Document that explains the chosen concept to the animator
1
Cooper Pairs
In superconductors,there exists an electron-lattice-electron interaction. This
indirect interaction proceeds when one electron interacts with the lattice
and deforms it;a second electron sees the deformed lattice and adjusts
itself to take advantage of the deformation to lower its energy. Thus,the
second electron interacts with the first electron via the lattice deformation.
The pair of electrons thus formed are known as Cooper Pairs.
Course Name: Superconductivity
Authors:
Anura.B.Kenkre
2
Learning Objectives
After interacting with this Learning Object, the learner
will be able to:
•
•
Describe the formation of a cooper pair.
Explain the relation between the intrinsic coherence length
and the size of a cooper pair.
3
1
2
Definitions of the
components/Keywords:
Certain metals and alloys exhibit almost zero electrical resistivity
when they are cooled to sufficiently low temperatures.This reduction in
the value of electrical resistivity to zero is known as superconductivity.

•The temperature at which the transition to the superconducting state
takes place is called the critical temperature(Tc)or the superconducting
transition temperature.
• In superconductors,there exists an electron-lattice-electron
3
4
5
interaction. This indirect interaction proceeds when one electron
interacts with the lattice and deforms it;a second electron sees the
deformed lattice and adjusts itself to take advantage of the
deformation to lower its energy. Thus,the second electron interacts
with the first electron via the lattice deformation. The pair of
electrons thus formed are known as Cooper Pairs.
• Superconducting coherence length(ξ)gives approximate spatial
dimension (size) of the Cooper pair.
4
Definitions of the components/Keywords
continued:
The coherence length (ξo) determined by the
energy gap at zero temperature,Eg(T=0)is called
Intrinsic coherence Length and it is given by the
formula:
where
is the fermi velocity(on the fermi surface) and
Is the Planck constant.
5
IMPORTANT NOTE TO THE ANIMATOR:
•All the instructions/labels or anything WRITTEN in blue
are CONTENT NOT TO BE DISPLAYED!
•All the instructions WRITTEN in black are CONTENT TO
BE DISPLAYED!
•This is not applicable for images as there can be
overlapping of these colours there. This should be
followed for all the instructions,labels,etc…
Kindly keep a note of this while displaying text in the
animation.
6
INSTRUCTIONS SLIDE
1
Master layout or diagram
2
• Make a schematic diagram of the concept
• Explain to the animator about the beginning and ending
of the process.
• Draw image big enough for explaining.
3
• In above image, identify and label different components
of the process/phenomenon. (These are like characters
in a film)
• Illustrate the basic flow of action by using arrows. Use
BOLD lines in the diagram, (minimum 2pts.)
4
5
• In the slide after that, provide the definitions of ALL the
labels used in the diagram
7
INSTRUCTIONS SLIDE
1
2
3
Master layout or diagram
• You may have multiple master
layouts.
– In this case, number the master
layout. ( e.g. Master layout 1)
– Each Master layout should be
followed by the stepwise description
of the animation stages related to it.
4
5
8
Master Layout1
1
At
T>Tc.
2
: electrons
3
4
5
:Atoms of lattice
Zoomed in
At
T=Tc.
For animation refrence see this link:
http://www.msm.cam.ac.uk/doitpoms//tlplib/superconductivity/cooper.php.
9
Master Layout2:
1
ANIMATION AREA
Interactivity:
TEMPERATURE
DEPENDANCE
2
Lower T
3
Higher T
COHERENCE
LENGTH
Aluminium(Al)
Tin(Sn)
4
Niobium(Nb)
:electrons
5
:Atoms of lattice
10
1
2
3
4
5
Animation design
• Please see the design template
provided in the next slide.
• This is a sample template, and you
are free to change as per your design
requirements.
• Try and recreate the
sections/subsections as shown in the
template.
11
Credits
What will you learn
Lets Learn!
Definitions
Test your understanding
Lets Sum up (summary)
(questionnaire)
Play/pause
Want to know more…
(Further Reading)
Restart
TEMPERATURE
DEPENDANCE
Lower T
Higher T
COHERENCE
LENGTH
Aluminium(Al)
Tin(Sn)
Niobium(Nb)
:electrons
:Atoms of lattice
12
1
Explain the process
2
3
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

