胡 暁Xiao Hu

強相関モデリングG計算科学センター

φ0=hc/2e

|ψ|

B

Js

λ

ξ

2007.7.19 NIMS seminar

超伝導量子超伝導量子渦糸状態の物理渦糸状態の物理

基礎と応用基礎と応用

VORTEX

Vortices in neutron star

17th17th centurycentury‘‘s vortex physicss vortex physics…whatever was the manner whereby matter was first set in motion, the vorticesvortices intowhich it is divided must be so disposed thateach turns in the direction in which it iseasiest to continue its movement for, in accordance with the laws of nature , a moving body is easily deflected bymeeting another body…

I hope that posterity will judge me kindly, not only as to the thingswhich I have explained, but also to thosewhich I have intentionally omitted so as to leave to others the pleasure of discovery.

Rene Descartes 1644

SuperconductivitySuperconductivity as a as a truetrue thermodynamicthermodynamic phasephase

Ideal conductor (Kammerling Onnes 1911)

Ideal diamagnet (Meissner-Ochsenfeld 1933)

Hg

< 10-5Ω

SuperconductivitySuperconductivity: : truetrue thermodynamicthermodynamic phasephase

JG Bednorz, KA Müller

TimeTime--line of Superconductorsline of Superconductors

GinzburgGinzburg--Landau theory for Landau theory for superconductivity in magnetic fieldsuperconductivity in magnetic field

( )π

ψψβψα8

221

21 22

42 AA ×∇+⎟

⎠⎞

⎜⎝⎛ −∇++=−

ce

imff ns

h

□ Superconductivity order parameter: Ψ=|Ψ|eiϕ

□ GL free energy functional: α=-α’(1-T/Tc) β>0 B=

∆

xA

αξ m42 −= h

□ Coherent length

( ) 22

2

2

241 ψπλ mc

e=

□ penetration depth B |ψ|

ξ

λ□ Supercurrent

⎟⎠⎞

⎜⎝⎛ −∇= AJ

ce

me 22 2 ϕψ h

□ Lower critical field: Hc1=φ0lnκ/4πλ2 Hc2=φ0/2πξ2

Flux quantum & phase diagram

□ Upper critical field:

Abrikosov

T

H

Meissner phase

Mixed phase

Normal phase

Hc2

Hc1

Tc

|ψ|

B

Js

λ

ξ

φ0=hc/2e

ϕ(0)- ϕ(L)=2π

~2x10-7gcm2

Magnetic field of Earth~ 1 flux quantum per

60μm x 60μm

□ Flux quantum

□ H-T phase diagram

type II superconductor

⎟⎠⎞

⎜⎝⎛ −∇= AJ

ce

me 22 2 ϕψ h

Observation of vortex lattice:SAN & STM

Hess et al, PRL 62 (1989) 214: STM on NbSe2

Park et al, 2000 SAN on Nb

Nobel Prize for Physics of 2003Nobel Prize for Physics of 2003

A. Abrikosov A. LeggettV. L. Ginzburg

Theoretical studies on Superconductivity and Superfluid

A.Schilling et al. 1997E.Zeldov et al. 1995

Experimental observation on phase transition:Experimental observation on phase transition:after discovery of highafter discovery of high--TcTc SCSC

□ 1st order transition

T~0

Abrikosov flux-line latticeFlux-line liquid

T≥Tm

RealReal--space distribution of flux linesspace distribution of flux lines

□ Transition between flux line lattice to entangled line liquid

X. Hu, S. Miyashita and M. Tachiki (1997)

Melting of fluxMelting of flux--line latticeline lattice

□ translational & rotational symmetry broken at Tm

□ structure factor

◇ T>Tm: flux line liquid ◇ T<Tm: flux line lattice

◇ correlation of density fluctuations

12

14

16

18

20

22

24

26

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

C[k

B]

T[J/kB]

Tm

Tv

First order thermodynamic phase transitionFirst order thermodynamic phase transition

0

0.2

0.4

0.6

0.8

1

0

4

8

12

16

20

0 0.2 0.4 0.6 0.8 1 1.2

Υc

ξϕ

Υc[J

/Γ2 ] ξ

ϕ [d]

T[J/kB]

X. Hu, S. Miyashita and M. Tachiki (1997)

the specific heat superfluid density

CitationCitation

□ H. Nordborg and G. Blatter -- Phys. Rev. B, 58 p.14556-14571 (1998).

The absence of an analytical description of the vortex lattice melting transition has led a large interest in numerical simulations. …….

The problems have been overcome recently [Hu et al. 1997], and a picture with a single first-order transition is emerging.

□ T. Schneider & J. M. Singer:

『Phase transition approach to high temperature superconductivity:Universal properties of cuprate superconductors 』

(Imperial College Press, 2000)

○ 1957: Abrikosov’s classic prediction of a lattice of quantized vortices

○ 1967: Eilenberger suggested the lattice could melt

○ 1987: Gammel et al. and Nelson suggested that melting observable in high-temperature superconductors

○ 1997: Numerical simulations revealed that phase coherence is destroyed as soon as the vortex lattice melts

absence of intermediate phase

CitationCitation

Steps in 10 years !?

