMqQncfLAWGDXQX3yZm2xnqY25sxqLtwIuHN4KmRbcyTgOyK+jR3/i3+rhFMP/upSvWTZQp/vXMahtoQi2gozV73H/X3KYDyUJTdpRQ50/MseRjuMee9RCjl73h7PC/LCeQOzl16cJzG1YbkCPYzrfrYPTHYHJknUIt/rSq+AO/5xaPYa6Bz2b1i/kFr/IWv+WX/JSfccou+29+qXf8hJbFgoMoFOwo3gXHwfomv+ZH7HPT+2FP5fSXAu7JLu5gNxqolnhMVY7XDrDbvC5dQ3cbjd5+lMSUlz/D6cgJCWA7HHEGElh+IB5MXkJBRvs42ZuzA10+XDMEP5UqOCO7ZjBLw3s+fyfHZ9kVmxbWAvmmYCpIpkKm0g4wD+gRYkv9dXajmJ5pydmyhWcii3P2WqZ1wQ2rLHpaetv4LtPDUzea4TTEtotZmeYxmBbQPQG8Go22RNvvAznBfVo5fXsOChvzc5V7cwurC6WlanazTtINukm30V/3aYke0wqidegzfaGv9G3iZ2GmcK1w/Yg6PpbpXKUTT6H0G52AUwY=</latexit>

B = By<latexit sha1_base64="PZrWF5QksLKPIeqH5z1iEGCj4lE=">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</latexit>

By (x) = B0

for x ! 1

for x = 0✓◆x
L

λL ~ 20—50 nm

マイスナー効果

B0

By(x)VacuumSuperconductor

B0 e–10λLx電流密度 j も同じ分布になる

円柱超伝導体の遮蔽電流
外部電流なし外部電流あり外部磁場あり外部磁場なしjBjj
超伝導体の表面のみを遮蔽電流は流れる<latexit sha1_base64="jD0Kj6HvXdPyUYhBiSUUIy3XaHg=">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</latexit>

電流の流れる面積が狭いので全電流は低い.

Js =

Z

S

jc (~r)d~r

Pippard方程式

Pippard方程式• Pippardが電子の平均自由行程を変化させると, 侵入深さ λLがある濃度から増大12することを発見- 電子の平均自由行程には依存しない<latexit sha1_base64="qC+UyZObWxe4zIf15IfN+1s39pc=">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</latexit>

p

1/ns
L /
✓
◆4
T
ns = 1 Tc

10^6 λ (cm)- 超伝導電子密度のみに依存

侵入深さ• London理論<latexit sha1_base64="XXsEWFE+OO49zb+dNGtSzHXFMW0=">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</latexit>

Pippardの測定

10

8

6

London理論

4
0

20

40

60

80

10^6 l (cm)

電子の平均自由行程
A. B. Pippard and W. L. Bragg, Procs of the Roy. Soc. of Lond. Ser. A.
Math. and Phys. Scienc. 216, 547 (1953).

Pippardの実験条件ではほぼ一定

Pippard方程式• 超伝導電子がξ0の範囲のベクトルポテンシャルの影響を受けるとして,ロンドン方程式を書き換えた.
<latexit sha1_base64="QIiZCyRvbYYLHqcl+F8nWGK8wdg=">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</latexit>1~js (~r, t) = - A(
~ ~r, t)⇤<latexit sha1_base64="oPc2bbd0P28WbGpPcUSFMu1KQis=">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</latexit>3~js (~r) = 4⇡⇠0 ⇤~⇢ = r~0 - ~r<latexit sha1_base64="J8hyJhtDGYCaNoVu51nkVMmbiDA=">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</latexit>⇠0<latexit sha1_base64="OH+hpWCYl8s2FcOO8Wnn11CwRZE=">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</latexit>Z✓◆~ r ))~⇢(~⇢ · A(
⇢
3 ~0
exp
d
r
⇢4
⇠0
~0

: コヒーレンス長電子が広がりを持っている.

