Фазовая диаграмма поверхностного сверхпроводника в параллейном магнитном поле

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Author: Димитрова О.В.

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Kô

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m ∂2Ω , =4 h ¯ ∂Q2

xx s

s

xx s

2 F

2

hel

2

hel 2

s

αβ s

¯

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®

36¹:·

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F

F

λ

F

F

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F

F

λ

λω

hel

∂Q Q=0

F

ω

α = − ν(F )T H

X

"

# p (ω 2 + H 2 + ∆2 ) p K(k) − ω 2 + (H + ∆)2 E(k) = 6 0, 2 2 ω + (H + ∆)

_7 >NE6<ûùè;61474;58;=>4HI<=P 7414N8HI74?4;63=@<£=
η=

∂Ωhel ∂Q

7 Q=0

ω

Q

89FP ;6536<=P ;=>!ùkN58M7414;6A ñ(K «

Ωhel (Q) = Ωhel (0) + ηQ + a ˜Q2 + ... , 2Ω hel a˜ = 2!1 ∂ ∂Q 2

¡Nè85<8>NG4>4<7EF<=P 1NP N8;6583þf>4Nùè;=1(74;=H

Q=0

ñK ï

X ∂f (H, ω) vF2 ∂ 2 Ωhel = ν( )T = F 2 ∂Q Q=0 2 ∂H ω " # X (ω 2 + ∆2 ) vF2 (ω 2 + ∆2 )2 + H 2 (ω 2 − ∆2 ) ν(F )T −p E(k) , = K(k) + p 2 + (H + ∆)2 2H 2 ω ω 2 + (H + ∆)2 (ω 2 + (H − ∆)2 ) ω

*HI<=P9û^@<87 ï4K ñ K ¥©7P9_HN<83657C@<í6B^BD7(ò474;=15N η HI<ûùè;=Hî;EP ;:< N3657_;6;=;D7414747CJD74B2úv7(òN LT Pk36;=>ø4>4<8<=P(ý;=AMí614;=>(£=7474<8E=<!N583þk>NE<ûùè;=1(74;=H ñ(K « ¡87(E°@<85<>(<£=N8814<;63=14fA;=@(58<>G3 N88<AHI<=P9û(ò4747GN8>NHI;65>4N4<>!P @N-kí658<A<8 N8357

k

Qhel

H

P

p ω 2 + (H + ∆)2 E(k) K(k) − 2

(ω 2 +H 2 +∆2 )

√ 2 ω ω +(H+∆) 2αH η =− = 2 × P 2 2 2 2 2 2 (ω 2 −∆2 ) 2˜ a vF √ (ω2 +∆ ) 2 K(k) + √ (ω2 +∆ ) +H ω − 2 2

N8HI;65874Hf¡ ?5<:4>4;P;;

E(k)

ñK

f>Nùè;6147( (ñ K ¨ 7 (ñ K ï HI<ûùM14<->NE<ûùM75M>!P4<

ω +(H+∆)

H →0

ω +(H+∆) (ω +(H−∆)2 )

X α ∂Ωhel αH π∆2 H ≈ − ν( )T =− ν(F )(1 − Y (T, ∆)), F 2 2 3/2 ∂Q Q=0 2 (ω + ∆ ) 2 ω X π∆2 ∂ 2 Ωhel vF2 vF2 ≈ ν( )T = ν(F )(1 − Y (T, ∆)) F ∂Q2 Q=0 4 (ω 2 + ∆2 )3/2 4 ω

«!¨

ñ(K ñ

3

vFQ / Tc0 pairing wave-vector

2,5

critical point

T/Tc0= 0.542

2

1,5

1

0,5

0.1 0

0

0.01 1

0,5

1,5

in-plane magnetic field

H / Tc0

2

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F

F

F

hel

2 F

c0

hel

−>

H −>

j

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s

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s

yy s

(1) y

(2) y

£ P ;

λ

2 F

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F

(chir) y

F

ω,p,λ

ˆjy(chir)

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«8ï

j/jmax quintized current

1

0

-1

0

1

2

H/Ho

in-plane magnetic field

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e¯ h 2m

2 F

o

s

o

c0

c0

s

(1) s

(2) s

(1) s

hel

(2) s

jquant

2πn e¯ h ns −Qhel + = , 2m 2πR

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2 F

o

o

2 vF 2αR

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max

e¯ h 2m

s

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XZ

ˆ int = H

ψα+ (r)ψα (r)u(r − Ri )d2 r.

