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Information of the LO
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Domain: Physics
Subject: Solid state Physics
Topic: Superconductivity
Sub-Topic: Formation of 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.
Level: UG
Authors: Anura Kenkre, Sameer Sahasrabudhe
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Learning objectives
After using this LO the user should be able to:
1.
2.
Describe the formation of a cooper pair.
Explain the relation between the intrinsic coherence length and
the size of a cooper pair.
Project OSCAR IDD Template 4.7
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Element groups in this LO
Name of the element group
Name of the elements in the
group
Microscopic View
Electrons
Importance in the LO
[1: highest, 5: lowest]
1
Atoms
Control panel
Temperature control panel
Button for : Temperature dependence
2
Button for increasing the temp
Button for decreasing the temp
Panel for coherence length
selection
Button for coherence length selection
Button for metal: aluminum
Button for metal: Tin
Button for metal: Niobium
Project OSCAR IDD Template 4.7
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Microscopic view
Name of the
element
Abbrevation
Write the name of
the element here
Create a
suitable
Provide a reference
Check if the image you have
abbrevation.
image, this can be copied copied is copyright free, else
Use this in the
from the web
mention that explicitly
ID Document
hereon
Atom
Electron
Reference Image
Functional / Interactivity details Connected to
Write details about how this
element works. Can also give
specific instructions, about the
motion here.
This is a static element. IT DOES
Create it using this reference. NOT MOVE AT ALL in this
animation. Include a + sign on
Use this colour only.
this. Size of the atom must
always
bebetween
a lot larger
EL moves
thethan
ATs,the
it
AT
EL
Legend for atoms and
Legend
electrons
Image for using in LO
:electrons
also collides with Ats. But an
important aspect is: It does not
Create it using this reference. deform while hitting the AT. The
Use this colour only.
movement of Els has to be
shown based on the paths
provided in the images. Include a
- sign on this.
This is a Legend to denote the
:Atoms of Create it using this reference. atoms and the electrons, and it is
lattice
a static element.IT DOES NOT
Use this colour only.
MOVE AT ALL in this animation.
Include a + sign on the atom and
Project OSCAR IDD Template 4.7
Write how is this placed in the LO.
Mention the before/next
connection of this element with
other element.
A grid has to be shown of 4x4 atoms.
Every point of the grid would be an
atom. Detailed visual is given in
Step 1
It is a dynamic element, and will be
animated based on the paths
provided in the slides explaining
the stepwise animation
It is not connected to any other
element. Kindly select a location for
it in the animation area so that the
students do not overlook it.
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Temperature control panel
Name of the
element
Abbrevation
Write the name of
the element here
Create a
suitable
Provide a reference
Check if the image you have
abbrevation.
image, this can be copied copied is copyright free, else
Use this in the
from the web
mention that explicitly
ID Document
hereon
Button for :
Temperature
dependence
TD
Button for increasing
T+
the temperature
Button for decreasing
Tthe temperature
Reference Image
TEMPERATURE
DEPENDANCE
Image for using in LO
Functional / Interactivity details Connected to
Write details about how this
element works. Can also give
specific instructions, about the
motion here.
Write how is this placed in the LO.
Mention the before/next
connection of this element with
other element.
Create an image which will
have a look of a button.
Choose a suitable colour.
This is a static element. IT DOES
NOT MOVE AT ALL in this
animation. It will have the
features of a regular button. Eg:
Hover, Press, Release. Pressing
this button will be indicated by
the text on the screen. Details of
this are mentioned in the
stepwise description slides.
This button is not physically shown
connected to any other element.
However, pressing this button will
have impact on: the title text, and
the two buttons T+ and T- (they will
get highlighted / activated)
Create an image which will
have a look of a button.
Choose a suitable colour.
This button will trigger change in: This button is connected to the
1. The temperature display area. button for decreasing the
temperature. When this button is
The action buttons for
clicked, the appropriate animation
temperature should be of the
will be shown to the user according
same size.
to the stp wise instructions.
This button will trigger change in: This button is connected to the
1. The temperature display area. button for increasing the
Create an image which will
temperature. When this button is
have a look of a button.Choose
The
action
buttons
for
clicked, the appropriate animation
Project
OSCAR
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a suitable
colour.IDD Template 4.7
temperature should be of the
will be shown to the user according
1
2
3
4
5
Panel for coherence length selection
Name of the
element
Abbrevation
Write the name of
the element here
Create a
suitable
Provide a reference
Check if the image you have
abbrevation.
image, this can be copied copied is copyright free, else
Use this in the
from the web
mention that explicitly
ID Document
hereon
Button for :
Temperature
dependence
Buttons for the
different metals
TD
Al
Sn
Reference Image
COHERENCE
LENGTH
Aluminium(Al)
Tin(Sn)
Image for using in LO
Create an image which will
have a look of a button.
Functional / Interactivity details Connected to
Write details about how this
element works. Can also give
specific instructions, about the
motion here.
Write how is this placed in th
Mention the before/next
connection of this element w
other element.