Pippard方程式• 不純物がある場合<latexit sha1_base64="4P9GZfW9vrEu7daFjMN+d8/cP10=">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</latexit>

1
1
1
1
! =
+
⇠0
⇠
⇠0 ↵l

l :平均自由行程
α: ~1 の数因子

• Vector potential A が ξ の範囲では一定とした場合のPippard 方程式<latexit sha1_base64="Y8dU+r8xJslw6Y0jjtIlVenssQ4=">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</latexit>~js (~r) = <latexit sha1_base64="rTV25GVfU1Zhcnb4HGj5O58qL4Y=">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</latexit>

⌘
=

1
µ0
r

L

L

r

~ ~r)
A(
2

⇠0
⇠

⇠0
1+
↵l

l が短くなるとλは増える
実験結果をよく説明している

超伝導の熱力学熱力学: 相• 相 : 互いに明確に区別できる巨視的な状態- 一組の状態変数で一義的に決定される* 水の場合: 1気圧で0度以下に冷やすと液相(液体)→固相(固体)に変化* 超伝導体の場合: 臨界磁場以下で高温(i)から臨界温度以下(ii)に冷やすと常伝導相から超伝導相に変化

B
Bc(T)

Bc(0)

(ii)

onducting
phase
超伝導相
(iii)

Normal conducting phase
常伝導相
臨界磁場のパラボリック則"(i)✓ ◆2 #T
Hc (T ) = Hc (0) 1 Tc
<latexit sha1_base64="E8va1X6QnPTICoApTGsU8khXMdk=">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</latexit>

Tc

T熱力学エネルギー I
Helmholtz自由エネルギー

F = U - TS
dF = dU - T dS
<latexit sha1_base64="3vqbsFilSB+Gs00O65kf/+58acw=">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</latexit><latexit sha1_base64="zeIIXuS1SxfVpFI1ETLVi5Gz3fU=">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</latexit>= Q + W - SdT - T dS
= W - SdT<latexit sha1_base64="k810OHWOfuAOBC2bWJHzmunhEqg=">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</latexit>

磁場による仕事~ · dM~W = µ0 H~ · dM~ - SdT
dF = µ0 H<latexit sha1_base64="c6uMrFqnYg3CZ722s0NL9rRAuCo=">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</latexit>~ ·M
G = F - µ0 H
~ · dH~ - SdT
dG = -µ0 M<latexit sha1_base64="Z6ME50Ulw+RRj2+WckesMskAXjY=">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</latexit>

Gibbs自由エネルギー

熱力学エネルギー II
Gibbs 自由エネルギー: 等温過程の時~ · dH~dG = -µ0 M<latexit sha1_base64="CzImMNk4bUFoAkcAh9dKyUPyUiI=">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</latexit>

常伝導体<latexit sha1_base64="NBw1zaqOWedSOoY27k2C6QDxNj8=">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</latexit>

Gn (H) = Gn (0)超伝導体~ = -H~M<latexit sha1_base64="7Z65YvsnqDhQfMk5lyMtFbTMoYU=">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</latexit>

より,

µ0
2
dGs = µ0 M(H) dH =d H
2<latexit sha1_base64="EwEafD9Fz0Fumm/4FM0dl+It49Y=">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</latexit>µ0 2
Gs (H) = Gs (0) +H
2<latexit sha1_base64="yJgRTTAC2V44B4TYrsYTJ7kjFTg=">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</latexit>

熱力学エネルギー III
Gibbs自由エネルギーの超伝導体と常伝導体の関係

F

FN N

µ0 2
Hc = Gn - Gs (0)2凝縮エネルギー
超伝導相ではマイスナー効果により磁場が排除された分だけ– 0.2

Free energy (mJ/mol)<latexit sha1_base64="LUCK5Q29mauM4P+HRYo52xvdNfA=">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</latexit>

– 0.1

FF S

– 0.3

NormalS– 0.4

Superconductor

– 0.5
– 0.6
– 0.7

Tc = 1.180 K

– 0.8
– 0.9
– 1.0
– 1.1
– 1.2
0

0.5

1.0

1.5

温度 (K)

Temperature (K)g

Gn = Gs (Hc )自由エネルギー

0<latexit sha1_base64="Gm2jogRnhIz15Jim0+AlWaysPfM=">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</latexit>

C. Kittel, Introduction to solid statephysics ( J.Wil. &Sons, Inc)

Bc2
2µ0

{

エネルギーは低い

gnormalgsuper

自由エネルギーが低い相が発現する(右図実線)

00Bc

B比熱のとび I<latexit sha1_base64="LUCK5Q29mauM4P+HRYo52xvdNfA=">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</latexit>µ0 2
Hc = Gn - Gs (0)2Tの関数であることを示す.

