| Course title | |||||
| 超伝導工学 [Advanced Superconductivity] | |||||
| Course category | courses for master's programs | Requirement | Credit | 2 | |
| Department | Year | ～ | Semester | Fall | |
| Course type | Fall | Course code | 1060410 | ||
| Instructor(s) | |||||
| 内藤 方夫 [NAITO Michio] | |||||
| Facility affiliation | Faculty of Engineering | Office | Email address | ||
| Course description |
| “Superconductivity” is a phenomenon of metals to lose electrical resistance at low temperatures. The phenomenon was discovered in 1911 by Kamerlingh Onnes, University of Leiden, but it took approximately 50 years to explain this phenomenon microscopically by the Bardeen, Cooper, and Schrieffer (BCS) theory, based on the formation of Cooper pairs. As inferred from this history, the "BCS” theory, which is the quintessence of superconductivity, is not to easy to understand. The reasons for the difficulty of understanding are firstly to require of the field theory via the second quantization as a tool for exact analytical description, and secondly to imagine the macroscopically coherent quantum state as a consequence of the theory. “Advanced superconductivity” as a course for master’s degree covers the elemental understanding of the phenomenon as superconductivity as well as the essence of the BCS theory. |
| Expected Learning |
| Course schedule |
|
Chapter 1 What is superconductivity? (week 1) Superconducting materials (elemental superconductor, compound superconductor and oxide superconductor) (week 2) Zero resistivity and Meissner effect, critical fields (week 3) Thermodynamics of superconducting transition, Landau theory for the second-order phase transition (analogy between magnetic/dielectric and superconducting transitions) (week 4) What is the order parameter (= mysterious physical quantity) in the normal-to-superconducting phase transitions? The answer is the phase of the macroscopic quantum wave function. Ginzburg-Landau theory Chapter 2 Electrons and phonons - electron-phonon interaction (week 5, 6) Electrons in a metal (free electron model, many-body Schroedinger equation based on the 2nd quantization expression, creation and destruction operators and anti-commutation relationship for Fermion, Fermi-Dirac statistics and distribution, Fermi energy, dielectric response and screening of electrons) (week 7, 8) Phonons (harmonic oscillator Hamiltonian based on the second quantization expression, phonon-quantization of lattice vibration, Bose statistics and distribution, commutation relationship for bosons) (week 9, 10) Electron-phonon interaction (derivation of the Froehlich Hamiltonian based on the Poisson equation, lattice resistivity, attraction between two electrons via exchange of a phonon-Cooper pairing) Chapter 3 BCS theory (week 11) BCS model: the Hamiltonian to describe the Cooper pair formation. (week 12, 13) Ground state of the BCS Hamiltonian: the BCS ground state does not preserves the number of electrons but makes the quantum phase coherent of electrons macroscopically. The energy gap to dissociate Cooper pairs, the expression of critical fields, etc. are naturally derived. The excited state is also derived from BCS Hamiltonian using the Bogoljubov transformation. (week 14, 15) Bose-Einstein condensation, Glauber expression for the coherent state, uncertainty between the particle number and the quantum phase. |
| Prerequisites |
| Electromagnetics I, II, Thermodynamics and Statistical Mechanics, Quantum mechanics I, II, Solid State Physics I, II are desirable, although not prerequisite, to have completed. |
| Required Text(s) and Materials |
| References |
|
M. Tinkham, “Introduction to Superconductivity: Second Edition”, (Dover Books on Physics) P. G. de Gennes, “Superconductivity of Metals and Alloys”, (Westview Press) S. Nakajima, “Introduction to Superconductivity”, (Shokabo Co., Ltd., written in Japanese) Charles Kittel, “Introduction to Solid State Physics”, (John Wiley and Sons, Inc., New York) |
| Assessment/Grading |
| Midterm tasks (twice) (30% x 2), final exam (40%). |
| Message from instructor(s) |
| The phenomena and theory of superconductivity is not easy tolearn. The passion for superconductivity and strong mind for understanding it are required. |
| Course keywords |
| Superconductivity, Cooper pair, Bardeen-Cooper-Schrieffer theory, Electron-phonon interaction, Bose-Einstein condensation |
| Office hours |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Language Subject |
| Last update |
| 9/21/2018 8:18:10 AM |