4

5
In this step, use an example to explain the concept. It
can be an analogy, a scenario, or an action which
explains this concept/process/topic
Try to use examples from day-to-day life to make it
more clear
You have to describe what steps the animator should
take to make your concept come alive as a series of
moving images.
Keep the examples simple to understand, and also to
illustrate/animate.
13
1
Analogy / Scenario / Action
ANALOGY FOR FORMATION OF COOPER PAIR:
2
3
4
Often this pairing of electrons is visualised in terms of ball bearings (the
“electrons”) resting on a rubber sheet (the “lattice”). Putting one ball bearing on
the sheet will cause it to stretch creating a depression in which the ball sits. This
lowers the gravitational potential energy of the ball by making it lower down. If
another ball is placed on the sheet, it too will form a depression, but if it is placed
near enough to the first the two will roll together and form a deeper depression.
This lowers the overall gravitational potential energy of the two balls and causes
there to be a coupling between them that would otherwise not be there without the
rubber sheet. The animation below gives an idea of how this occurs. In practice,
this is only a schematic representation of the microscopics of the interaction within
electron pairs.
Note for the animator:You can have a look at this video link for
the animation of this analogy:
http://www.youtube.com/watch?v=tWJXVpuYkhc
5
14
1
Stepwise description of process

2

3



4
5
The goal of the document is to provide instructions to an animator
who is not a expert.
You have to describe what steps the animator should take to make
your concept come alive as a moving visualization.
Use one slide per step. This will ensure clarity of the explanation.
Add a image of the step in the box, and the details in the table
below the box.
You can use any images for reference, but mention about it's
copyright status

The animator will have to re-draw / re-create the drawings

Add more slides as per the requirement of the animation
15
1
Step 1:
Refer to master layout 2.
Description of the action/ interactivity
2
3
4
5
•Initially, show a pop up near the interactivity asking the user to select either
‘temperature dependence’ or ‘coherence length'. Until they click on either, the options
below each will remained greyed out.
•When they select either, the corresponding option will be clickable..For example, If they
select coherence length, only then the options for Aluminium, tin and niobium will get
clickable.
•Keep the action buttons all of the same size and you can use a suitable colour scheme
for them as well.
•Include a play, pause and restart button so that the user has control.
•When the user clicks on temperature dependence, go to slide 17 and let the options
below ‘temperature dependence' get clickable.
•If the user clicks on Coherence length go to slide 26,and at the same time the options
for Aluminium, tin and niobium will get clickable.
•If the user clicks on niobium. go to slide 27.
•If the user clicks on tin, go to slide 28.
•If the user clicks on Aluminium. go to slide 29.
16
1
2
Step 2:
FOR TEMPERATURE:
T1>>Tc
3
4
5
Fig 1
For the action buttons refer to master layout.
Description of the action/
interactivity
•Put a blank slide and let the text in Fig 1
appear.
•Let this slide remain for 2 seconds.
•Then go to step 3.
•If the user clicks on lower T action button
then go to step 4.
•Do not allow the user to click on higher T
action button.
Text to be displayed (if any)
(DT)
17
1
Step 3:
:electrons
Title: Motion of electrons at temperature T1>>Tc.
:Atoms of lattice
Electron 1
2
Fig 2
3
For the action buttons refer to master layout.
Description of the action/ interactivity
Always keep the size of the atoms of the lattice a lot larger than the size of the electrons.
Move the electrons along the paths shown by the arrows in Fig2.
The arrow shows the direction of motion and entire motion of one electron is depicted in one colour. For
example,in Fig 2,entire motion of electron 1 is depicted by black coloured arrow.
The electrons hit the atoms of the lattice and move along the path shown by the respective arrows.
Show the movement of the electrons along the different coloured arrows simultaneously.
Show this animation step for a time length of 8 seconds.
Do not let the electrons pass through the atoms of the lattice or through each other while moving in their
respective paths indicated by arrows.
REPEAT THE ANIMATION TILL THE TEMPERATURE VALUE CHANGES.
The arrows are there to show the path along which the electron will move. The arrows are not to be shown on
screen.
Include + and – signs on the atoms of lattice and the electrons respectively.
•If the user clicks on lower T action button then go to step 4.
18
•Do not allow the user to click on higher T action button.