This is a static element. IT DOES
NOT MOVE AT ALL in this
animation. It will have the
features of a regular button. Eg:
Hover, Press, Release. Pressing
this button will be indicated by
the text on the screen. Details of
this are mentioned in the
stepwise description slides.
This button is not physically sh
connected to any other eleme
However, pressing this button
have impact on: the title text,
the three buttons for Al, Sn an
(they will get highlighted /
activated)
This button is connected to th
button for the other metals. W
Create an image which will
This button will trigger change in:
this button is clicked, the
have a look of a button.Choose 1. The coherence length display
appropriate animation will be
a suitable colour.
area.
shown to the user according to
step wise instructions.
This button is connected to th
button for the other metals. W
Create an image which will
This button will trigger change in:
Project
IDD
Template 4.7 1. The coherence length display this button is clicked,
6 the
haveOSCAR
a look of
a button.
appropriate animation will be
Section 3: Stepwise description of action
This section is about giving more information about the
actual animation in the LO:
Basic
information
of the LO
Information
about the
elements in this
LO
Stepwise
description of
the action to
be animated
Assessment
activities for
the users
References
•In the subsequent slides, fill out the details of the actual action in
the LO, in a stepwise format.
•You can provide an image, explaining the position of the element
groups at the start of the animation.
•You can show the change of location, size, colour or any other
attribute by creating more images for explanation.
•Write the details of the action in the table provided
•You are free to add user interactivity at any given point in the
animation, where you feel it is appropriate and required. Refer to
the Interactivity guidelines provided in the attached presentation
titled ‘interactivity options.ppt’
•Use one slide per step. This will ensure clarity of the explanation.
Project OSCAR IDD Template 4.7
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Section 3: Stepwise description of action
• A sample of step wise instructions is shown below:
Description of the action / interactivity
Audio narration
On screen text
1. Show the positions of the element groups CD, GR
and MV as shown in the image in the next slide.
2. Display temperature as in the element TM. Show
T= 4.4K.
3.Show movement of electrons along the paths
shown in the MV element group. Don’t show
the paths. (This is the fastest speed of their
movement. Show the movement of an electron
from left to right in 1 sec)
4. Show a pop up ‘Click to change the temperature‘
on the TM bar. Simultaneously highlight those
buttons
Text for the popup:
Click to change the
temperature
Click on these
buttons to change
the temperature
4a. If the user clicks on
which means ‘to go to
lower temperature‘, go to Step 2 (Slide 8)
4b. Don’t allow the user to click on
. Disable it.
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Section 3: Stepwise description of action
Sample of a supportive image for step 1
Microscopic view
Change the
temperature and
observe the
motion of
electrons in the
Microscopic view
Circuit diagram
Project OSCAR IDD Template 4.7
Graphical representation
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Step 1
Description of the action /
interactivity
Initially, show a pop up near the interactivity asking the
user to select either ‘temperature dependence’ or
‘coherence length.
Audio narration
No audio narration
On screen text
No text to be displayed.
When the user clicks on temperature dependence, go to
step 2 and let the options below ‘temperature dependence'
get clickable.
If the user clicks on Coherence length go to step 8 and at
the same time the options for Aluminium, tin and niobium
will get clickable.
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Supportive image for step 1
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Step 2
Description of the action /
interactivity
When the user has selected TD, Put a blank slide and let
the text in Fig 1 appear.
Let this slide remain for 2 seconds.
Audio narration
No audio narration
On screen text
No text to be displayed.
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.
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Supportive image for step 2
FOR TEMPERATURE:
T1>>Tc
Fig 1
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Step 3
Description of the action /
interactivity
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.
These arrows are not to be displayed on screen.
Audio narration
On screen text
No audio narration.
Show the movement of the electrons along the different
coloured arrows simultaneously.
Show this animation step for a time length of
approximately 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
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.
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Supportive image for step 3
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Step 4
Description of the action /
interactivity
Audio narration
On screen text
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.
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Supportive image for step 4
FOR TEMPERATURE:
T2>>Tc (T2<T1)
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Step 5
Description of the action /
interactivity
Audio narration
On screen text
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. These arrows are not to
be displayed on screen.
Show this animation step for a time length of
approximately 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.
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.
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Supportive image for step 5
Fig 4
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Step 6
Description of the action /
interactivity


Audio narration
On screen text
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.
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Supportive image for step 6
FOR TEMPERATURE:
T3=Tc (T3<T2)
Fig 5
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Step 7
Description of the action /
interactivity
Audio narration
On screen text
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.
When electron1 moves along the blue arrow,(don’t show
the blue arrow on screen) 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.
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 Fig6.
Show this animation step for about 2 seconds.
Show the 2 electrons getting paired by means of a dotted
elliptical shape between them, as shown in Fig7.
The atoms of the lattice remain bent as in previous slide.
Show this animation step for about 2 seconds.
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.
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Supportive image for step 7
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Supportive image for step 7
F
Fig 7
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Step 8
Description of the action /
interactivity
Audio narration
On screen text
When the user selects the radio button for ‘coherence
length’ display the text in Fig 8.
