Low temperature physics The Home page. aqpl.mc2.chalmers.se/~delsing/superconductivity

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1 The Home page aqpl.mc2.chalmers.se/~delsing/superconductivity

2 Info about the course The course treats three closely related topics: Superconductivity, superfluid helium, and cryogenics The course gives 7.5 ECTS credits and runs in the third quarter Schedule Tuesdays Wednesdays Fridays The Book: J.R. Waldram "Superconductivity of Metals and Cuprates A few e-books are also available Laborations: There will be two laborations: Josephson Effect and Superfluid Helium, You should deliver a written report after each laboration. Exam, Wednesday March 15, There is a written exam at he end of the course. Typically there are 10 short questions to test the understanding of basic concepts, and then there are 5-6 problems.

3 Contents of the Course SUPERCONDUCTIVITY Introduction to Superconductivity, demonstration, phenomenology Thermodynamics of superconductors Electromagnetics of superconductors, the London equations GL-theory, Superconductors in magnetic field GL-theory, Vortex, SN interfaces Microscopic theory, 2nd quantization, BCS BCS, Density of states, energy gap Josephson effects, Tunneling Superconducting devices, overview High temperature superconductors SUPERFLUIDITY Introduction to superfluids, Helium-4, two-fluid model Bose Einstein condensation, superfluid phenomena Helium-3 Fermi liquid and superfluidity CRYOGENICS Low temperature properties of materials Cooling, principles, liquification Cooling methods T< 1K, Thermometry Two laborations Weekly hand in excercises

4 The Book J.R. Waldram: Superconductivity of Metals and Cuprates Available e-books V.V. Schmidt: The Physics of Superconductors Introduction to Fundamentals and Applications C.P. Poole: Superconductivity (3rd Edition) M. Tinkham: Introduction to Superconductivity (2nd Edition) W. Buckel, R. Kleiner: Superconductivity: An introduction (2016)

5 Schedule Lectures Tuesdays Wednesdays Fridays Preliminary schedule for FMI036 Superconductivity and Low Temperature Physics 2017 Low temperature physics 2004 Calendar Study Date Time Lect Room Contents Waldram Tinkham Schmidt Poole Teacher Week Week. Tu Kollektorn SC1 Introduction to SC, demonstration Ch.1, Ch.1 Ch.1 Ch. 2-3 PD 3 1 W Kollektorn SC2 Phenomenology, 2-fluid model, Thermodynamics Ch.1, Ch.1, 5 Ch.1 Ch. 4-5 PD Fr Fasrummet SC3 Electromagnetics of SCs London equations Ch Ch.2 Ch.2 Ch. 6,11,12,14 PD Tu NO LECTURE 4 2 W NO LECTURE Fr Kollektorn SC4 GL-theory, SCs in magnetic field Ch.3, 4 Ch.4 Ch.3 Ch. 6,11,12,14 PD Tu Kollektorn SC5 GL-theory, Vortex, SN interfaces, Ic Ch.3, 4 Ch.4 Ch.3, 5 Ch. 6,11,12,14 PD 5 3 W Kollektorn SC6 Microscopic theory, 2nd quantization, BCS Ch.7, 8, App. A Ch.3 Ch. 6 Ch. 7,15 PD Fr Kollektorn SC7 BCS, Density of states, Excitations Ch.7, 8, App. A Ch.3 Ch. 6, Ch. 7,15 PD Tu Kollektorn NO LECTURE 6 4 W Kollektorn NO LECTURE Fr Kollektorn SD1 Josephson effects, Tunneling Ch.6, Ch Ch.3 Ch. 4 Ch. 15. PD Tu Kollektorn SD2 Squids and superconducting devices Ch.6, Ch Ch.6, 7 Ch. 15 Ch. 15 PD 7 5 W NO LECTURE Th F4202/C509 Lab1&2 Laboration 1&2 CP/GA Fr Kollektorn HTS1 High temperature superconductors Ch Ch. 9 Ch. 8 AK Tu Kollektorn HTS2 High temperature superconductors Ch Ch. 9 Ch. 8 AK W Kollektorn 4He 1 Introduction: Review superfl.4he PD 8 6 Th F4202/C509 Lab1&2 Laboration 1&2 CP/GA Th F4202/C509 Lab1&2 Laboration 1&2 CP/GA Fr Kollektorn 4He 2 4He: condensate and excitations, 2-fluid model PD Tu Kollektorn 3He 3He: Fermi liquid and superfluidity PD 9 7 Tu F4202/C509 Lab1&2 Reserve time CP/GA W Kollektorn Cryo1 Cooling methods, liquification, Thermometry PD Fr Kollektorn Cryo2 Low temperature properties of materials, lab visit Ch.1 PD Tu NO LECTURE 10 8 W NO LECTURE Fr Kollektorn Summary Questions, Exam examples PD 11 9 W Exam

