1. Superconductivity and Superfluidity PHYS3430 Professor Bob Cywinski “Superconductivity is perhaps the most remarkable physical property in the Universe” David Pines

2. Superconductivity and Superfluidity PHYS3430 Professor Bob Cywinski “Superconductivity is perhaps the most remarkable physical property in the Universe” David Pines

3. Superconductivity and Superfluidity PHYS3430 Professor Bob Cywinski “Superconductivity is perhaps the most remarkable physical property in the Universe” David Pines

4. Superconductivity and Superfluidity PHYS3430 Professor Bob Cywinski “Superconductivity is perhaps the most remarkable physical property in the Universe” David Pines

5. Superconductivity and Superfluidity Text Books Introduction to Superconductivity A C Rose-Innes and E H Rhoderick Pergamon Press Superfluidity and Superconductivity Dr Tilley and J Tilley Institute of Physics Publishing Introduction to Superconductivity and High-T c Materials M Cyrot and D Pavuna World Scientific plus appropriate chapters in Solid State Physics books Good introduction to phenomenology, without too much maths - now quite out of date Both topics covered well, but it flips between the two topics too much and tries to draw too many analogies A good introduction, and cheap, but now hard to get Lecture 1

6. Superconductivity and Superfluidity Syllabus Lectures will focus primarily on superconductivity but the salient features of the phenomenon of superfluidity in liquid helium will be discussed towards the end of the course We shall cover the history of superconductivity and the early phenomenological theories leading to a description of the superconducting state The microscopic quantum mechanical basis of superconductivity will be described, introducing the concepts of electron pairing, leading to the BCS theory Superconductivity as a manifestation of macroscopic quantum mechanics will be presented, together with the implication for superconducting devices, such as SQUIDS An overview of the principal groups of superconducting materials, and their scientific and industrial interest will be given Lecture 1

7. Superconductivity and Superfluidity Discovery of Superconductivity Whilst measuring the resistivity of “pure” Hg he noticed that the electrical resistance dropped to zero at 4.2K Discovered by Kamerlingh Onnes in 1911 during first low temperature measurements to liquefy helium In 1912 he found that the resistive state is restored in a magnetic field or at high transport currents 1913 Lecture 1

8. Superconductivity and Superfluidity The superconducting elements Transition temperatures (K) Critical magnetic fields at absolute zero (mT) Transition temperatures (K) and critical fields are generally low Metals with the highest conductivities are not superconductors The magnetic 3d elements are not superconducting Nb (Niobium) T c =9K H c =0.2T Fe (iron) T c =1K (at 20GPa) Fe (iron) T c =1K (at 20GPa)...or so we thought until 2001 Lecture 1

9. Superconductivity and Superfluidity 19101930195019701990 20 40 60 80 100 120 140 160 Superconducting transition temperature (K) Superconductivity in alloys and oxides Hg Pb Nb NbC NbN V 3 Si Nb 3 Sn Nb 3 Ge (LaBa)CuO YBa 2 Cu 3 O 7 BiCaSrCuO TlBaCaCuO HgBa 2 Ca 2 Cu 3 O 9 (under pressure) HgBa 2 Ca 2 Cu 3 O 9 (under pressure) Liquid Nitrogen temperature (77K) Lecture 1

10. Superconductivity and Superfluidity Zero resistance? In a metal a current is carried by free conduction electrons - ie by plane waves temperature resistivity Plane waves can travel through a perfectly periodic structure without scattering….. ….but at finite temperatures phonons destroy the periodicity and cause resistance “ideal metal” T5T5 TT Take, eg, pure copper with a resistivity at room temperature of 2  cm, and a residual resistivity at 4.2K of 2  10 -5  cm ………….a typical Cu sample would thus have a resistance of only 2  10 -11  at 4.2K Even at T=0, defects such as grain boundaries, vacancies, even surfaces give rise to residual resistivity Residual resistivity “impure metal” Lecture 1

11. Superconductivity and Superfluidity Zero resistance? In a metal a current is carried by free conduction electrons - ie by plane waves Plane waves can travel through a perfectly periodic structure without scattering….. ….but at finite temperatures phonons destroy the periodicity and cause resistance Even at T=0, defects such as grain boundaries, vacancies, even surfaces give rise to residual resistivity Take, eg, pure copper with a resistivity at room temperature of 2  cm, and a residual resistivity at 4.2K of 2  10 -5  cm ………….a Cu typical sample would thus have a resistance of only 2  10 -11  at 4.2K Lecture 1

12. Superconductivity and Superfluidity Zero resistance? The resistance of pure copper is so small is there really much difference between it and that of a superconductor? Take an electromagnet consisting of a 20cm diameter coil with 10000 turns of 0.3mmx0.3mm pure copper wire R 300K = 1 k  R 4.2K = 0.01  Pass a typical current of 20 Amps through the coil P 300K = 0.4MW P 4.2K = 4 Watts At 4.2K this is more than enough to boil off the liquid helium coolant! Lecture 1

13. Superconductivity and Superfluidity Measuring zero resistance Can we determine an upper limit for the resistivity of a superconductor? This enables the decay constant of the effective R-L circuit to be measured: Using this technique, no discernable change in current was observed over two years:  sc  10 -24 .cm !! This is done by injecting current into a loop of superconductor i The current generates a magnetic field, and the magnitude of this field is measured as a function of time B Lecture 1

14. Superconductivity and Superfluidity Measuring zero resistance In practice the superconducting ring is cooled in a uniform magnetic field of flux density B A to below T C If the area of the ring is A, the flux threading the loop is BABA Cool the ring in an applied magnetic field - Now change B A : by Lenz’s law a current will flow to oppose the change, hence then decrease the field to zero Lecture 2

15. Superconductivity and Superfluidity Measuring zero resistance In practice the superconducting ring is cooled in a uniform magnetic field of flux density B A to below T C If the area of the ring is A, the flux threading the loop is Now change B A : by Lenz’s law a current will flow to oppose the change, hence In a “normal” loop, the Ri term quickly kills the current, but if R=0 Therefore Li+AB A = constant (=total flux in loop) i Currents will flow to maintain the field in the loop…. So if R=0 the current will persist forever !! forever emf

16. Superconductivity and Superfluidity …..and the corollary Li+AB A = constant (=total flux in loop) If and Ri = 0 such that The flux in the superconducting loop must remain constant however the field changes Therefore if a loop is cooled into the superconducting state in zero field and then the magnetic field is applied supercurrents must circulate to maintain the total flux threading the loop at zero. A superconducting cylinder can therefore provide perfect magnetic shielding A Meissner Shield Lecture 2