<latexit sha1_base64="9wHr1n27mduD9F//qsm/jcWyNps=">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</latexit>µ0 2
Hc (T ) = Gn (T ) - Gs (0, T )2
Tで微分<latexit sha1_base64="PlbFmQHbNZsChkpSix76pJ3YoVk=">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</latexit>

✓

@gs
@T

◆

✓
◆
2
@gn
µ0 dHc (T )
=+
@T
2
dT

dHc (T )Ssup - Snorm = µ0 Hc (T )dT<latexit sha1_base64="Tp5UXlzb2F71UdUIyMwxA+8bE2A=">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</latexit>

エントロピー

比熱のとび II
臨界磁場のパラボリック則を代入✓◆"

dHc (T )dT◆2<latexit sha1_base64="awAkEVpFSHxYjqLf+jrHE4+/kFs=">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</latexit>

2µ0 H2c (0) T
Ssup - Snorm = Tc
Tc
@S
比熱は CV = T@T<latexit sha1_base64="HKs+qYjGcXjpFLwExMOYTcoxKN4=">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</latexit>

1-

✓

T
Tc

◆2 #

なので

<latexit sha1_base64="vx96ht5K6/7Aa1y7782+Jmu9YS4=">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</latexit>

sup
norm
CV (T ) - CV (T ) = µ0 T"✓

d2 Hc (T )+ Hc (T )dT 2が得られる.
2
H
sup
c (0)
norm
CV (Tc ) - CV (Tc ) ⌘ CV (Tc ) = 4µ0
Tc<latexit sha1_base64="YZ8FARpE62vdzN7wVZRlgVuvaYg=">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</latexit>

Rutgersの関係式#

比熱のとび III<latexit sha1_base64="YZ8FARpE62vdzN7wVZRlgVuvaYg=">AAAHXHicnVRbaxNBFD6ptampta2CD/qyGIUW2mZSgoogFFPFB8EWepNsGzeTSbJ2b91LbFjigz74oPjgvxPBZ18Ff4DfTDc2F7Mt7rKzZ775znfOnLnUPMsMQsa+ZSYuTV6eyk5fyc1cnb02N79wfTdwI5+LHe5arr9fMwJhmY7YCc3QEvueLwy7Zom92lFZju+1hR+YrrMddjxxYBtNx2yY3AgBVee/aOXDWA/FSRgHkdftVncX0bM9/vRYW9JWzkYd17eHh3VxHJltTd8QVmho5YHBnPa4pNtRlekN3+Cx3uLa4doiW+rGPU5Xt4yasGJx/MiPwiaS7Oaq83m2ytSjjRrFxMhT8my6CxPfSac6ucQpIpsEORTCtsigAG+FisTIA3ZAMTAflqnGBXUpB98ILAGGAfQIbRO9SoI66EvNQHlzRLHw+fDU6F7CqcNuKPT0L+NrfdwcmP+OEit1mWUH/1qiagMNqQX0fM8e9+KeFWqrKjTVjEI6+ZtzoOoxPmJP3cPbq954tvdfyiHsk5R1iRHZhmodtg/tdF2Otz8HWSNtCNXY1y3BPrNPrMUy6JvAl5P1C9hrtsX22Qf2hr1kr1iHNZjz/pf4yF5QWSlwZCGgI9gROBzje+wde8Yc1rR+GnOp2Tlo36o6wV+1y/hHqra+wtPqMOqdXouLKlf6mCuoswnUVJU6GFBpYx3SVLZx7qRHr9JCVSttRr15yMrbGE0/nSGUH6oIcsU8hZwfY/DULI+cv/GeHvgdtT/4uft5tErjT2P6TM5umYbS1DDmqrYDpoAlV0juQQ7MAnqKGGpnmsldJ3dzS516Q/FkZkHKXAu0o3DJKig/U506GbtAG0N3reTUlXYDvQKt4WVUwu5xEVV62Crb/hioCW764vC9Pmrsrq0W76+Wtkr59SfJnT9Nt+kOLWJ/PaB1ek6byJbT78ytTD5zd+pHdjI7k509pU5kEp8bNPBkb/4Bt/2QMg==</latexit>

sup
norm
CV (Tc ) - CV (Tc ) ⌘CV (Tc ) = 4µ0

2
Hc (0)

Tc
Rutgersの関係式

Cv

引用: 丹羽雅昭, 超伝導の基礎, 東京電機大学出版

Tc
常伝導相

T
超伝導相 比熱が不連続に

μ0M

第II種超伝導体

(a)
Hc
H

• 第I種

第I種

- 臨界磁場, 電流が低い.

* 磁石の電線としては実用的ではない.

