# Superconductivity and Low Temperature Physics 1

## Module PH2031

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

### Module version of WS 2022/3 (current)

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions | ||||||
---|---|---|---|---|---|---|

WS 2022/3 | WS 2021/2 | WS 2020/1 | WS 2019/20 | WS 2018/9 | WS 2017/8 | WS 2010/1 |

### Basic Information

PH2031 is a semester module in German or English language at Master’s level which is offered in winter semester.

This Module is included in the following catalogues within the study programs in physics.

- Specific catalogue of special courses for condensed matter physics
- Specific catalogue of special courses for Applied and Engineering Physics
- Complementary catalogue of special courses for nuclear, particle, and astrophysics
- Complementary catalogue of special courses for Biophysics

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workload | Contact hours | Credits (ECTS) |
---|---|---|

150 h | 60 h | 5 CP |

Responsible coordinator of the module PH2031 is Rudolf Gross.

### Content, Learning Outcome and Preconditions

#### Content

This module provides a detailed discussion of the fascinating properties and applications of superconductivity. The following specific topics will be addressed:

- history of superconductivity
- foundations (superconducting materials,superconductors in an applied magnetic field, type-I and type-II superconductors, thermodynamics of superconductors)
- phenomenological description of superconductivity (London- and Ginzburg-Landau theory)
- flux quantization, Josephson-effects, superconducting quantum interference devices
- foundation of the microscopic Bardeen-Cooper-Schrieffer theory
- critical currents of superconductors
- foundations of high temperature superconductivity
- applications of superconductivity

#### Learning Outcome

After successful completion of the module the students are able:

- to describe the the historical development of the research field of superconductivity
- to list the basic properties of superconductors and to identify their relevance for applications
- to describe the behavior of superconductors in an external magnetic field and to explain the difference between type-I and type-II superconductors
- to illustrate the thermodynamic properties of superconductors
- to present the basic ideas behind the phenomenological theories of superconductivity (London theory, Ginzburg-Landau theory) and to apply their basic results for the description of perfect conductivity, the Meißner effect, fluxoid quantization as well as the characteristic length scales of superconductors
- to explain the foundations of BCS-theory
- to describe the phenomenaon of flux pinning and to explain its relevance for the critical currents of type-II superconductors
- to describe the basic properties of high temperature superconductors
- to list the most relevant applications of superconductors

#### Preconditions

Basic knowledge on condensed matter physics and quantum mechanics.

### Courses, Learning and Teaching Methods and Literature

#### Courses and Schedule

Type | SWS | Title | Lecturer(s) | Dates | Links |
---|---|---|---|---|---|

VO | 2 | Superconductivity and Low Temperature Physics 1 | Gross, R. |
Thu, 12:00–14:00, PH HS3 |
eLearning documents |

UE | 2 | Exercise to Superconductivity and Low Temperature Physics 1 | Gross, R. | dates in groups |
eLearning documents |

#### Learning and Teaching Methods

This module consists of a lecture and an exercise course.

In the thematically structured lecture the learning content is presented by blackboard work, beamer presentation). With cross-references between different topics the universal concepts in physics are shown. The students are involved in scientific discussions to stimulate their analytic and physics-related intellectual power.

In the exercise groups the learning content is deepened and exercised using problem examples and calculations. Thus the students are able to explain and apply the learned physics knowledge independently.

#### Media

Lecture Notes, exercise sheets, supplementary literature, PowerPoint slides, movies, etc.

#### Literature

- Lecture notes and handouts
- R. Gross & A. Marx:
*Festkörperphysik*, De Gruyter Oldenbourg, (2012) - M. Tinkham:
*Introduction to Superconductivity*, Dover Publications, (2004) - K. Fossheim & A. Sudboe:
*Superconductivity: Physics and Applications*, Wiley, (2004) - W. Buckel & R. Kleiner:
*Supraleitung: Grundlagen und Anwendungen*, Wiley-VCH, (2012) - P.G. de Gennes:
*Superconductivity of Metals and Alloys*, Westview Press, (1999)

### Module Exam

#### Description of exams and course work

There will be an oral exam of 25 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

For example an assignment in the exam might be:

- What are the fundamental properties of superconductors?
- Which families of superconducting materials do you know and what are the maximum transition temperatures within these families?
- Describe the difference between an perfect conductor and a superconductor.
- What are the two London equations, how can they be derived and which properties of superconductors do they describe?
- Explain the flux quantization in multiply-connected superconductor. How has flux quantization been measured and what can be learnt from the experimental result?
- Describe the thermodynamic properties of superonductors (magnetization, entropy density and specific heat) and sketch their phase diagram.
- Discuss the difference between type-I and type-II superconductors. What are their characteristic magnetic fields?
- What are the characteristic length scales of superconductors and what is their meaning?
- What is the isotope effect of superconductors and what can be learnt from it?
- How can an attractive interaction between two conduction electrons emerge in metals?
- What are the possible symmetries of the pair wave function?
- Describe the foundations of the BCS theory.
- What is a Josephson junction? What are the basic equations describing their properties?
- Discuss the critical current density of type-I and type-II superconductors.
- Discuss the characteristic properties of cuprate superconductors.

Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.

#### Remarks on associated module exams

The exam for this module can be taken together with the exam to the associated follow-up module
PH2032: Supraleitung und Tieftemperaturphysik 2 / *Superconductivity and Low Temperature Physics 2*
after the follwoing semester. In this case you need to register for *both* exams in the following semester.

#### Exam Repetition

The exam may be repeated at the end of the semester. There is a possibility to take the exam in the following semester.