Search result: Catalogue data in Spring Semester 2018

Doctoral Department of Physics Information
More Information at: Link
Doctoral and Post-Doctoral Courses
Please note that this is an INCOMPLETE list of courses.
402-0318-00LSemiconductor Materials: Characterization, Processing and DevicesW6 credits2V + 1US. Schön, W. Wegscheider
AbstractThis course gives an introduction into the fundamentals of semiconductor materials. The main focus in this semester is on state-of-the-art characterization, semiconductor processing and devices.
ObjectiveBasic knowledge of semiconductor physics and technology. Application of this knowledge for state-of-the-art semiconductor device processing
ContentSemiconductor material characterization (ex situ): Structural and chemical methods (XRD, SEM, TEM, EDX, EELS, SIMS), electronic methods (Hall & quantum Hall effect, transport), optical methods (PL, absorption sepctroscopy);
Semiconductor processing: E-beam lithography, optical lithography, structuring of layers and devices (RIE, ICP), thin film deposition (metallization, PECVD, sputtering, ALD);
Semiconductor devices: Bipolar and field effect transistors, semiconductor lasers, other devices
Lecture notesLink
402-0484-00LExperimental and Theoretical Aspects of Quantum Gases Information
Does not take place this semester.
W6 credits2V + 1UT. Esslinger
AbstractQuantum Gases are the most precisely controlled many-body systems in physics. This provides a unique interface between theory and experiment, which allows addressing fundamental concepts and long-standing questions. This course lays the foundation for the understanding of current research in this vibrant field.
ObjectiveThe lecture conveys a basic understanding for the current research on quantum gases. Emphasis will be put on the connection between theory and experimental observation. It will enable students to read and understand publications in this field.
ContentCooling and trapping of neutral atoms

Bose and Fermi gases

Ultracold collisions

The Bose-condensed state

Elementary excitations



Interference and Correlations

Optical lattices
Lecture notesnotes and material accompanying the lecture will be provided
LiteratureC. J. Pethick and H. Smith, Bose-Einstein condensation in dilute Gases,
Proceedings of the Enrico Fermi International School of Physics, Vol. CXL,
ed. M. Inguscio, S. Stringari, and C.E. Wieman (IOS Press, Amsterdam,
402-0486-00LFrontiers of Quantum Gas Research: Few- and Many-Body Physics
Does not take place this semester.
W6 credits2V + 1U
AbstractThe lecture will discuss the most relevant recent research in the field of quantum gases. Bosonic and fermionic quantum gases with emphasis on strong interactions will be studied. The topics include low dimensional systems, optical lattices and quantum simulation, the BEC-BCS crossover and the unitary Fermi gas, transport phenomena, and quantum gases in optical cavities.
ObjectiveThe lecture is intended to convey an advanced understanding for the current research on quantum gases. Emphasis will be put on the connection between theory and experimental observation. It will enable students to follow current publications in this field.
ContentQuantum gases in one and two dimensions
Optical lattices, Hubbard physics and quantum simulation
Strongly interacting Fermions: the BEC-BCS crossover and the unitary Fermi gas
Transport phenomena in ultracold gases
Quantum gases in optical cavities
Lecture notesno script
LiteratureC. J. Pethick and H. Smith, Bose-Einstein condensation in dilute Gases, Cambridge.
T. Giamarchi, Quantum Physics in one dimension
I. Bloch, J. Dalibard, W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008)
Proceedings of the Enrico Fermi International School of Physics, Vol. CLXIV, ed. M. Inguscio, W. Ketterle, and C. Salomon (IOS Press, Amsterdam, 2007).
Additional literature will be distributed during the lecture
Prerequisites / NoticePresumably, Prof. Päivi Törmä from Aalto university in Finland will give part of the course. The exercise classes will be partly in the form of a Journal Club, in which a student presents the achievements of a recent important research paper. More information available on Link
402-0470-17LOptical Frequency Combs: Physics and Applications
Does not take place this semester.
W6 credits2V + 1UJ. Faist
AbstractIn this lecture, the goal is to review the physics behind mode-locking in these various devices, as well as discuss the most important novelties and applications of the newly developed sources.
ObjectiveIn this lecture, the goal is to review the physics behind mode-locking in these various devices, as well as discuss the most important novelties and applications of the newly developed sources.
ContentSince their invention, the optical frequency combs have shown to be a key technological tool with applications in a variety of fields ranging from astronomy, metrology, spectroscopy and telecommunications. Concomitant with this expansion of the application domains, the range of technologies that have been used to generate optical frequency combs has recently widened to include, beyond the solid-state and fiber mode-locked lasers, optical parametric oscillators, microresonators and quantum cascade lasers.
In this lecture, the goal is to review the physics behind mode-locking in these various devices, as well as discuss the most important novelties and applications of the newly developed sources.