4
5

1
Step 4:
FOR TEMPERATURE:
2
T2>>Tc (T2<T1)
3
4
Fig 3
For the action buttons refer to master layout.
Description of the action/
interactivity
Put a blank slide and let the text in Fig 3
appear.
Let this slide remain for 2 seconds.
Then go to step 5.
•If the user clicks on lower T action button
then go to step 6.
•If the user clicks on Higher T action button
then go to step2.
Text to be displayed (if any)
(DT)

5
19
1
Step 5:
Title: Motion of electrons at a lower temperature T2>T c. (T2<T1)
IMPORTANT NOTE TO THE ANIMATOR: Keep the speed of the electrons in Fig 4 slower
as compared to their speed in Fig 2.
Fig 4
2
: electrons
:Atoms of
lattice
3
For the action buttons refer to master layout.
Description of the action/ interactivity
Always keep the size of the atoms of the lattice a lot larger than the size of the electrons.
Move the electrons along the path shown by the arrows. In Fig4.
Compared to previous figure, show fewer number of collisions (because temp is lower).
•The arrow shows the direction of motion and entire motion of one electron is depicted in one colour.
The electrons hit the atoms of the lattice and move along the path shown by the respective arrows.
Show the movement of the electrons along the different coloured arrows simultaneously.
• Show this animation step for a time length of 10 seconds.
•Do not let the electrons pass through the atoms of the lattice or through each other while moving in their
respective paths indicated by arrows.
•REPEAT THE ANIMATION TILL THE TEMPERATURE VALUE CHANGES.
•The arrows are there to show the path along which the electron will move. The arrows are not to be shown on
screen.
•Include + and – signs on the atoms of lattice and the electrons respectively.
•If the user clicks on lower T action button then go to step 6.
20
•If the user clicks on Higher T action button then go to step2.

4
5

1
Step 6:
FOR TEMPERATURE:
2
T3=Tc (T3<T2)
3
4
Fig 5
For the action buttons refer to master layout.
Description of the action/ interactivity
Put a blank slide and let the text in Fig 5 appear.
Let this slide remain for 2 seconds.
Then go to step 7.
•If the user clicks on Higher T action button then
go to step 4.
•Do not allow the user to click on lower T action
button.
Text to be displayed (if any)
(DT)

5
21
1
Step 7:
Title: At T=Tc, Lattice distortion.
Note for the animator:The black arrow is there to show the path along which the electron
will move and the blue arrow is for naming the electron..The arrows are not to be shown
on screen.
:Atom of the lattice
:Electron
2
NET
POSITIVE
CHARGE
3
ELECTRON 1
( )
ELECTRON 1
Fig 6
For the action buttons refer to master layout.
4
Description of the action/ interactivity
Always keep the size of the atoms of the lattice a lot larger than the size of the electrons.
First show the lattice without electrons and arrows and then zoom in to take a close up so that
only 6 atoms of the lattice as shown in Fig6,can be seen.
Move the electron 1 along the BLUE arrow as shown in Fig6 above.
When electron1 moves along the blue arrow, bend the atoms of the lattice as shown in the
above Fig6.
• Show this animation step for about 2 seconds.
•Keep the shape of the atoms spherical even when the lattice bends.
•Include + and – signs on the atoms of lattice and the electrons respectively.
•If the user clicks on Higher T action button then go to step 4.
•Do not allow the user to click on lower T action button.
Audio
naration


5
22
Step 8:
1
Title: At T=Tc ,Lattice distortion
Note for the animator:The black arrow is there to show the path along which the electron
will move and the red arrow is for naming the electron..the arrows are not to be shown
on screen.
:Atom of the lattice
:Electron
2
3
ELECTRON 2
( )
NET
POSITIVE
CHARGE
ELECTRON 1
Fig 7
For the action buttons refer to master layout.
4
Description of the action/ interactivity
As soon as the atoms of the lattice bend towards electron 1,show electron 2
coming in and moving along the black arrow as shown in Fig7.
• Show this animation step for about 2 seconds.
•Keep the shape of the atoms spherical even when the lattice bends.
Include + and – signs on the atoms of lattice and the electrons respectively.
•If the user clicks on Higher T action button then go to step 4.
•Do not allow the user to click on lower T action button.
Audio
narration

5
23
1
Step 9:
Title: cooper pair getting formed.
Note for the animator:The black arrow is there for naming the cooper pair..the arrow is
not to be shown on screen.
:Atom of the
lattice
:Electron
2
COOPER PAIR
Fig 8
3
For the action buttons refer to master layout.
Description of the action/ interactivity
4
5
Always keep the size of the atoms of the lattice a lot larger than the size
of the electrons.
Show the 2 electrons getting paired by means of a dotted elliptical shape
between them, as shown in Fig8 above.
The atoms of the lattice remain bent as in previous slide.
Show this animation step for about 2 seconds.
•Keep the shape of the atoms spherical even when the lattice bends.
•Include + and – signs on the atoms of lattice and the electrons
respectively.
•If the user clicks on Higher T action button then go to step 4.
•Do not allow the user to click on lower T action button.
Audio narration

