Vortex Dynamics in Vortex Dynamics in Type II Type II

SuperconductorsSuperconductors

Yuri V. ArtemovYuri V. ArtemovPh.D. Student in Physics

Mentor:

Brian B. SchwartzBrian B. SchwartzProfessor of Physics

CUNY Fall 1998

OverviewOverview

• Properties of superconductors

• Two types of superconductors

• Theories of superconductivity

• Vortices in type II superconductors

• Interaction between vortices

• Interaction with defects• Vortex dynamics• Proposed research• Vortices and computers• Summary

Perfect conductor

yrs10dtdI

I

0ρ

5

Properties of Properties of SuperconductorsSuperconductors

Meissner effect

cTT

0B

cTT Magnetic fielddestroys s/c

cHH cHH

0

Ic Bc

Electric currentdestroys s/c

Two Types of Two Types of SuperconductorsSuperconductors

Magnetization

Magnetic Field

Critical Field

-4M

HHc

-4M

HHc1 Hc2

H

B

Hc1 Hc2

H

B

Hc

Type IIType I

T

Hc

Tc

Superconductor

Normal Metal

T

Hc

Tc

Superconductor

Normal Metal

Mixed State

Theories of Theories of SuperconductivitySuperconductivity

• London Equation

field magneticofenergy

2

currentpermanent ofenergy kinetic

s2

0 rd8π

Hrdnmv

2

1FF

0HH0F 2

H λx

eH

• BCS Theory

• Ginzburg-Landau Theory

2/1c MT

•Electrons can attract via phonons

•Attraction leads to energy gap 1.76Tc

isotope effect

EF EF

2Normal Metal Superconductor

Amc

e4

m

eiB

4

cj

0Ac

e2

im2

1

T4H,

T

T

TTT

8

HA

c

e2i

m2

1

2FF

22

**s

2

2/12

c

2

c

c0

2242

n

II type21

I type21

parameter GL

Te24

mcT

Tm2T

2/1

2

2

2/12

H

r

Vortices in Type II Vortices in Type II SuperconductorsSuperconductors

quantumflux e2

hc,rzHH 020

2

rK

2H 02

0

r,er22

H

r,r

ln2

H

/r2

0

20

Magnetic Field

j

r

Current

r

Order Parameter

Interaction between Interaction between VorticesVortices

B

J

FL

Lorenz type force

Jc

F 0L

BB

FLJ

Repulsion

ss0

L vnh2

1J

cF

Triangular lattice

2102

012

12012

112221

2

12

212121

2

21

221202

rrK

2H,

4

HU

dHHdHH8

U

ddHHHH8

F

rHrHrH

rrrrzHH

Interaction with Interaction with DefectsDefects

B

J

FL

Jc

F 0L

Flux Creep

Activation energy behavior

Pinning

• Vacancies, voids, inhomogeneities, where superconductivity is weak

• Pinning decreases energy losses caused by flux creep

Vortex DynamicsVortex Dynamics

• Collective behavior– Vortices interact strongly

• Effects of disorder– Interaction with pinning centers

• Many degrees of freedom– 1012 vortices in a sample

• Threshold dynamics– Can be driven to marginally

stable state

Proposed ResearchProposed Research

Study the dynamics of vortices in type II superconductors

Given a superconductor with a certain pinning landscape, how do vortices move inside it?

How do microscopic pinning parameters affect measured macroscopic quantities?

How do vortices start moving when slowly driven towards the threshold of instability?

How to characterize dynamical instabilities in a superconductor?

Vortices and Vortices and ComputersComputers

Vortices can be studied using computer simulations– A powerful theoretical tool to

answer questions raised above– Allows to study phenomena hard to

observe experimentally Vortices can be effectively

visualized using modern 3D design software– Making them more understandable

to non-physics audience Tools to be used

– Powerful workstations at the CUNY New Media Lab

– Softimage 3D software– DirectX technology with Visual C++

and Visual Basic– Matlab, Mathematica– Java & WWW

SummarySummary

General properties of superconductors

Type I and type II superconductors

Theories of superconductivity

Vortices in type II superconductors

Vortex interactions and dynamics

Proposed research Using computers to

study and visualize vortices