• 第II種- 高い臨界磁場(b)μ 0M- 鉛, 水銀 等の純金属

Meissner phase
Hc1

Hc2
H

* 0< H< Hc1 : 完全遮蔽

第II種

* Hc1 < H < Hc2 ：混合状態- 高磁場磁石に適用可能- NbTi, Nb3Sn, ニオブ 等

Meissner
phase

Mixed phase第II種超伝導体における混合状態• 局所的に磁場の侵入を許す.
• フラクソイドが形成される.
Magnetic eld

Fluxoid

Super vortex
current
Field free
regionfi(詳細は鈴木氏による次の講義「超伝導磁石の基礎」を参照)

Ginzburg Landau理論

Ginzburg Landau 理論 I
• 秩序パラメーター: 強磁性体の場合は磁化 M となる.
強磁性体スピンの向き秩序が無い : M=0
T > Tc

秩序が有る : M≠0 ：対称性の破れ
T=0<latexit sha1_base64="1W7PQu+c+c4RCkHVpvCdDQyaGQU=">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</latexit>

自由エネルギー ：2

F(M, T ) = F(0, T ) + ↵M +

2

M

4

Ginzburg Landau 理論 II
1

α=0

0.5

α<0

F

F (M,T)

α>0

00
平衡状態
−0.5
0

平衡状態
0.5

<latexit sha1_base64="1W7PQu+c+c4RCkHVpvCdDQyaGQU=">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</latexit>

M

1

1.5

M

F(M, T ) = F(0, T ) + ↵M2 +2M4

α → α (T-Tc)<latexit sha1_base64="NXwHSQfmGQy6363B3we0OacAdf8=">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</latexit>

F(M, T ) = F(0, T ) + ↵✏M2 +✏ = (T - Tc )/Tc

2

M4

Ginzburg Landau 理論 II• Ginzburg-Landau理論- 超伝導の秩序パラメーターを波動関数(疑似波動関数)とした.
2<latexit sha1_base64="+ipdZoDtMT7bFRaX5OUTQxkJCtc=">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</latexit>

4

Fs = Fn + ↵✏| | + | |✏ = (T - Tc )/Tc
1

T = Tc0.5

T < TcF

F (T, ψ)T > Tc00<latexit sha1_base64="5quDYu4bucxV5U4fDQjkhQZrMYI=">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</latexit>−0.5
00.5 |ψ0||ψ|1

1.5 | 0 | =

s

↵
2

✓

T - TcTc◆

Ginzburg Landau 理論 III• GL展開 : 運動エネルギーの項と磁場エネルギーの項を付け加える
2
4~~
fs =fn + ↵✏| (r)| + | (r)|
⇣
⌘
2
2
1
1
~ ~r) (~r) +~ ~r)~ - e⇤ A(~ ⇥ A(
+
-i
h
r
r
2m⇤
2µ0
<latexit sha1_base64="plmPhvJ6ZtwYklpaXXnNDMwJMuI=">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</latexit>

運動エネルギー

磁場エネルギー• GL展開の空間積分し, 自由エネルギーの最小値を求めるため, 変分をとる<latexit sha1_base64="Wef5+LQ4ZXbnzYQ+b+FaVkcUF98=">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</latexit>

Fs =

Z "

2

↵✏ | | +

4

| |

V

1
+
2m⇤

⇣
⌘
⇤~
~
-ihr - e A

2

#

~ 2
~ ⇥ A||r+d~r = 02µ0Ginzburg Landau 理論 IV• 変分法によって得られる方程式 :Ginzburg-Landau方程式

⌘2
1 ⇣
2
⇤~
~
~
~
~
~
-ihr - e A(r)(r) + 2 (r)| (r)| (~r) = -↵✏ (~r)
⇤
2m
i e⇤2
⇤ h
e
2~
⇤
~js (~r) = -ih~ (~r)) - (r~ ⇤ (~r)) (~r) ~
~
|
(
r
)(
r
(
r
)|
A(~r)
⇤
⇤
2m
m
<latexit sha1_base64="o1EfmVSMqyw6fC2ZxpGtDBWRW0g=">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</latexit><latexit sha1_base64="QGHnfFq7WroKusldpkNIp05rEDo=">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</latexit><latexit sha1_base64="5quDYu4bucxV5U4fDQjkhQZrMYI=">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</latexit>

|

0| =

<latexit sha1_base64="KgSBLeBKkhVnqNpqh67WcEI0/jM=">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</latexit>

s

↵
2

✓

T - TcTc⇤2◆~js (~r) = e ↵
m⇤ 2

✓

◆

T - Tc ~A(~r)
TcGinzburg Landau 理論 V
<latexit sha1_base64="Y8dU+r8xJslw6Y0jjtIlVenssQ4=">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</latexit>