24
1
Step 10: Title: cooper pair drifting through the material.
Note for the animator:The orange arrows are there to show the path along which the
electron will move..The arrows are not to be shown on screen.
:Atom of the
lattice
:Electron
2
Fig 9
3
For the action buttons refer to master layout.
Description of the action/ interactivity
Audio
narration
Always keep the size of the atoms of the lattice a lot larger than the size of
the electrons.
Show the 2 electrons travelling together along the direction shown by the
orange arrow.
This movement is shown in Fig9.
The atoms of the lattice remain bent as in previous slide.
• Show this animation step for about 2 seconds.
•Keep the shape of the atoms spherical even when the lattice bends.
•Include + and – signs on the atoms of lattice and the electrons respectively.
•If the user clicks on Higher T action button then go to step 4.
•Do not allow the user to click on lower T action button.

4
5
25
Step 11:
We will now explore the relation
between Intrinsic Coherence length and
the Cooper Pair size...
Description of the action/ interactivity
Audio
narration
When the user selects the radio button for ‘coherence length’
display the text above.

For the action buttons refer to master layout.
26
1Step12:Intrinsic Coherence length for Niobium(Nb)
Fig 7
:Electron
2
:Atom of the
lattice
ξξo
Niobium(Nb)
metal sheet.
3
Nb
Description of the action/
interactivity
Show the niobium metal sheet
appearing first.
Show the animation given in slides 22 to
25.
Then show the double headed arrow
inFig7 above appearing along with the
symbol ξ0
Then display the text given beside.
Make the cooper pair move along the
path shown by the blue arrow.(blue arrow
not to be displayed)
 Always keep the size of the atoms of the
lattice a lot larger than the size of the
electrons.
Include + and – signs on the atoms of
lattice and the electrons respectively.
Text to be displayed (if any)
(DT)

4
5
The intrinsic coherence length for Niobium is
3.8×10 -6cm.

27
1
Step13:Intrinsic Coherence length for Tin(Sn)
Fig 8
ξo
2
3
:Electron
:Atom of the
lattice
Sn
Description of the action/
interactivity
Show the tin metal sheet appearing first.
Show the animation given in slides 22 to
25.
Then show the double headed arrow
inFig7 above appearing along with the
symbol ξ0
Then display the text given beside.
Make the cooper pair move along the
path shown by the blue arrow. (blue arrow
not to be displayed)
 Always keep the size of the atoms of the
lattice a lot larger than the size of the
electrons.
Include + and – signs on the atoms of
lattice and the electrons respectively.
Tin(Sn) metal
sheet.
Text to be displayed (if any)
(DT)


4
5
The intrinsic coherence length for Tin
is 23×10 -6cm.

28
1 Step14:Intrinsic Coherence length for Aluminium(Al)
Fig 7
ξo
:Electron
2
3
:Atom of the
lattice
Al
Description of the action/
interactivity
Show the aluminiuim metal sheet
appearing first.
Show the animation given in slides 22
to 25.
Then show the double headed arrow
inFig7 above appearing along with the
symbol ξ0
Then display the text given beside.
Make the cooper pair move along the
path shown by the blue arrow. (blue
arrow not to be displayed)
 Always keep the size of the atoms of
the lattice a lot larger than the size of
the electrons.
Include + and – signs on the atoms
of lattice and the electrons
Aluminium(Al)
Metal sheet.
Text to be displayed (if any)
(DT)

4
5
The intrinsic coherence length for Aluminium is
160×10 -6cm.