If the user selects Aluminium then go to step 11
If the user selects tin then go to step 10
If the user selects Niobium then go to step 9
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Supportive image for step 8
We will now explore the relation
between Intrinsic Coherence length
and the Cooper Pair size...
Fig 8
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Step 9
Description of the action /
interactivity
Audio narration
On screen text
Show the niobium metal sheet appearing first.
Show the animation given in step 7
Then show the double headed arrow inFig9 above
appearing along with the symbol ξ0
Then display the text given alongside.
The intrinsic coherence
length for Niobium is
3.8×10 -6cm.
Make the cooper pair move along the path shown by the
blue arrow.(blue arrow not to be displayed)
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Supportive image for step 9
Fig 9
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Step 10
Description of the action / interactivity
Audio narration
On screen text
Show the tin metal sheet appearing first.
Show the animation given in step 7.
Then show the double headed arrow inFig10 appearing
along with the symbol ξ0
Then display the text given alongside.
The intrinsic coherence
length for Tin is 23×10 -6cm.
Make the cooper pair move along the path shown by the
blue arrow.(blue arrow not to be displayed)
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2
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5
Supportive image for step 10
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4
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Step 11
Description of the action / interactivity
Audio narration
On screen text
Show the aluminium metal sheet appearing first.
Show the animation given in step 7.
Then show the double headed arrow inFig11 appearing
along with the symbol ξ0
Then display the text given alongside.
The intrinsic coherence
length for Aluminium is
160×10 -6cm.
Make the cooper pair move along the path shown by the
blue arrow.(blue arrow not to be displayed)
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2
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Supportive image for step 11
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Section 4: Assesment activities
This section is about creating assessment activities for the users of this LO :
Basic
information
of the LO
Information
about the
elements in this
LO
Stepwise
description of
the action to
be animated
Assessment
activities for
the users
References
•Create a questionnaire in the subsequent slides
•You can have minimum of 5 and maximum of 10 questions in the questionnaire
•Provide justification to be displayed, for every question
•A sample questionnaire is given below:
1. At what temperature does the sample enter the superconducting state?
Answers: a)4.4K
b)4.3K
c)4.15K
d)4.10K
Correct Answer: C
Feedback/Justification to be displayed:
If user clicks correct answer then display “Correct! Make sure you can explain the reasoning!”
If user clicks incorrect answer then display “Have a look at the animation and Try again!”
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2
3
4
5
Question 1:As the temperature decreases what happens to the
number of collisions?
Answers: a) Increase b) decrease
c) no change
d)becomes zero.
Correct answer:b
Feedback/Justification to be displayed:
• If user clicks correct answer then display_ “Correct! Make
sure you can explain the reasoning!”
• If user clicks incorrect answer then display_” Go back to
Temperature Dependence, vary the temperatures and then
try again.”__________
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2
3
4
5
Question 2: cooper pairs are formed at what temperature?
Answers: a)
above Tc
b) below Tc
c)At all times d)at
T= Tc.
Correct answer: d
Feedback/Justification to be displayed:
• If user clicks correct answer then display “Correct! Make
sure you can explain the reasoning!” _____________
• If user clicks incorrect answer then display__” Go back to
Temperature Dependence and notice the temperature at
which cooper pairs are formed. Then come back and try
again.”________
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Question 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
-6
Correct answers: 12
23
31
Feedback/Justification to be displayed:
• If user clicks correct answer then display_ “Correct! Make
sure you can explain the reasoning!” ____________
• If user clicks incorrect answer then display_” Go back to the
coherence length, observe the coherence length for the
different metals and then try again.”__________
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Question 4: For different metals, as the intrinsic coherence
length increases, what happens to the size of cooper pairs?
Answers:
a)Increases
c)remains same
b)decreases
d)becomes zero.
Correct answer: a
Feedback/Justification to be displayed:
• If user clicks correct answer then display__ “Correct! Make
sure you can explain the reasoning!” ___________
• If user clicks incorrect answer then display_ _” Go back to
the coherence length, observe the coherence length and the
corresponding size of the cooper pair for the different
metals and then try again.”__________
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2
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5
Question 5: When the cooper pairs are formed, what happens
to the shape of the lattice?
Answers:
a)bends away from the electrons
b)bends towards the electrons
c)stays as it is
d)distorts unevenly.
Correct answer: b
Feedback/Justification to be displayed:
• If user clicks correct answer then display____ “Correct! Make
sure you can explain the reasoning!” _________
• If user clicks incorrect answer then display___” Go back to
Temperature Dependence, Observe the formation of the
cooper pair carefully, then come back and try
again.”________
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Questionnaire
Explore:
What could be the effect of the value of the band gap energy(Eg),on the
existence of the cooper pair?
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Section 4: References
This section is for providing further references to the users of this LO :
Basic
information
of the LO
Information
about the
elements in this
LO
Stepwise
description of
the action to
be animated
Assessment
activities for
the users
References
•You can provide web links or other reading material
•Categorize the references as given in the next slide
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References
Website links for further reading:
http://www.msm.cam.ac.uk/doitpoms//tlplib/superconductivity/co
oper.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)
Project OSCAR IDD Template 4.7
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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.
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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.
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