Chapt 1: Fundamentals of optical frequency comb generation
- Physics of mode-locking: time domain picture
Propagation and stability of a pulse, soliton formation
- Dispersion compensation
Solid-state and fiber mode-locked laser
Chapt 2: Direct generation
Microresonator combs: Lugiato-Lefever equation, solitons
Quantum cascade laser: Frequency domain picture of the mode-locking
Mid-infrared and terahertz QCL combs
Chapt 3: Non-linear optics
Chapt 4: Comb diagnostics and noise
Jitter, linewidth
Chapt 5: Self-referenced combs and their applications
Chapt 6: Dual combs and their applications to spectroscopy
402-0498-00LCavity QED and Ion Trap Physics Information
Does not take place this semester.
W6 credits2V + 1UJ. Home
AbstractThis course covers the physics of systems where harmonic oscillators are coupled to spin systems, for which the 2012 Nobel prize was awarded. Experimental realizations include photons trapped in high-finesse cavities and ions trapped by electro-magnetic fields. These approaches have achieved an extraordinary level of control and provide leading technologies for quantum information processing.
ObjectiveThe objective is to provide a basis for understanding the wide range of research currently being performed on fundamental quantum mechanics with spin-spring systems, including cavity-QED and ion traps. During the course students would expect to gain an understanding of the current frontier of research in these areas, and the challenges which must be overcome to make further advances. This should provide a solid background for tackling recently published research in these fields, including experimental realisations of quantum information processing.
ContentThis course will cover cavity-QED and ion trap physics, providing links and differences between the two. It aims to cover both theoretical and experimental aspects. In all experimental settings the role of decoherence and the quantum-classical transition is of great importance, and this will therefore form one of the key components of the course. The topics of the course were cited in the Nobel prize which was awarded to Serge Haroche and David Wineland in 2012.

Topics which will be covered include:

Cavity QED
(atoms/spins coupled to a quantized field mode)
Ion trap
(charged atoms coupled to a quantized motional mode)

Quantum state engineering:
Coherent and squeezed states
Entangled states
Schrodinger's cat states

The quantum optical master equation
Monte-Carlo wavefunction
Quantum measurements
Entanglement and decoherence

Quantum information processing
Quantum sensing
LiteratureS. Haroche and J-M. Raimond "Exploring the Quantum" (required)
M. Scully and M.S. Zubairy, Quantum Optics (recommended)
Prerequisites / NoticeThis course requires a good working knowledge in non-relativistic quantum mechanics. Prior knowledge of quantum optics is recommended but not required.
402-0466-15LQuantum Optics with Photonic Crystals, Plasmonics and MetamaterialsW6 credits2V + 1UG. Scalari
AbstractIn this lecture, we would like to review new developments in the emerging topic of quantum optics in very strongly confined structures, with an emphasis on sources and photon statistics as well as the coupling between optical and mechanical degrees of freedom.
Content1. Light confinement
1.1. Photonic crystals
1.1.1. Band structure
1.1.2. Slow light and cavities
1.2. Plasmonics
1.2.1. Light confinement in metallic structures
1.2.2. Metal optics and waveguides
1.2.3. Graphene plasmonics
1.3. Metamaterials
1.3.1. Electric and magnetic response at optical frequencies
1.3.2. Negative index, cloacking, left-handness

2. Light coupling in cavities
2.1. Strong coupling
2.1.1. Polariton formation
2.1.2. Strong and ultra-strong coupling
2.2. Strong coupling in microcavities
2.2.1. Planar cavities, polariton condensation
2.3. Polariton dots
2.3.1. Microcavities
2.3.2. Photonic crystals
2.3.3. Metamaterial-based