29
1
Interactivity and Boundary limits

2


3

4
5

In this section, you will add the ‘Interactivity’ options to the
animation.
Use the template in the next slide to give the details.
Insert the image of the step/s (explained earlier in the
Section 3) in the box, and provide the details in the table
below.
The details of Interactivity could be:
 Types: Drop down, Slider bar, Data inputs etc.
 Options: Select one, Multiple selections etc
 Boundary Limits: Values of the parameters, which won’t
show results after a particular point
 Results: Explain the effect of the interaction in this column
Add more slides if necessary
30
INSTRUCTIONS SLIDE
Self- Assessment Questionnaire for
Learners
• Please provide a set of questions that a user
can answer based on the LO. They can be of
the following types:
– These questions should be 5 in number and can be of
objective type (like MCQ, Match the columns, Yes or
No, Sequencing, Odd One Out).
– The questions can also be open-ended. The user
would be asked to think about the question. The
author is requested to provide hints if possible, but a
full answer is not necessary.
– One can include questions, for which the user will
need to interact with the LO (with certain
parameters) in order to answer it.
31
INSTRUCTIONS SLIDE
Questionnaire for users to test their
understanding
• Please make sure that the questions can be
answered by interacting with the LO. It is
better to avoid questions based purely on
recall.
32
Questionnaire
1. As the temperature decreases what happens to the number of
collisions?
Answers: a) Increase
d)becomes zero.
b) decrease
c)
no change
Correct Answers:1)b
Feedback:
 If user clicks correct answer then display
“Correct! Make sure you can explain the
reasoning!”

If user clicks incorrect answer then display
“Play with the simulation and Try again!”

Display one question on one page..When the user selects his answer,
compare with the correct answer and display the appropriate feedback.
33
Questionnaire
2.cooper pairs are formed at what temperature?
Answers: a) above Tc
b) below Tc
c)At all times
d)at T= Tc.
Correct Answers: 2)d
Feedback:
 If user clicks correct answer then display
“Correct! Make sure you can explain the
reasoning!”

If user clicks incorrect answer then display
“Play with the simulation and Try again!”

34
Questionnaire
3. Match the following:
metal
Intrinsic coherence length
(cm)
1)Aluminium(Al)
1) 3.8 ×10
-6
2)Tin(Sn)
2)160 ×10
-6
3)Niobium(Nb)
3)23×10
Correct Answers:
3)1
2
2
3
3
1
-6
*Note:allow the user to match the coloums by
means of arrows.
Feedback:
 If user clicks correct answer then display
“Correct! Make sure you can explain the
reasoning!”

If user clicks incorrect answer then display
“Play with the simulation and Try again!”

35
Questionnaire
4. For different metals, as the intrinsic coherence length increases, what happens
to the size of cooper pairs?
Answers:
a)Increases
d)becomes zero.
b)decreases
c)remains same
Correct Answers:4)a
Feedback:
 If user clicks correct answer then display
“Correct! Make sure you can explain the
reasoning!”

If user clicks incorrect answer then display
“Play with the simulation and Try again!”

36
Questionnaire
5.When the cooper pairs are formed, what happens to the shape of the
lattice?
Answers:
electrons
a)bends away from the electrons
b)bends towards the
c)stays as it is
d)distorts unevenly.
Correct Answers:5)b
Feedback:
 If user clicks correct answer then display
“Correct! Make sure you can explain the
reasoning!”

If user clicks incorrect answer then display
“Play with the simulation and Try again!”

37
Questionnaire
Explore:
What could be the effect of the value of the band gap energy(Eg),on the
existence of the cooper pair?
38
Links for further reading
Reference websites:
http://www.msm.cam.ac.uk/doitpoms//tlplib/superconductivity/c
ooper.php
http://www.superconductors.org/oxtheory.htm
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/coop.html#c2
Books:

Introduction to Solid state physics-Charles Kittel(chapter 12)

Solid state physics-MA Wahab.(chapter 17)

Solid state physics-Ashcroft/Mermin. (Chapter 34)
39
INSTRUCTIONS SLIDE
Summary
• Please provide points to remember to
understand the concept/ key terms of the
animation
• The summary will help the user in the quick
review of the concept.
40
Summary
Certain metals and alloys exhibit almost zero electrical resistivity when
they are cooled to sufficiently low temperatures. This reduction in the
value of electrical resistivity to zero is known as superconductivity.
The temperature at which the transition to the superconducting state takes place is
called the critical temperature(Tc)or the superconducting transition temperature.
In superconductors, there exists an electron-lattice-electron interaction.
This indirect interaction proceeds when one electron interacts with the
lattice and deforms it; a second electron sees the deformed lattice and
adjusts itself to take advantage of the deformation to lower its energy.
Thus, the second electron interacts with the first electron via the
lattice deformation and gets paired with it. The pair of electrons thus
formed are known as Cooper Pairs.
The coherence length (or the Cooper-pair size) ξo determined by the energy gap at
zero temperature,Eg(T=0)iscalled Intrinsic coherence Length.
41