Condensed Matter 2

Owner	Bachelor Natuur- en Sterrenkunde (joint degree)
Coordinator	dr. Erik van Heumen
Part of	Minor Natuurkunde en Sterrenkunde: Advanced Physics, year 1Minor Physics and Astronomy: Energy and Sustainability, year 1Exchange Programme Faculty of Science, specialisation BSc Physics and Astronomy, year 1Dubbele bachelor Wis- en Natuurkunde, year 3Bachelor Bèta-gamma, major Natuurkunde, year 3Bachelor Physics and Astronomy (Joint Degree), year 3

Course manual 2021/2022

Course content

The quantum mechanical understanding of solids forms the basis for the technological explosion that is currently unfolding around us. Apart from this great societal importance, solids also harbor a secret world of physical miracles unrealized anywhere else in nature. From magnetic monopoles to M-theory black holes, it all emerges from the immense complexity of a near infinite number of interacting electrons. The overall aim of this course is to provide you with a solid understanding (pun intended) of basic and more advanced topics in contemporary condensed matter physics.

After a brief recap of some basic concepts from GM-1 we dive into the electronic structure of solids using the so-called tight binding approximation. With this scheme we can understand the basic electronic properties of any solid. We make a detour into the optical properties of solids to see how everyday colors around us come to be and how these can be explained using the electronic structure of solids. We then turn our attention to the complexity of interacting electrons under the influence of quantum mechanics. We will see how different manifestations of the electromagnetic interaction result in ordered electronic states, such as magnets and superconductors. During the course we will also touch upon the role of fundamental symmetries and how these provide a basis for understanding phase transitions between differently ordered states.

Study materials

Syllabus

• Syllabus

Objectives

• After the course the student has a working understanding of the basic principles of the physics of solids.
• The student is able to explain basic band structure concepts (such as reciprocal spaces, density of states and the Fermi surface).
• The student is able to use these concepts to explain the differences between metals, semi-conductors and insulators.
• The student is able to use a ‘central’ equation to derive the electronic structure of simple solids. 
• The student is able to explain the optical properties of solids using the Drude-Lorentz model.
• The student is able to link the semi-classical Drude-Lorentz model to the electronic structure of solids.
• The student is able to explain the origin of colors of solids.
• The student is able to explain why some materials are transparent and others opaque
• The student is able to explain different forms of magnetic order (paramagnetism, ferromagnetism en anti-ferromagnetism).
• The student can name qualitative differences between these orders based on the temperature dependence of the magnetic susceptibility.
• The student is able to derive a criterion for the occurrence of spontaneous magnetisation (Stoner’s criterion for ferromagnetism).
• The student is able to calculate the spinwave spectrum of ferro- and anti-ferromagnets.
• The student can explain the low temperature behaviour of the magnetisation using spinwave theory.
• At the end of the course the student is able to provide a qualitative explanation of superconductivity
• At the end of the course the student is able to explain important propertie of superconductors (perfect diamagnetism, zero resistance) in terms of the penetration depth and the superconducting gap.

Teaching methods

• Lecture
• Seminar
• Self-study

Lectures and exercise classes. There will also be a number of pre-recorded derivations. 

Learning activities

Attendance

Programme's requirements concerning attendance (TER-B):

• Each student is expected to participate actively in each component of the programme that he/she signed up for. A student that does not attend the first two seminars of a course, will be administratively removed from the seminar group. A request for reregistration for the seminars can be applied to the programme coordinator.
• If a student cannot attend an obligatory component of a programme's component due to circumstances beyond his control, he must report in writing to the relevant teacher as soon as possible. The teacher, if necessary after consulting the study adviser, may decide to issue the student a replacing assignment.
• It is not allowed to miss obligatory commponents of the programme if there is no case of circumstances beyond one's control.
• In case of participating qualitatively or quantitatively insufficiently, the examiner can expel a student from further participation in the programme's component or a part of that component. Conditions for sufficient participation are set down in advance in the course manual.
• In addition to the above mentioned rules, in the first semester of the first year a student should be present in at least 80% of the seminars. Moreover, participation to midterm tests and obligatory homework is required. If the student does not comply with these obligations, the student is expelled from the resit of this course. Students in the double Bachelor's degree programme Mathematics and Physics are exempted from this requirement. In case of personal circumstances, as described in OER-A Article A-6.4, a different study plan will be made in consultation with the study advisor.

Assessment

Item and weight	Details
Final grade
60% Tentamen
40% Assignments
1 (33%) Reading assignments	Must be ≥ pass
1 (33%) Take home 1
1 (33%) Take home 2
1 (33%) Take home 3

• Take-home exercises will be provided during the course. The exercise will cover a selection of the learning objectives.
• The final exam will consist of at least one exercise on the first part (Ch 1 & 2) and at least one exercise on the final part (Ch 3,4 & 5) of the course.

The take-home exercises build on your understanding of the concepts from the lectures and exercise classes. The final exam will consist of problems similar to those covered in the exercise classes. The grading will be 40% take-home problems and 50% final exam. You are required to submit all take-home problems and your exam grade should be > 5.0. 

Inspection of assessed work

The date, time and location of the inspection moment are in the DataNose timetable.

Assignments

Take home exercise 1

• Tight binding model of a Dirac semi-metal

Take home exercise 2

• Optical conductivity of a Dirac semi metal

Take home exercise 3

• The Lieb-Mattis model

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Timetable

The schedule for this course is published on DataNose.

Additional information

Recommended prior knowledge: Gecondenseerde materie 1, Quantumfysica 1 en 2, Elektriciteit en magnetisme, Thermische fysica. 

If you have not followed Condensed Matter 1, the first two weeks will require a somewhat larger amount of time investment. However, the course is fully contained and all necessary knowledge will be discussed during lectures.

Processed course evaluations

Below you will find the adjustments in the course design in response to the course evaluations.

Contact information

Coordinator

• dr. Erik van Heumen