3. Photon generation and statistics
3.1. Purcell emitters
3.1.1. Single photon sources
3.1.2. THz emitters
3.2. Microlasers
3.2.1. Plasmonic lasers: where is the limit?
3.2.2. g(1) and g(2) of microlasers
3.3. Optomecanics
3.3.1. Micro ring cavities
3.3.2. Photonic crystals
3.3.3. Superconducting resonators
402-0516-10LGroup Theoretical Methods in Solid State Physics
Does not take place this semester.
W12 credits3V + 3UD. Pescia
AbstractThis lecture introduces the fundamental concepts of group theory and their representations. The accent is on the concrete applications of the mathematical concepts to practical quantum mechanical problems of solid state physics and other fields of physics rather than on their mathematical proof.
ObjectiveThe aim of this lecture is to give a fundamental knowledge on the application of symmetry in atoms, molecules and solids. The lecture is intended for students at the master and Phd. level in Physics that would like to have a practical and comprehensive view of the role of symmetry in physics. Students in their third year of Bachelor will be perfectly able to follow the lecture and can use it for their future master curriculuum. Students from other Departement are welcome, but they should have a solid background in mathematics and physics, although the lecture is quite self-contained.
Content1. Groups, Classes, Representation theory, Characters of a representation and theorems involving them.

2. The symmetry group of the Schrödinger equation, Invariant subspaces, Atomic orbitals, Molecular vibrations, Cristal field splitting, Compatibility relations, Band structure of crystals.

3. SU(2) and spin, The double group, The Kronecker Product, The Clebsch-Gordan coefficients, Clebsch-Gordan coeffients for point groups,The Wigner-Eckart theorem and its applications to optical transitions.
Lecture notesThe copy of the blackboard is made available online.
LiteratureThis lecture is essentially a practical application of the concepts discussed in:

- L.D. Landau, E.M. Lifshitz, Lehrbuch der Theor. Pyhsik, Band III, "Quantenmechanik", Akademie-Verlag Berlin, 1979, Kap. XII
- Ibidem, Band V, "Statistische Physik", Teil 1, Akademie-Verlag 1987, Kap. XIII and XIV.
402-0536-00LFerromagnetism: From Thin Films to SpintronicsW6 credits3GR. Allenspach
AbstractThis course extends the introductory course "Introduction to Magnetism" to the latest, modern topics in research in magnetism and spintronics.
After a short revisit of the basic magnetism concepts, emphasis is put on novel phenomena in (ultra)thin films and small magnetic structures, displaying effects not encountered in bulk magnetism.
ObjectiveKnowing the most important concepts and applications of ferromagnetism, in particular on the nanoscale (thin films, small structures). Being able to read and understand scientific articles at the front of research in this area. Learn to know how and why magnetic storage, sensors, memories and logic concepts function. Learn to condense and present the results of a research articles so that colleagues understand.
ContentMagnetization curves, magnetic domains, magnetic anisotropy; novel effects in ultrathin magnetic films and multilayers: interlayer exchange, spin transport; magnetization dynamics, spin precession.
Applications: Magnetic data storage, magnetic memories, spin-based electronics, also called spintronics.
Lecture notesLecture notes will be handed out (in English).
Prerequisites / NoticeThis course can be easily followed with having attended the "Introduction to Magnetism" course before.
Language: English (German if all students agree).
402-0532-00LQuantum Solid State MagnetismW6 credits2V + 1UA. Zheludev, K. Povarov
AbstractThis course is based on the principal modern tools used to study collective magnetic phenomena in the Solid State, namely correlation and response functions. It is quite quantitative, but doesn't contain any "fancy" mathematics. Instead, the theoretical aspects are balanced by numerous experimental examples and case studies. It is aimed at theorists and experimentalists alike.
ObjectiveLearn the modern theoretical foundations and "language", as well as principles and capabilities of the latest experimental techniques, used to describe and study collective magnetic phenomena in the Solid State.
Content- Magnetic response and correlation functions. Analytic properties. Fluctuation-dissipation theorem. Experimental methods to measure static and dynamic correlations.

- Magnetic response and correlations in metals. Diamagnetism and paramagnetism. Magnetic ground states: ferromagnetism, spin density waves. Excitations in metals, spin waves. Experimental examples.

- Magnetic response and correlations of magnetic ions in crystals: quantum numbers and effective Hamiltonians. Application of group theory to classifying ionic states. Experimental case studies.

