Electrical Resistivity in Superconductors The electrical resistivity of many metals and alloys drops suddenly to zero when the specimen is cooled to a sufficiently low temperature. This phenomenon is known as Superconductivity. Course Name: Superconductivity Author/s Anura Kenkre Sameer Sahasrabudhe

Learning objectives After interacting with this Learning Object, the learner will be able to: – Explain the meaning of electrical resistivity in superconductors. – Predict the effect of temperature changes on the electrical resistivity of superconducting samples

Definitions and Keywords The electrical resistivity of many metals and alloys drops suddenly to zero when the specimen is cooled to a sufficiently low temperature. This phenomenon 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. Add more slides if required

Master Layout:A: Circuit diagram Ammeter Temperature Control Voltmeter Ammeter reading Voltmeter reading Temperature reading Slide only for reference::NOT TO BE ANIMATED

Master Layout:B: Visual representation Path on which the electrons are moving Slide only for reference::NOT TO BE ANIMATED

Master Layout:C: Graph Blinking red dot denoting: Temperature Slide only for reference::NOT TO BE ANIMATED

Instructions/ Working area Credits Tab 02Tab 03Tab 04Tab 05Tab 06Tab 07Introduction Graphical representation Change the temperature and observe the motion of electrons in the Microscopic view Microscopic view Electrical Resistivity in Superconductors 1

mA Voltmeter Superconducting Sample placed in cryostat for cooling T=4.3K Instructions/ Working area Credits Tab 02Tab 03Tab 04Tab 05Tab 06Tab 07Introduction Graphical representation Microscopic view Electrical Resistivity in Superconductors 2

mA Voltmeter Superconducting Sample placed in cryostat for cooling T=4.2K Instructions/ Working area Credits Tab 02Tab 03Tab 04Tab 05Tab 06Tab 07Introduction Graphical representation Microscopic view Electrical Resistivity in Superconductors 3

mA Voltmeter Superconducting Sample placed in cryostat for cooling T=4.15K Instructions/ Working area Credits Tab 02Tab 03Tab 04Tab 05Tab 06Tab 07Introduction Graphical representation Microscopic view Electrical Resistivity in Superconductors 4

Analogy / Scenario / Action Slide only for reference::NOT TO BE ANIMATED

Step 1: Audio Narration (if any) ‏ Text to be displayed (if any) ‏ (DT) Description of the Action / Interactivity T1: Title of the step, to appear as heading of the screen (if any) ‏ Screen as shown in Slide Show the Animation design screen (Slide 7) 2.The temperature meter shows T= 4.4K as shown. 3.The electrons are seen moving in the 'microscopic view window. (They are at their fastest speed at this setting) 4.A pop up will appear on the ‘Click to change the temperature' – If the user clicks on ‘click to go to lower temperature', go to Step 2 (Slide 8) – If the user to clicks 'click to go to higher temperature', show the feedback pop-up 'Making it more would be...so try to lower it'. Click on these buttons to change the temperature

Step 1: Audio Narration (if any) ‏ Text to be displayed (if any) ‏ (DT) Description of the Action / Interactivity T1: Title of the step, to appear as heading of the screen (if any) ‏ Display this if the temperature is lowered:If the temperature is lowered, you can se that the electrons move slower. 1.Show the changes in A, B and C as per the slide numbers:8, 9, 10 2.Keep the unit of change to 0.5, and decrease the speed of the electrons respectively. – Ex: 4.4, 4.35, 4.3, 4.25, 4.2, 4.15, 4.1, 4.05, 4.0, 3.95, 3.9, etc 3.Show the appropriate feedback, based on the temperature selected by the user – Ex: for all the settings above 4.4, display: – For all the settings below 4.15, display: Screen as shown in Slide 7