6 Examination The course ends with a written exam in study week 9 (calendar week 11) Time: Tuesday, March 15, Reexams Early-April and Mid-August The following aids are allowed: Tefyma, Physics Handbook, Stand Math Tables or similar, Calculator. A formula sheet will be distributed with the exam. Problem 1 consists of 10 short questions (10p) to test the understanding of basic concepts. For Problem 2-6 you need to calculate or explain something in more detail (20p). Max points: 30p. Grading: Grade 3: 15p in total and at least 5p on problem 1 Grade 4: 20p in total and at least 5p on problem 1 Grade 5: 25p in total and at least 5p on problem 1 You can also earn extra points by handing in home problems (see: Exercises).

7 Exercises During the course you are expected to solve a number of exercises. In total 6 problems. If you hand in correctly solved problems you will earn points on the exam. The problems are posted on the web page. The deadline for handing in the solutions is Friday the week after. Send the solved problems as pdf-files by to Ida-Maria Svensson (ida-maria.svensson@chalmers.se) or hand in to Per at one of the lectures. In total there will be 30 points on the exam, if you hand in x solved exercises you get: 0.75 x points extra towards the grade 3 (15 points needed) 0.50 x points extra towards the grade 4 (20 points needed) 0.25 x points extra towards the grade 5 (25 points needed)

8 Heike Kamerlingh-Onnes Leiden 1908: Liquefication of He 1911: Superconductivity Low temperature physics 2004

The generated field is equal in size to the external field and thus cancel the external field. Thus B=0.

9 Superconductivity, R=0, B=0 When you apply an external magnetic field to a metal circulating currents are generated via induction, so called Eddy currents. These currents generates in turn a magnetic field which is oriented in the opposite direction compared to the external field. The generated field is equal in size to the external field and thus cancel the external field. Thus B=0. However for a normal metal there is always resistance which will eventually damp out the circulating currents, and therefore B 0 in a normal metal. For a superconductor which has no resistance B is in fact zero.

The Meissner effect, B=0 B = µ 0 ( H + M ) = µ 0 µ r

current generates the M-field När man lägger på ett

somm I sin tur generer ett motriktat magnetfält.

10 The Meissner effect, B=0 B = µ 0 ( H + M ) = µ 0 µ r H = µ 0 ( 1+ χ)h Superconductor: The screening current generates the M-field När man lägger på ett extern magnet fält M = H, χ = på en metall genereras via M H induktion = 1 alltid i.e. the superconductor is a perfect diamagnet en ström, somm I sin tur generer ett motriktat magnetfält. Detta fält blir lika stort men motsatt riktat och tar ut det externa fältet exakt.

Difference between perfect conductor and superconductor Zero resistance, or perfect conductivity, is not the entire story with superconductors.

11 Difference between perfect conductor and superconductor Zero resistance, or perfect conductivity, is not the entire story with superconductors. Perfect conductivity does not explain the Meissner effect, whereby magnetic flux is expelled from the interior of superconducting materials by screening currents, even if the flux was present before the material became superconducting. Thus a superconductor is not only a perfect conductor but also a perfect diamagnet. Perfect conductor B/ t=0 Can be derived from R=0 Superconductor B=0 Stronger statement

12 Difference between perfect conductor and superconductor Perfect conductor B/ t=0 Superconductor B=0

13 A levitating magnet Low temperature physics 2004

14 Levitating things Low temperature physics 2004

15 The periodic table which elements are superconductors Low temperature physics 2004 Which elements are SC: Nb, Ta, Pb, Sn, In, Al, Nb highest T C =9.2K Two regions in the periodic table Which elements are not superconducting, Alkali, rare earth, magnetic, and coin metals, Why are good conductors such as Cu, Ag, not SC, whereas more resistive metals such as Pb and Sn are? This indicates that the mechanism has something to do with electron phonon scattering

16 Parameters for Superconductors Low temperature physics 2004 Tc Density λ ξ κ 2Δ Hc Θ Debey γ K kg/l nm nm mev Gauss K mj/mol/k Nb 9,25 8, ,03 3, , ,8 Pb 7,196 11, ,45 2, ,0 96 3,1 V 5,4 6,11 1, , ,82 Ta 4,47 16,65 1, , ,15 Sn 3,722 7, ,16 1, , ,78 In 3,408 7, ,05 1, , ,67 Re 1,697 21,01 0, , ,35 Al 1,175 2, ,01 0, , ,35 Ga 1,083 5,91 0,328 58, ,6 Mo 0,915 9,01 0,277 96, ,83 Zn 0,85 7,13 0,257 54, ,66 Zr 0,61 6,51 0,185 47, ,77 Cd 0,517 8, ,15 0,157 28, ,69 Ti 0,4 4,57 0,121 56, ,3 Hf 0,126 13,31 0,038 12, ,21 W 0,015 19,3 0,005 1, ,9

