Information of the LO 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 Project OSCAR IDD Template 4.7

Learning objectives After using this LO the user should be able to: 1.Describe the formation of a cooper pair. 2.Explain the relation between the intrinsic coherence length and the size of a cooper pair Project OSCAR IDD Template 4.7

Element groups in this LO Name of the element groupName of the elements in the group Importance in the LO [1: highest, 5: lowest] Microscopic ViewElectrons 1 Atoms Control panelTemperature control panelButton 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

Microscopic view Project OSCAR IDD Template 4.7

Temperature control panel Project OSCAR IDD Template 4.7

Panel for coherence length selection Project OSCAR IDD Template 4.7

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 This section is about giving more information about the actual animation in the LO : 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. Section 3: Stepwise description of action 7Project OSCAR IDD Template 4.7

A sample of step wise instructions is shown below: Description of the action / interactivityAudio narrationOn 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) Text for the popup: Click to change the temperature 4. Show a pop up ‘Click to change the temperature‘ on the TM bar. Simultaneously highlight those buttons 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. Section 3: Stepwise description of action 8Project OSCAR IDD Template 4.7

Sample of a supportive image for step 1 Graphical representation Change the temperature and observe the motion of electrons in the Microscopic view Microscopic view Circuit diagram Section 3: Stepwise description of action 9Project OSCAR IDD Template 4.7

Step 1 Description of the action / interactivity Audio narrationOn screen text Initially, show a pop up near the interactivity asking the user to select either ‘temperature dependence’ or ‘coherence length. No audio narration 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 Project OSCAR IDD Template 4.7

Supportive image for step Project OSCAR IDD Template 4.7 SELECT

Step 2 Description of the action / interactivity Audio narrationOn screen text 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. No audio narration 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 Project OSCAR IDD Template 4.7

Supportive image for step Project OSCAR IDD Template 4.7 FOR TEMPERATURE: T 1 >>T c Fig 1

Step 3 Description of the action / interactivity Audio narrationOn screen text 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. 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 Project OSCAR IDD Template 4.7

Supportive image for step Project OSCAR IDD Template 4.7

Step 4 Description of the action / interactivity Audio narrationOn 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 step Project OSCAR IDD Template 4.7

Supportive image for step Project OSCAR IDD Template 4.7 FOR TEMPERATURE: T 2 >>T c (T 2 <T 1 )

Step 5 Description of the action / interactivity Audio narrationOn 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 step Project OSCAR IDD Template 4.7

Supportive image for step Project OSCAR IDD Template 4.7 Fig 4

Step 6 Description of the action / interactivity Audio narrationOn 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 Project OSCAR IDD Template 4.7

Supportive image for step Project OSCAR IDD Template 4.7 FOR TEMPERATURE: T 3 =T c (T 3 <T 2 ) Fig 5

Step 7 Description of the action / interactivity Audio narrationOn 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 Project OSCAR IDD Template 4.7

Supportive image for step Project OSCAR IDD Template 4.7

Supportive image for step Project OSCAR IDD Template 4.7 F Fig 7

Step 8 Description of the action / interactivity Audio narrationOn 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 Project OSCAR IDD Template 4.7

Supportive image for step Project OSCAR IDD Template 4.7 We will now explore the relation between Intrinsic Coherence length and the Cooper Pair size... Fig 8

Step 9 Description of the action / interactivity Audio narrationOn 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 ξ 0 Then display the text given alongside. The intrinsic coherence length for Niobium is 3.8× cm. Make the cooper pair move along the path shown by the blue arrow.(blue arrow not to be displayed) Project OSCAR IDD Template 4.7

Supportive image for step Project OSCAR IDD Template 4.7 Fig 9

Step 10 Description of the action / interactivityAudio narrationOn 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 ξ 0 Then display the text given alongside. The intrinsic coherence length for Tin is 23× cm. Make the cooper pair move along the path shown by the blue arrow.(blue arrow not to be displayed) Project OSCAR IDD Template 4.7

Supportive image for step Project OSCAR IDD Template 4.7

Step 11 Description of the action / interactivityAudio narrationOn 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 ξ 0 Then display the text given alongside. The intrinsic coherence length for Aluminium is 160× cm. Make the cooper pair move along the path shown by the blue arrow.(blue arrow not to be displayed) Project OSCAR IDD Template 4.7

Supportive image for step Project OSCAR IDD Template 4.7

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 This section is about creating assessment activities for the users of this LO : 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: Section 4: Assesment activities 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!” 33Project OSCAR IDD Template 4.7

Question 1: As the temperature decreases what happens to the number of collisions? Answers: a)Increaseb)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.”__________ Project OSCAR IDD Template 4.7

Question 2: cooper pairs are formed at what temperature? Answers: a)above T c b)below T c c)At all timesd) ‏ at T= T c. 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.”________ Project OSCAR IDD Template 4.7

Question 3: Match the following: 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.”__________ Project OSCAR IDD Template 4.7 metal Intrinsic coherence length (cm) 1)Aluminium(Al) 1) 3.8 × )Tin(Sn) 2)160 × )Niobium(Nb) 3)23× 10 -6

Question 4: For different metals, as the intrinsic coherence length increases, what happens to the size of cooper pairs? Answers:a)Increasesb)decreases c)remains samed)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.”__________ Project OSCAR IDD Template 4.7

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 electronsc)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.”________ Project OSCAR IDD Template 4.7

Questionnaire Explore: What could be the effect of the value of the band gap energy(Eg),on the existence of the cooper pair?

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 This section is for providing further references to the users of this LO : You can provide web links or other reading material Categorize the references as given in the next slide Section 4: References 40Project OSCAR IDD Template 4.7

References Website links for further reading: oper.php 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

INSTRUCTIONS SLIDE 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. Summary 42

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. 43