Superconductivity

Graduate school – Institute of Physics

Superconductivity

Prof. Fernando Assis Garcia

Course content:

Macroscopic properties

Microscopic properties

Lecture by lecture

Lec1: General introduction 

Historical introduction, defining properties of superconductors and materials survey.

Lecture notes / Reading:

Lec2: Magnetic properties of superconductors  

An ideal superconductor in a magnetic field, London equations and its consequences.

Lecture notes / Reading: 

Lec3:  Ginzburg-Landau  theory   I

Class description

Lecture notes / Reading: 

Lec4:  Ginzburg-Landau  theory   II, Josephson junctions

Class description

Lecture notes / Reading: 

Lec5:  Electron gas and second quantization  

In class we will discuss in detail how the excitations of the electron gas can be described by electron-hole pairs.  

Lecture notes / reading: Madelung's  Introduction to Solid State Theory, sections 2.1.1 to 2.1.4 (including) + appendix A of the same book (or any other introduction to the method of sencond quantization). 

Lecture notes / Reading:  

Lec6:  Electronic structure of crystals  

Description

Lecture notes / Reading:

Lec7: Phonons 

Lattice vibrations and their quantization (phonons), longitudinal and acoustic phonons. 

Lecture notes  / Reading: +/or Madelung's  Introduction to Solid State Theory 3.3.1 to 3.3.4 (including)

Lec8: Electron-phonon coupling 

We shall discuss the derivation of the electron-phonon Hamiltonian and the effective electron-electron interaction by exchange of phonons. 

Lecture notes / Reading: +/or Madelung's  Introduction to Solid State Theory, sections 4.1.1 and  4.1.2  or class notes. 

Lec9: The BCS theory of superconductivity 1

We shall write down the BCS Hamiltonian, discuss the formation of Cooper pairs and calculate the superconducting ground state and the excitations of the ground state.  

Lecture notes / Reading: +/or Madelung's  Introduction to Solid State Theory, sections  5.1, 5.2 ,  5.3 and 5.4

Lec10: The BCS theory of superconductivity  2  (flipped, tutorial)

We shall compare the results of the BCS to experiments and discuss the microscopic derivation of the Meissner effect. 

Lecture notes / Reading: Madelung's  Introduction to Solid State Theory, sections  5.5 and 5.6

Lec11: The BCS theory of superconductivity  3 (flipped, tutorial)

We shall compare the results of the BCS to experiments and discuss the microscopic derivation of the Meissner effect. 

Lecture notes / Reading: Madelung's  Introduction to Solid State Theory, sections  5.5 and 5.6

Lec12  Unconventional supercondutivity 1  

We shall derive the momentum dependent gap equations for unconventional pairing states in a superconductor  and discuss the gap symmetry of of cuprates.

Lecture notes / Reading: Madelung's  Introduction to Solid State Theory, sections  5.5 and 5.6

Lec13: Unconventional supercondutivity 2 

We shall discussthe generalized gap equation, includig triplet pairing, and experimental signatures of unconventional superconductivity

Lecture notes / Reading:

Lec14:   Elements of group theory

Lecture description

Class notes / Reading

Lec15:   Symmetries and unconventional superconductivity

We shall present some elements of group theory and then put it  in the perspective of superconductity. The conceptual divide between unconventional and conventional superconductors will become clear. 

Lecture notes / Reading:

Grading 

Grading will have two parts:  in class exercises (up to 30%) + term paper (up to 70%)

In class fast exercises: fast problems to fix concepts presented in each class.  This will  contribute  up to  2% for each class to your final grande.   

Guidelines for you term paper

Subjects for your paper term

Below I list the seminar subjects. If you want to talk about something else, you need my approval. Choose your subject as soon as possible and ask me for references (I will probably only indicate one specific material so you will have to search for it)

Heavy Fermion Superconductors: 

Non-centrosymmetric superconductors:  

Ferromagnetic Superconductors: 

FFLO state: 

Iron Based Superconductors

Quasi crystals and superconductors

Organic superconductors: 

Cuprate superconductors:

Problem sets

The problem sets are learning tools. You do it verify your understanding. They are not mandatory. 

Problem set I

Problem set II

Problem set III

Problem set IV

Lecture format

Mixed blackboard + power point presentation; students will de asked to discuss and solve a fast problem (30 minutes) during all lectures. 

References

Objective: in this course, we intend to provide an in-depth discussion of the phenomenon of superconductivity. We shall discuss both the macroscopic and microscopic properties of a superconductor. We aim to start from the fundamental phenomenological theories, going towards the discussion of more current topics by the end of the course. Superconductivity is one of the central problems in condensed matter physics, and education in this field is not complete without a proper course on this subject. 

Justification: Superconductivity is undoubtedly one of the central problems in condensed matter physics and is around for more than a century. Yet, many solid-state physics courses do not offer a proper introduction to this phenomenon. Here, in a series of 10 lectures, we shall present the theory and phenomenology of superconductors, having in mind that we need to fill the gap that most students have on their education in this field. Therefore, we shall start from the very beginning, discussing some of the basic properties of a superconductor, and reach the discussion of advanced topics in the field concerning unconventional superconducting states.