17 A15 Superconductors Nb 3 Ge Nb 3 Si Nb 3 Sn Nb 3 Al V 3 Si Ta 3 Pb V 3 Ga Nb 3 Ga V 3 In 23.2 K 19 K 18.1 K 18 K 17.1 K 17 K 16.8 K 14.5 K 13.9 K

1986: High Tc Superconductors, Cuprates 1986:

18 1986: High Tc Superconductors, Cuprates 1986: Bednorz Müller LaBaCuO 36K 1987: Paul Chu YBa 2 Cu 3 O 7 93K 1988: Bi 2 Sr 2 Ca 2 Cu 3 O x 110K Tl 2 Ba 2 Ca 2 Cu 3 O K HgBa 2 Ca 2 Cu 3 O 8 135K Sn 1.4 In 0.6 Ba 4 Tm 5 Cu 7 O K 2001: MgB 2 39K The Breakthrough 1986

19 2001: Superconductivity in MgB 2 From Jochen Mannhart (Lecture Saas Fee) found in 2001 by J. Akimitsu Mg B T c = 39 K J. Akimitsu From Jochen Mannhart (Lecture Saas Fee)

2008: Superconductivity in Ferro Pnictides Bulk SC in Ba 0.6 K 0.4 Fe 2 As 2 T c = 56 K 80 70 This morning (Gd,Th)OFeAs T c =56.

20 2008: Superconductivity in Ferro Pnictides Bulk SC in Ba 0.6 K 0.4 Fe 2 As 2 T c = 56 K This morning (Gd,Th)OFeAs T c =56.3K RE 3+ TM 2+ O 2- Pn 3- La Pr Nd Gd Sm Fe Ni O F As P T C [K] /01/ /04/ /07/2006 Sm(O,F)FeAs Pr(O,F)FeAs and Nd(O,F)FeAs La(O,F)FeP LaOFeP La(O,F)FeAs La(O,F)FeAs LaONiP GdFeAsO(1-d) Sm(O,F)FeAs Gd(O,F)FeAs (La,Sr)OFeAs From Jochen Mannhart (Lecture Saas Fee) 28/10/ /02/ /05/ /08/ /12/ /03/ /06/ /09/ /01/2009

21 2015: Superconductivity in H 2 S at high pressure H2S is responsible for the smell of rotten eggs T c = Mbar = 155 GPa From Jochen Mannhart (Lecture Saas Fee)

Theories of Superconductivity Two fluid model, Phenomenological One fluid with super electrons and

superconductor, based on the two fluid model Ginzburg Landau Theory GL describes phase

BCS Theory, Microscopic Theory Describes a quantum mechanical ground state for the superconducting

22 Theories of Superconductivity Two fluid model, Phenomenological One fluid with super electrons and one fluid with normal electrons, n S, n n London equations Describes electromagnetics of the superconductor, based on the two fluid model Ginzburg Landau Theory GL describes phase transitions, Strictly speaking only valid close to Tc but it work pretty well also at lower T. BCS Theory, Microscopic Theory Describes a quantum mechanical ground state for the superconducting condensate. No theory for High-Tc Superconductors yet. Lev Landau Vitaly Ginzburg Bardeen, Cooper och Schrieffer - BCS

23 Superconductivity, R=0, B=0 Electromagnetic properties of Superconductors (SC) R=0, Critical temperature T c B=0, Meissner effect, screening currents, Penetration depth l. Maximum Magnetic field: The critical field H c and its temperature dependence, T,H,I surface

24 Superconductivity, Thermal Properties Specific heat C p has a discontinuity at T c, jump in C p indicates phase transition Heat conductivity graph, perfect electrical conductor very poor thermal conductor, The electronic part of the heat conductivity k decreases rapidly below Tc, this indicates an energy gap for excitations, =1,76 k B T C,

25 Type I vs. Type II Superconductors Magnetization Type I: Either Superconducting or Normal B=0 up to Hc Positive SN interface energy => minimize number of interfaces Intermediate state, few domains Type II: B=0 up to Hc1, gradually increasing up to Hc2 Negative SN interface energy, Mixed state between Hc1 and Hc2, many domains

Superconductivity and Quantum Coherence

Superconductivity and Quantum Coherence Lent Term 2008 Credits: Christoph Bergemann, David Khmelnitskii, John Waldram, 12 Lectures: Mon, Wed 10-11am Mott Seminar Room 3 Supervisions, each with one examples