Critical Current Trends in Type II Superconductors With Pinning

What are Superconductors?• Superconductors are identified by two

traits: – Perfect Conductivity

• Once currents are set up in superconductors, the currents can have a characteristic decay time of 100000 years.

Information from: Introduction to Superconductivity second edition, by Michael TinkhamPhoto from: http://en.wikipedia.org/wiki/File:CERN-cables-p1030764.jpg

– Perfect Diamagnetism. • Also known as Meissner effect• Superconductors completely

expel all magnetic fields• Because of this trait, there is a

critical field where the magnetic field over comes the diamagnetism and destroys the super conducting state.

• In reality, magnetic fields actually penetrate a short distance into the superconductor.

– This distance is known as the London penetration depth, λ– For all my simulations, λ = 5ξ

» ξ is the coherence length, and depends on the superconducting material, but is generally on the order of nanometers.

Photo from: http://picasaweb.google.com/lh/photo/jFNTtqIqGzJsAK0TAN9_UgInformation from: Introduction to Superconductivity second edition, by Michael Tinkham

Superconductor types?

• There are two types of superconductors, determined by the Ginzburg-Landau parameter к

•• If , it is a type I superconductor• If , it is a type II superconductor• In all of my simulation, к = 5, and therefore I deal

only with type II super conductors

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Information from: Introduction to Superconductivity second edition, by Michael Tinkham

Type II Superconductors• In type II superconductors, mixed states can be

achieved, where both superconducting areas and normal areas are present.

• Instead of completely destroying superconductivity, magnetic field lines are able to penetrate all the way through, but are then pinched together creating normal regions

• Super currents then rotate around these normal areas

• The locations where the magnetic field lines are pinched together and pass through are called vortices.

Information from: Introduction to Superconductivity second edition, by Michael Tinkham

Steady state• The vortices will move at

first, but they will eventually evolve into a steady state (at least for the zero current case)

• Moving is bad, because the moving vortices create resistance within the super conductor.

• As long as a steady state is reached, the perfect conductivity is maintained

The red is super conducting area, and the blue are the normal regions associated with the vortices.

Effects of varying Size

13ξ by 13ξ 20ξ by 20ξ15ξ by 15ξ

These are all at zero current (J=0) in a magnetic field of 2.5 T

• Increasing the size allows for more vortices to fill the space.

Effects of Varying the Magnetic Field around the Superconductor

• Increasing the magnetic field forces more field lines to penetrate through the material, creating more vortices.

• At a certain critical field, the material is no longer super conducting.

From top left to bottom right, these are at magnetic fields ranging from 2.0 T to 5.0 T, each new plot increases by a 0.5 T increment. The current is zero for all cases. Red is super conducting area, and blue is non super conducting area.

Changing Currents• When a current runs through a super

conductor, it exerts a force on the vortices. • There is a critical current at which the

vortices no longer reach a steady state, and instead continue to move.

• This matters because when vortices move, they create resistance, and ideally we want as little resistance as possible.

All simulations that follow are run in 13ξ by 13ξ size samples in a magnetic field of 2.5 T

J= 0.0 J= 0.2Jc J= 0.4Jc

J= 0.6Jc J= 0.8Jc J= 1.0Jc

These all still reach a steady state

J= 1.2Jc J= 1.4Jc

J= 1.8JcJ= 1.6Jc

J= 1.0Jc

• These do not reach a steady state

• notice that as the current continues to increase beyond this systems critical current, the frequency that vortices move into and out of the system increases

Normal Inclusions.• By adding normal material impurities to the

super conducting material, you can ‘pin’ vortices to the location of the normal inclusion, thus preventing them from moving.

• However, there is still a critical current at which point the vortices will not be able to reach a steady state.

• We want that critical current to be as high as possible.

Without normal inclusions, the 1.3 by 1.3 square looks like it did before

These are steady state orientations obtained in systems with normal inclusions.

These are steady state orientations obtained in systems with normal inclusions.

The black shapes represent the location size and shape of the normal inclusions

Number of Normal Inclusions

• Increasing the number of normal inclusions increases the critical current, but as a trade off. If too many are added, the sample loses its superconductivity.

• Jc still represents the critical current for the case with no normal inclusions.

