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Applied Superconductivity 1: from Josephson Effects to RSFQ Logic

Module PH2030

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 2022/3WS 2021/2WS 2010/1

Basic Information

PH2030 is a semester module in 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
  • Focus Area Experimental Quantum Science & Technology in M.Sc. Quantum Science & Technology
  • 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 workloadContact hoursCredits (ECTS)
150 h 60 h 5 CP

Responsible coordinator of the module PH2030 is Kirill Fedorov.

Content, Learning Outcome and Preconditions


Despite the fact that sometimes the phemomenon of superconductivity is still considered exotic, it meanwhile has a number of important practical applications. In this module, the foundations as well as the most relevant present and future applications of superconductivity are discussed, starting from what is commonly referred to as the macroscopic quantum model of superconductivity. This model is subsequently applied for the description and understanding of Josephson effects and Superconducting Quantum Interference Devices (SQUIDs). The latter are ubiquitous in various industrial and scientific applications as the most sensitive magnetic field sensors available at the moment. Finally, the application of superconducting circuits for the realization of classical digital electronics in the form of Rapid Single Flux Quantum (RSFQ) logic has attracted strong interest. RSFQ logic remains at the forefronts of modern research activities and has important impact on many other novel subfields, such as quantum information processing, where the RSFQ circuits might potentially play an important role as an interface to quantum subsystems.

Regarding the application of superconductivity in electronics and for sensors the course addresses the following topics:  

  • macroscopic quantum model of superconductivity
  • Josephson effects
  • Josephson junctions and Superconducting Quantum Interference Devices (SQUIDs)
  • Josephson vortices
  • superconducting digital electronics

Learning Outcome

After successful completion of the module the students are able to:

  • to describe and apply the physical foundations related to superconducting electronics and sensors as well as superconducting quantum devices and circuits. 
  • to explain the macroscopic quantum model of superconductivity and to apply it to the description of weakly coupled superconductors.
  • to illustrate and interprete the Josephson effects.
  • to list and explain the basic properties of Josephson junctions and Superconducting QUantum Interference Devices (SQUIDs).
  • to describe the foundations of superconducting digital electronics.


No preconditions in addition to the requirements for the Master’s program in Physics.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Learning and Teaching Methods

The modul consists of a lecture and exercise classes.

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.


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


  • Lecture notes and handouts
  • R. Gross & A. Marx, Festkörperphysik, de Gruyter, 3. Auflage (2018)
  • Tinkham: Introduction to Superconductivity
  • K. K. Likharev: Dynamics of Josephson Junctions and Circuits Gordon and Breach Science Publishers, New York (1986)
  • T. P. Orlando, K. A. Delin: Foundations of Applied Superconductivity, Addison-Wesley, New York (1991)
  • Fossheim, Sudbo: Superconductivity - Physics and Applications
  • Buckel, Kleiner: Supraleitung
  • de Gennes: Superconductivity of Metals and Alloys
  • Claude Cohen-Tannoudji: Quantum Mechanics, Volume I, Wiley-Interscience (2006)

Module Exam

Description of exams and course work

There will be an oral exam of 30 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:

  • Explain the foundations of the macroscopic quantum model of superconductivity
  • Discuss how the current-phase and energy-phase relation can be derived from the macroscopic quantum model of superconductivity
  • Show how the London equations and the fluxoid quantization can be derived from the current-phase and energy-phase relation
  • How can we describe the basic properties of weakly coupled superconductors in the framework of the macroscopic quantum model?
  • What are Josephson junctions and which basic equations can we use for their description?
  • What are the characteristic length and time scales of Josephson junctions?
  • Discuss the dynamics of Josephson junctions in the voltage state. Which equations can be used to describe their dynamics?
  • Discuss the behavior of Josephson junction in an applied magnetic field and at an applied ac voltage
  • Explain the physical foundations, the operation principle and applications of superconducting quantum interference devices

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

Exam Repetition

The exam may be repeated at the end of the semester.

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