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Topology and New Kinds of Order in Condensed Matter Physics

Module PH2246

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 SS 2017

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
SS 2022SS 2021SS 2020SS 2019SS 2018SS 2017

Basic Information

PH2246 is a semester module in English language at Master’s level which is offered in summer semester.

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

  • Specific catalogue of special courses for condensed matter physics
  • Focus Area Theoretical 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
  • Complementary catalogue of special courses for Applied and Engineering Physics
  • Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)

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

Total workloadContact hoursCredits (ECTS)
300 h 100 h 10 CP

Responsible coordinator of the module PH2246 in the version of SS 2017 was Frank Pollmann.

Content, Learning Outcome and Preconditions


With the discovery of the integer and fractional quantum Hall effect in the 1980s, it was realized that not all phases of matter occurring in nature can be understood using Landau’s theory. The quantum Hall state represents a distinct phase of matter which can occur even when there is no local order parameter or spontaneous breaking of a global symmetry. Phases of this new kind are now usually referred to as topological phases. This lecture course gives an introduction to different theoretical aspects of topological phases and their experimental signatures. The following topics are covered in the course: 

  • Kosterlitz–Thouless transitions
  • Graphene, Dirac Hamiltonian and Chern insulators
  • Topological insulators in 2D and 3D
  • Weyl semi-metals
  • Symmetry protected topological phases
  • Topological superconductors and Majorana chains
  • Spin liquids and frustrated magnetism
  • Axiomatic description of topological order
  • Exactly solvable models: toric code and string net models
  • Topological quantum computing

Learning Outcome

At the end of this module, the students will have an overview of the recent developments and open questions related to topological phases of matter in condensed matter physics.


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

no info


no info


  • Topological Insulators and Topological Superconductors, A. Bernevig with T. Hughes
  • Field Theories of Condensed Matter Physics, E. Fradkin
  • Quantum Field Theory of Many-Body Systems, X.-G. Wen
  • Lecture notes by John Preskill:
  • Review article by Chetan Nayak et al.:

Module Exam

Description of exams and course work

The achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using presentations independently prepared by the students. The exam of 25 minutes consists of the presentation and a subsequent discussion.

For example an assignment in the exam might be:

  • Non-local order parameters for symmetry protected topological phases
  • Experimental detection of topological edge states in ARPES experiments
  • Realization of Majorana modes in semiconductor nanowires
  • Quantum Hall states in optical lattice experiments

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

There will be a bonus (one intermediate stepping of "0,3" to the better grade) on passed module exams (4,3 is not upgraded to 4,0). The bonus is applicable to the exam period directly following the lecture period (not to the exam repetition) and subject to the condition that the student passes the mid-term of sensibly preparing at least 50% of the problems for presentation in the tutorials

Exam Repetition

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

Current exam dates

Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.

Exam to Topology and new kinds of order in condensed matter physics
Mon, 2023-10-16 till 23:59 Dummy-Termin. Wenden Sie sich zur individuellen Terminvereinbarung an die/den Prüfer(in). Anmeldung für Prüfungstermin zwischen 18.09.2023 und 21.10.2023. // Dummy date. Contact examiner for individual appointment. Registration for exam date between 2023-Sep-18 and 2023-Oct-21. till 2023-09-30 (cancelation of registration till 2023-10-09)
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