Study on interlayer Josephson vorticesStudy on interlayer Josephson vortices

□ Intrinsic pinning to IJV by CuO2 layer: Tachiki & Takahashi (1989)

Q New quantum phase ?

x

yc

H

□ high-Tc SC: profound layered structure

◇ reduction of c-axis fluctuations ◇ a minimal c-axis separation

◇ commensurate constrain on vortex configuration

□ Commensurate magnetic fields

A1 B1 A2 A3 B2

x-axis rescaled by γ

X. Hu, M. B. Luo and Y. Q. Ma (2005, 2007)

SmecticSmectic and twoand two--step freezing at step freezing at

◇ smectic phase

ρK1>0, ρK2=ρK4=0

◇ liquid-smectic: 2nd order

◇ smectic-crystal: 1st order

□ freezing at strong pinning

(1,0,2)

( )20 23 nsBAm γφ= n=2

□ two-step freezing

ρK2

2πsπs

ρK1

ρK3

ρK4

Only smectic of period 2s is stable.

T decreasing

□ Experimentally confirmed by T. Nishizaki and N. Kobayashi (2007)

Pinning and Pinning and depinningdepinning of vorticesof vortices□ basic science levitation car, superconducting grid, …

Fishing effect of superconductivity

Advantage of using superconductor: stable gap

DepinningDepinning transition and creep motiontransition and creep motion

0.05

t=330 t=1200

ab-plane

c axis

Dynamics of vortices driven by currentDynamics of vortices driven by current□ I-V characteristics

□ Temperature rounds the sharp T=0 depinning transition.

0

0.03

0.06

0.09

0.12

0.15

0.05 0.1 0.15 0.2 0.25 0.3

T=0.0005T=0.001T=0.003T=0.005T=0.007T=0.01

F

BG

VG

T

B

Fc0

M.B. Luo and X. Hu (2007)

DepinningDepinning transition and creep motiontransition and creep motion□ Scaling theory:

□ Depin transition: F>Fc

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −−= 1exp 0/1

0 FF

TUTvv ccδ

( ) ( )βFFFTv c0114.0,0 −=→

□ Creep motion: Fc0/2<F<Fc0

○ Arrhenius law

v0=2.6, Uc=0.027 T≤Uc/3

010.0754.0/1 ±== δβ

○ Fc0=0.23, β=0.8

0

2

4

6

8

-200 -150 -100 -50 0 50

T=0.0005T=0.001T=0.003T=0.005T=0.007T=0.01

(1-Fc0

/F)T-1/βδ

y=2.6+0.14xβ

y=2.6exp(0.027x)

Fc0

=0.2315

δ=1.326βδ=1

( ) ( )fTSTFTv βδδ /1/1, −=F

Ff c01−=

(1-Fc0/F) /T

☐ Kim-Anderson theory: successful and famousbut based on single-particle assumption

DepinningDepinning transition and creep motion: weak pinningtransition and creep motion: weak pinning□□ vv--F characteristicsF characteristics

□ creep law: ( )( )3/20

/1 )1(exp~ TUFFTv cc−δ

( ) ( )fTSTFTv βδδ /1/1, −=

2/33.2;65.0 =⇒== βδδβ□ exponents: non-Arrhenius type

0

0.003

0.006

0.009

0.012

0.015

0.005 0.01 0.015 0.02 0.025 0.03

T=0.00008T=0.0002T=0.0004T=0.0006T=0.0008T=0.001T=0.002

F

0

0.07

0.14

0.21

0.28

0.35

-120 -80 -40 0 40

T=0.00008T=0.0002T=0.0004T=0.0006T=0.0008T=0.001T=0.002

(1-Fc0

/F)T-1/βδ

y=0.15+0.008xβy=0.15exp(0.0345x)

Fco

=0.0255

δ=2.3βδ=1.5

□□ scalingscaling

Spectrum of electromagnetic waveSpectrum of electromagnetic wave

□ THz gap: no good way to generate THz wave

○ electronics: up to sub THz ○ photonics: above THz

☐ ideal for imaging dry dielectric substances: paper, plastics and ceramics. ○ refractive index the THz phase information.

THz imaging systems important for security screening

☐ three-dimensional tomographic T-ray imaging systems

Why terahertz?

☐ manipulation of bound atoms

potential for future quantum computers.

☐ observation on evolution of multi-particle charge interactions by THz spectroscopy.

Why terahertz?

☐ Active fields range from cancer detection to genetic analysis

○ collective vibrational modes of many proteins and DNA molecules occur in the THz range.

☐ a powerful way: quantum cascade laser

Cascade

Cascade

Quantum cascade laser

For τ2<τ32, one can achieve n3>n2the so-called inversion population

☐ GaAs/AlGaAs: frequency fixed○ 4.4 THz ○ operation T=liquid N2○ output 10mW at lower T

Terahertz emission using Terahertz emission using IJJsIJJs of BSCCOof BSCCO☐ ac Josephson relation

dtd

eV γ

2h

=

dc ac transformer

γ=ϕ1−ϕ2-A

ϕ1

ϕ2

☐ Frequency can be tuned continuously!

Activities

NIMS School for Vortex Physics

International Workshop

Activities

Group members

Dr. Y. NonomuraDr. A. Tanaka

Dr. Q.-H. Chen

Dr. M.-B. Luo

Dr. Y.-M. Nie

Dr. M. Kohno

S.-Z. Lin

Dr. K. Matsushita

Prof. M. Tachiki

H. Liu

Thank you !