1

Pippard方程式から得られる式~js (~r) = -GL理論から得られる式⇤2e↵~js (~r) =
m⇤ 2

µ0

~ ~r)
A(
2

<latexit sha1_base64="KgSBLeBKkhVnqNpqh67WcEI0/jM=">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</latexit>

侵入深さ<latexit sha1_base64="kkiG6cYD7Fco2l4cZeHbT8TDIBs=">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</latexit>(T ) =

s

✓
◆
1/2
⇤
2 m
Tc
↵e⇤2 µ0 Tc - T

侵入深さは温度の関数
Tcで発散

✓

◆

T - Tc ~A(~r)
TcGinzburg Landau 理論 VI
秩序パラメーターの書換え:<latexit sha1_base64="fU0peqs9ZCzk+T45UrGaIDA37Sc=">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</latexit>(~r) = | (~r)| exp(i'(~r)),⇤(~r) = | (~r)| exp(-i'(~r)),1次元のGL方程式:
Vacuum<latexit sha1_base64="PY0Md9xSeq3B8W24D5kXEMi/oPo=">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</latexit>22

h @ (x)+ ↵✏ (x) + 2
⇤
2
2m @x

3

規格化秩序パラメーターの導入
s
(x)
2
0
(x) =
=
(x)
↵(-✏)
0
<latexit sha1_base64="TUom8fhRoVyoAYo2yVOexvSoMYE=">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</latexit>

Superconductor(x) = 0(x) = | (x)| とした (位相の項を無視)<latexit sha1_base64="CUixF4t43TxnxfWEI6TCpLmP+qM=">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</latexit>

y

B0
0

x

Ginzburg Landau 理論 VII
1次元のGL方程式 (規格化秩序パラメーター):<latexit sha1_base64="wSAEdJm5rRqGuj1KnD4fm+SNtZk=">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</latexit>

d2 0 (x)1= 2
2dx⇠ (T )<latexit sha1_base64="RdJy1MEKgxeFfAUvX8m5lbXVtjQ=">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</latexit>⇠(T ) ⌘

境界条件:

<latexit sha1_base64="phGtVzOapNhvKVBCa25A/BHFMTY=">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</latexit>

d

0

s

(x) ✓

h2

0

h
Tc
=p
⇤
2m ↵(-✏)
2m⇤ ↵ Tc - T

x ! 1,<latexit sha1_base64="RQK+GopFAQd10QIsgJ9DHSC+WFY=">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</latexit>/dx = 0,0,=1

解 (規格化秩序パラメーター) :<latexit sha1_base64="Oclgvz9UWfs5TiU8CQ5x/HPWaxY=">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</latexit>

(x)
◆1/2

x = 0,
0<latexit sha1_base64="3Bo7JxwQKYXGcoWfYLCQ/8JCUbs=">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</latexit>

解:

03

=0

✓
◆
x
0
(x) = tanh p
2⇠(T )
s
✓
◆
↵(-✏)
x
0
(x) = 0 (x) =tanh p2
2⇠(T )

Ginzburg Landau 理論 VIII
1

GLパラメーター
⇤

✓

(T )
m
2
=
= ⇤
⇠(T )
e h µ0◆1/2

ξ(T): コヒーレンス長, 回復距離

ψ' (x)<latexit sha1_base64="MJYZB1WXtv2scUFW7qZ1ZGmO1A4=">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</latexit>

ロンドン方程式

00⇤2<latexit sha1_base64="aB9YYwMEoqd/HcPsWWjy59eZgaA=">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</latexit>~js (~r) = - ns e A(
~ ~r)
m⇤
GL方程式
~ =r
~
r
<latexit sha1_base64="cf5kzKcDQdPAa7INfDuhKcMSE20=">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</latexit>

⇤

= 0,

for x

<latexit sha1_base64="3Bo7JxwQKYXGcoWfYLCQ/8JCUbs=">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</latexit>

⇠(T )

⇤2
e
2~
~js (~r) = ~
~
|
(
r
)|
A(
r
)
m⇤

<latexit sha1_base64="gSObodMBc3Jwouuat+w5bUe24HI=">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</latexit>

⇤2

ξ (T)

✓
◆
x
0
(x) = tanh p
2⇠(T )

x
⇤2

e
e
2~
~
- ⇤ ns A(~r) = - ⇤ | (~r)| A(~r)
mm<latexit sha1_base64="FIXUxpthi1+MNBrkmKbkmevswBE=">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</latexit>

秩序パラメーター, ψ(r) は電子の数密度を表す.