- Magnetic response and correlations in magnetic insulators. Effective Hamiltonians. Magnetic order and propagation vector formalism. The use of group theory to classify magnetic structures. Determination of magnetic structures from diffraction data. Excitations: spin wave theory and beyond. "Triplons". Measuring spin wave spectra.
Lecture notesA comprehensive textbook-like script is provided.
LiteratureIn principle, the script is suffient as study material. Additional reading:

-"Magnetism in Condensed Matter" by S. Blundell
-"Quantum Theory of Magnetism: Magnetic properties of Materials" by R. M. White
-"Lecture notes on Electron Correlations and Magnetism" by P. Fazekas
Prerequisites / NoticePrerequisite:
402-0861-00L Statistical Physics
402-0501-00L Solid State Physics

Not prerequisite, but a good companion course:
402-0871-00L Solid State Theory
402-0257-00L Advanced Solid State Physics
402-0535-00L Introduction to Magnetism
402-0538-16LIntroduction to Magnetic Resonance for Physicists
Does not take place this semester.
W6 credits2V + 1UC. Degen
AbstractThis course provides the fundamental principles of magnetic resonance and discusses its applications in physics and other disciplines.
ObjectiveMagnetic resonance is a textbook example of quantum mechanics that has made its way into numerous applications. It describes the response of nuclear and electronic spins to radio-frequency magnetic fields. The aim of this course is to provide the basic concepts of magnetic resonance while making connections of relevancy to other areas of science.
After completing this course, students will understand the basic interactions of spins and how they are manipulated and detected. They will be able to calculate and simulate the quantum dynamics of spin systems. Examples of current-day applications in solid state physics, quantum information, magnetic resonance tomography, and biomolecular structure determination will also be integrated.
ContentFundamentals and Applications of Magnetic Resonance
- Historical Perspective
- Bloch Equations
- Quantum Picture of Magnetic Resonance
- Spin Hamiltonian
- Pulsed Magnetic Resonance
- Spin Relaxation
- Electron Paramagnetic Resonance and Ferromagnetic Resonance
- Signal Detection
- Modern Topics and Applications of Magnetic Resonance
Lecture notesClass Notes and Handouts
Literature1) Charles Slichter, "Principles of Magnetic Resonance"
2) Anatole Abragam, "The Principles of Nuclear Magnetism"
Prerequisites / NoticeBasic knowledge of quantum mechanics is not formally required but highly advantageous.
402-0528-12LUltrafast Methods in Solid State PhysicsW6 credits2V + 1UY. M. Acremann, S. Johnson
AbstractThis course provides an overview of experimental methods and techniques used to study dynamical processes in solids. Many processes in solids happen on a picosecond to femtosecond time scale. In this course we discuss different methods to generate femtosecond photon pulses and measurement techniques adapted to time resolved experiments.
ObjectiveThe goal of the course is to enable students to identify and evaluate experimental methods to manipulate and measure the electronic, magnetic and structural properties of solids on the fastest possible time scales. These "ultrafast methods" potentially lead both to an improved understanding of fundamental interactions in condensed matter and to applications in data storage, materials processing and computing.
ContentThe topical course outline is as follows:

0. Introduction
Time scales in solids and technology
Time vs. frequency domain experiments
Pump-Probe technique

1. Ultrafast processes in solids, an overview
Electron gas
Spin system

2. Ultrafast optical-frequency methods
Ultrafast laser sources
Broadband techniques
Harmonic generation, optical parametric amplification
Advanced pump-probe techniques

3. THz-frequency methods
Mid-IR and THz interactions with solids
Difference frequency mixing
Optical rectification

4. Ultrafast VUV and x-ray frequency methods
Synchrotron based sources
Free electron lasers
Higher harmonic generation based sources
X-ray diffraction
Time resolved X-ray microscopy
Coherent imaging