ôK ¬H

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α

p

ipr

α

i

int

V

−i(p−p0 )Ri

+ α

i

0

α

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p,p0

α

λα

λp

−i(p−p0 )Ri + pλ

int

i

λµ

0

λµ

p,p0

0

i(ϕp −ϕp0 )

λ

p

imp

2

F

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QI7438K¨¨Lv74N8£=>NHIHI8<3=HI<8£=!P @Nv4< u ¡36<<858;653589ÿ ýv74;O?;=19 l (u T^7ùM1(4;5FGb@<HI;=@3=14<8;O36<4>!(ùè;61474;D;=>ø14;6AKL^<8í=B^B^74ò474;61(5 ¬ K h.c.)

∗ ∗ 3Q v−3Q uQ v−Q

11

l13

l14

Q Q 3Q 3Q Ts X 2 2 G p+ = G −p + G p− G −p − ; 2 ω,p,λ 2 2 2 2 X

5Q = Ts G p+ 2 ω,p,λ

Q Q 3Q 3Q 2 G p+ G −p + G p− G −p − . 2 2 2 2

+

¥ K¬ ª ¥ K ¬¬K

¥©;6EP ; G *B291(@4ò4747óÆ>4741Nk14<>4HN 14<£6<HI;5N4 NK üb9HIHNn4<74HI(9û39EûN8HI;61(4;53þ1N ν( ) R dξ R 77415;=£6>Nî(< ξ f?(743(;6583þK 021(5;6£=>N 4< ϕ 8f?474344;6583þ34<HI<8ýÿX4>4<7EF<=Pýv;=AB2914@4ò47(7 1/pω + (λH ± nQ) ¡ £ P ; n = 1, 3, 5. ¥4<49?(748úv7(;=3þGN81N 7(57(?4;=36@474;^f>Nùv;=147(M4<=P 365N743= T = 1.779T 7 Q = 2.647T 7k<365N8úèN(3þM39HIHN24< ω >NN83=2?47(3;61414<4K¥>4;6E69ûû5N5; H = 0.525T HI 14NúO7 F

2π dϕ 0 2π

2

2

S

S

c0

S

c0

«

c0

u*Q

uQ

-p-Q/2

p+3Q/2

coeff.=1

p+3Q/2

u3Q

u*Q -p-Q/2

-p+3Q/2

coeff.=1 u*Q -p-Q/2 p+3Q/2

u*Q

v-Q

p-Q/2

v-Q*

-p+3Q/2 p-5Q/2

-p-Q/2

v-Q

p-Q/2

u3Q

u*Q

-p+3Q/2

coeff.=1/2

u*Q

p+3Q/2

p-Q/2

u3Q

v-Q

v-Q* -p-Q/2

-p+3Q/2 p-Q/2

v-Q

u*Q

v-Q

QI7438K ¨«(L7N8£=>4N8HIHI <83=HI<£6!P @Nk4< u ¡436<<858;6583659ÿ ýv74;?;=14N8H l u u v |u | 7 (l + l )u u v |v | -K }Áý;M;=35_(;65F7@<HI;=@3=1(<_3=<(>ùè;=1(14f;M4<8@NEûN8141(fH1N >4743914@;8¡NR5N8@ùè;k3kEFN8HI;=1(<A36;ø u 1N v K 1Nû?4;=147n7ø5;èùè;k3FN8HIf;¡#4<í658<HÁ9HI 7ø14; >47439;6HfK 13

14

∗2 3Q Q −Q

−Q

∗2 12 3Q Q −Q

2

ï

Q

2

@ <í=B^B^74ò474;61(54;=>4;P |u| 7 |v| k<83=HI<H[(>4<3658<H#^4<8>P @; ; @<í6B^BD7(ò474;=15:4;6>4;P (|u| |v| + |u| |v| ) k<83=HI<H[(>4<3658<H# ; 0.00152674 − @<í6B^BD7(ò474;=15:4;6>4;P |u| |v| k<3=8HI<H 4>4<35<H# ; −0.00120067 − 8

D1 = 0.00106053 − D2 = D3 =

8

2

6

4

6

2

4

l7 = 0.674254; l8 = 0.103447; l9 = 0.191039; l13 = 0.00491175;

l10 = 0.170477;

l11 = 0.206894;

l12 = 0.0325726;

l14 = 0.021198.

W

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