• Future currents will be expressed in terms of Jc

J = 0

J= 1.0Jc

J= 1.3JcNot Steady

J= 1.6JcNot Steady

Not Steady

J= 1.8JcNot Steady

Not Steady

Not Steady

Not Steady

J = 0

J= 1.0Jc

J= 1.3Jc

J= 1.6Jc

J= 1.8Jc

Size of Normal Inclusions

• Generally, increasing the size of the normal inclusions will increase the critical current, but if you continue to increase the size, eventually the critical current will start to fall again.

Critical Current vs. Size of Square Oriented Normal Inclution

0

0.5

1

1.5

2

0 0.5 1 1.5 2 2.5

Size of normal inclutions (in ξ)

Criti

cal C

urre

nt (

in J

c)

Critical Current vs. Size of Two Virtical Line Oriented Normal Inclusions

0

0.5

1

1.5

0 0.5 1 1.5 2 2.5

Size of normal inclusion (in ξ)C

ritic

al

Cur

rent

(in

Jc

)These show the position

of the normal inclusions, they display them at a size of 1ξ, though size varies in these trials.

• These two trials compare the size of the normal inclusions to the system’s critical current.

• There is not enough data to give an accurate trend line. These lines just to give the over all trends.

• Increasing the size of normal inclusions increases the critical current to a point, then starts to decrease it.

• There is not necessarily one peak either.

• This shows that there can be local minima, which quite possibly were present in the other trials, though not observed.

Critical Current vs. Size Single Centered Normal Inclusion

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.5 1 1.5 2 2.5 3 3.5

Size of normal inclusion (in ξ) Cr

itica

l Cur

rent

(in

J c)

Changes in Orientation of Normal Inclusions

• The position of the normal inclusions matters as well.

• These three cases have the same number of normal inclusions, yet very different critical currents above a radius of 1ξ and peak critical currents at different normal inclusion radii

Series1 Series2

Critical Current vs. Size of different Possible Orientations for Four Normal Inclusions

-0.5

0

0.5

1

1.5

2

0 0.5 1 1.5 2 2.5

Size of normal inclusion (in ξ)

Crit

ical

Cur

rent

(in

Jc)

Series1Series2Series3

Series3

• If a normal inclusion is too close to the edge, it acts as a channel for spawning vortices, aiding in there movement through the superconductor, and greatly reducing the critical current. This can explain the sudden drop off in Series2 (the system on the right)

• These are both at the same current, with the same number and size of normal inclusions and a similar orientation.

• The system on the left has a critical current between 1.0 Jc and 1.3 Jc while the system on the right’s critical current is bellow 0.6 Jc

• When vortices get too close to each other it also causes a drop off in critical current.

Normal Area of 4π

J=1.4Jc d=0.25 J=1.0Jc d=0.18 J=0.8Jc d=0.0

Normal Area of 9π

J=1.5Jc d=0.15 J=1.0Jc d=0.08 J=1.2Jc d=0.0

• These two sets of three trials have the same amount by area of normal inclusion, but different critical currents.

• d is the distance between the edges of the normal inclusions• The bottom center photos critical current is between 1.0Jc and 1.3Jc, so it

could be behaving very close to how the bottom right photo is at a current of 1.2Jc

• This also further shows that more normal inclusions is better (even with the same amount of normal area)

Critical Current=1.4-1.5Jc Critical Current=1.0-1.3Jc Critical Current=0.8-1.0Jc

Critical Current=1.5-1.6Jc Critical Current=1.0-1.3Jc Critical Current=1.2-1.3Jc

• The last two slides imply that you can optimize your normal inclusion orientation.– First, by balancing the ratio between the distance

between the edges of the system and the edges of the normal inclusions with the distance between the edges of the normal inclusions and other inclusions.

• It appears from my simulations that the highest critical current will appear when the distance between the edges of the square and the edges of the normal inclusions is some what greater.

• The ratio does not depend on r0, but the actual distances do– Second, by choosing an orientation that allows more

space between the edges of the system and the edges of the vortices.

• For example, a square orientation vs. a diamond orientation. The square is better.

• If you look at the case without normal inclusions, you will see that the vortices will stop in one orientation, then eventually move again to an orientation with more space between the vortices.

Why Research this?

• If, with further research, optimized orientations can be found. It would be possible to build superconductors with higher critical currents, and thus, more useful superconductors.

• All high temperature superconductors are type II