Step 1: Audio Narration (if any) ‏ Text to be displayed (if any) ‏ (DT) Description of the Action / Interactivity T1: Title of the step, to appear as heading of the screen (if any) ‏ Set the specific limit for the interactivity to --- attempts. Ensure the correctness of the 'feedback' to be displayed for every attempt which is OUTSIDE the chosen range for this particular sample – Ex: 4.4 to After the ---attempts. Display a box with: 'Answer the questions in the following questionnaire to test your understanding' 3.Change the screen to the animation design slide number XX and display the questionnaire. Screen as shown in Slide 7

Step 1: Audio Narration (if any) ‏ Text to be displayed (if any) ‏ (DT) Description of the Action / Interactivity T1: Title of the step, to appear as heading of the screen (if any) ‏ Display appropriate feedback for the answers submitted by the user. 2.After the user finishes the questionnaire, display the summary as given in slide XX Screen as shown in Slide 7

Step 1: Audio Narration (if any) ‏ Text to be displayed (if any) ‏ (DT) Description of the Action / Interactivity T1: Title of the step, to appear as heading of the screen (if any) ‏ Display appropriate feedback for the answers submitted by the user. 2.After the user finishes the questionnaire, display the summary as given in slide XX Screen as shown in Slide 7

Instructions for the animator Instruction to the learner Results and Output Boundary limits Interactivity type Interactivity option 1: Step No: 1 Image/graphic for explaining the interactivity options Interactivity options in this animation is already explained in STEPS earlier. 2.Please follow them Lowest for showing animation in 'B' is ______ Highest for showing animation in 'B'is ______

Questionnaire: The questions along with the answer options are given in the next few slides Justification is also provided for the incorrect answers, which has to be displayed in case the user selects incorrect answers. APPENDIX 1

Links for further reading Reference websites: Books: Introduction to Solid state physics-Charles Kittel(Chapter 12) Solid state physics-MA Wahab.(Chapter 17) Solid state physics-Ashcroft/Mermin. (Chapter 34) APPENDIX 2

20 Questionnaire 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 Answers: 1)C Feedback: 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! ”

21 Questionnaire 2. What happens to the resistivity of the sample as the temperature decreases? Answers: a)increases b)decreases c)remains same d) ‏ becomes zero Correct Answers: 2)b Feedback: 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! ”

22 Questionnaire 3. What happens to the resistivity of the sample at the transition temperature? Answers: a)increases b)decreasesc)remains same d) ‏ becomes zero Correct Answers: 3)d Feedback: 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! ”

23 Questionnaire 4. What happens to the resistivity of the sample below the transition temperature? Answers: a)returns to normalb)decreases furtherc)it is zerod) ‏ increases a lot. Correct Answers: 4)c Feedback: 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! ”

24 Questionnaire 5. What happens to the number of collisions between the electron and the atoms of the lattice as the temperature decreases? Answers: a)increasesb)decreases c)remains constant d) ‏ becomes zero. 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 “Have a look at the animation and Try again! ”

Questionnaire What happens to the electrons when the material enters the superconducting state? Answers: a)each electron flows through the sample without any resistance b)each electron flows through the sample with lot of resistance c)Two electrons pair up and flow together through the sample without any resistance. d)Two electrons pair up and flow through the sample with lot of resistance. Correct Answers: 6)c Feedback: If user clicks on correct answer then display ”Yes !The electrons pair up and flow through the sample together. These pair of electrons are known as Cooper Pairs. Have a look at the animation on Cooper Pairs to get a better understanding of this concept.” If user clicks incorrect answer then display “Have a look at the animation and Try again!”

Summary When you reduce the temperature sufficiently, certain metals conduct electricity without any resistance. This phenomenon is known as Superconductivity. The resistivity of the metals goes on reducing as you lower the temperature and becomes zero at the superconducting transition temperature. The temperature at which the transition to the superconducting state takes place is called the critical temperature(Tc)or the superconducting transition temperature. When the metal enters the superconducting state, the electrons in the metal pair up and flow through the sample together. These pair of electrons are known as Cooper Pairs. APPENDIX 3