5. Electron spectroscopy in the time domain
Lecture notesWill be distributed.
LiteratureWill be distributed.
Prerequisites / NoticeAlthough the course "Ultrafast Processes in Solids" (402-0526-00L) is useful as a companion to this course, it is not a prerequisite.
402-0558-00LCrystal Optics in Intense Light FieldsW6 credits2V + 1UM. Fiebig
AbstractBecause of their aesthetic nature crystals are termed "flowers of mineral kingdom". The aesthetic aspect is closely related to the symmetry of the crystals which in turn determines their optical properties. It is the purpose of this course to stimulate the understanding of these relations with a particular focus on those phenomena occurring in intense light fields as they are provided by lasers.
ObjectiveIn this course students will at first acquire a systematic knowledge of classical crystal-optical phenomena and the experimental and theoretical tools to describe them. This will be the basis for the core part of the lecture in which they will learn how to characterize ferroelectric, (anti)ferromagnetic and other forms of ferroic order and their interaction by nonlinear optical techniques. See also Link.
ContentCrystal classes and their symmetry; basic group theory; optical properties in the absence and presence of external forces; focus on magnetooptical phenomena; density-matrix formalism of light-matter interaction; microscopy of linear and nonlinear optical susceptibilities; second harmonic generation (SHG); characterization of ferroic order by SHG; outlook towards other nonlinear optical effects: devices, ultrafast processes, etc.
Lecture notesExtensive material will be provided throughout the lecture.
Literature(1) R. R. Birss, Symmetry and Magnetism, North-Holland (1966)
(2) R. E. Newnham: Properties of Materials: Anisotropy, Symmetry, Structure, Oxford University (2005)
(3) A. K. Zvezdin, V. A. Kotov: Modern Magnetooptics & Magnetooptical Materials, Taylor/Francis (1997)
(4) Y. R. Shen: The Principles of Nonlinear Optics, Wiley (2002)
(5) K. H. Bennemann: Nonlinear Optics in Metals, Oxford University (1999)
Prerequisites / NoticeBasic knowledge in solid state physics and quantum (perturbation) theory will be very useful. The lecture is addressed to students in physics and students in materials science with an affinity to physics.
402-0726-12LPhysics of Exotic AtomsW6 credits2V + 1UP. Crivelli
AbstractIn this course, we will review the status of physics with exotic atoms including the new exciting advances such as anti-hydrogen 1S-2S spectroscopy and measurements of the hyperfine splitting and the puzzling results of the muonic-hydrogen experiment for the determination of the proton charge radius.
ObjectiveThe course will give an introduction on the physics of exotic atoms covering both theoretical and experimental aspects. The focus will be set on the systems which are currently a subject of research in Switzerland: positronium at ETHZ, anti-hydrogen at CERN and muonium, muonic-H and muonic-He at PSI. The course will enable the students to follow recent publications in this field.
ContentReview of the theory of hydrogen and hydrogen-like atoms
Interaction of atoms with radiation
Hyperfine splitting theory and experiments: Positronium (Ps),
Muonium (Mu) and anti-hydrogen (Hbar)
High precision spectroscopy: Ps, Mu and Hbar
Lamb shift in muonic-H and muonic-He- the proton radius puzzle
Weak and strong interaction tests with exotic atoms
Anti-matter and gravitation
Applications of antimatter
Lecture notesscript
LiteraturePrecision physics of simple atoms and molecules, Savely G. Karshenboim, Springer 2008

Proceedings of the International Conference on Exotic Atoms (EXA 2008) and the 9th International Conference on Low Energy Antiproton Physics (LEAP 2008) held in Vienna, Austria, 15-19 September 2008 (PART I/II), Hyperfine Interactions, Volume 193, Numbers 1-3 / September 2009

Laser Spectroscopy: Vol. 1 Basic Principles Vol. 2 Experimental Techniques von Wolfgang Demtröder von Springer Berlin Heidelberg 2008
402-0883-63LSymmetries in PhysicsW4 credits2VN. Beisert
AbstractThe course gives an introduction to symmetry groups in physics. It explains the relevant mathematical background (finite groups, Lie groups and algebras as well as their representations), and illustrates their important role in modern physics.
ObjectiveThe aim of the course is to give a self-contained introduction into finite group theory as well as Lie theory from a physicists point of view. Abstract mathematical constructions will be illustrated with examples from physics.
Contentsymmetries in two and three dimensions, groups and representations, finite group theory, point and space groups, structure of simple Lie algebras, finite-dimensional representations; advanced topics such as: representations of SU(N), classification of simple Lie algebras, conformal symmetry
402-0883-18LExercises in Symmetries in PhysicsW2 credits1GN. Beisert
AbstractThe course supplements an introductory lecture to symmetry groups in physics. It practices and deepens the mathematical background and applications in physics by working out and discussing homework exercises. Quiz problems in class will test familiarity with conceptual questions. Particular issues of the lecture can be discussed in more detail.
ObjectiveThe aim of the course is to obtain a solid foundation in techniques for and concepts of finite group theory and Lie theory. Participants will practice performing computations and derivations in this topic and learn to apply the relevant methods to physics problems.
Contentsymmetries in two and three dimensions, groups and representations, finite group theory, point and space groups, structure of simple Lie algebras, finite-dimensional representations; advanced topics such as: representations of SU(N), classification of simple Lie algebras, conformal symmetry
Prerequisites / NoticeThis course is based on the contents of the lecture 402-0883-63V Symmetries in Physics which should be attended in parallel
402-0364-17LCosmic Structure Formation and Radiation ProcessesW6 credits2V + 1US. Cantalupo
AbstractIn this course, the students will investigate the properties and origin of the largest baryonic structures in the universe through the study of their radiation. We will span a large range in the universe’s history and radiation spectrum: from X-ray emitting ICM to Cosmic Web UV emission and absorption, to HI radio emission during Reionization. A strong focus will be also put on research practice.
ObjectiveContent goals/objectives include:

- The students will learn how to investigate and characterise the physical properties of the largest baryonic structures in the universe by studying in detail the mechanisms that produce and modify the electromagnetic radiation detectable with astronomical observing facilities.

- The students will learn that radiation processes are an active agent in shaping the formation and evolution of cosmic structures in the universe from the largest scales associated with intergalactic gas to galaxies.

Practice goals/objectives include:

- Through this course, the students will learn/consolidate the fundamental skills in research practice including: i) asking relevant questions, ii) making testable predictions, iii) reducing complex problems in smaller units, iv) finding relevant variables in physical problems, v) effectively sharing and communicating the results.

In order to achieve these goal, the course is designed through inquiry-based activities that will cover the following topics:

- Inferring the physical properties of the Intra Cluster Medium in Galaxy Clusters (X-ray, high-energy radiation processes)
- Detecting and studying Intergalactic gas in the Cosmic Web in absorption and emission (UV/optical absorption and emission of Hydrogen Ly-alpha radiation, Radiative Transfer)
- The physics of Radiative Cooling and how radiation processes shape cosmic structure formation.
- Cosmic Reionization and radio emission from neutral hydrogen in the early universe.
Lecture notesClass material will include: i) power point and black-board presentations, ii) material developed in the class during the activities by the students, iii) research papers and reviews, iv) extracts from books.

Some of the material will be available online but it is expected that a large fraction of the material/notes will be produced during the classroom activities. Class attendance and active participation are fundamental factors for both learning and assessment during this course and for the exam.
Prerequisites / NoticeThe course is geared towards Master and Ph.D students in astrophysics and the physical sciences with no particular prerequisites on previous classes or study background. The only prerequisites necessary for this class are: i) motivation, ii) curiosity, iii) willingness to actively participate.

This course is mostly based on the course 402-0364-17L Radiation Processes in Astrophysics that was taught in FS 2017. Therefore it is not possible to get credits for both courses.
402-0888-18LFractionalization of Particles in PhysicsW6 credits2V + 1UC. Chamon
AbstractThe course will cover fractionalization phenomena in one and two spatial dimensions. It will survey the theoretical methods used to understand fractionalization, including bosonization, Chern-Simons theory, quantum anomalies, and use of topological invariants. These methods will be applied in several examples.
ObjectiveIn condensed matter physics, the electron need not be “fundamental” in the sense that it may have little relation to the low-lying charge excitations due to strong interaction effects. In the fractional quantum Hall effect, for example, a very strong magnetic field enhances dramatically the importance of Coulomb interactions among electrons over their kinetic energy; so much so that elementary charge excitations carry a fractional charge of the electron.

The aim of this course is to explain by way of examples, often motivated but not limited to condensed matter physics, how interactions, either among particles or between particles and their background, can modify the quantum numbers of the “elementary” building blocks of matter, in short the fractionalization of particles in physics.

The course will cover fractionalization phenomena in one and two spatial dimensions. It will survey the theoretical methods used to understand fractionalization, including bosonization, Chern-Simons theory, quantum anomalies, and use of topological invariants. These methods will be applied in the study of fractionalization of charge in material systems in 1D and 2D, and in the study of topological insulators and superconductors.
Content1. One-dimensional (1D) systems
• Fermiology on the lattice and in the continuum
• Symmetries
• Sublattice grading and spectral folding
• A model for polyacetylene
• The Peierls instability for polyacetylene
• The Su-Schrieffer-Heeger (SSH) model

2. Zero-modes and fractionalization in 1D
• Point defects in the dimerization
• Zero modes bound to topological defects
• Zero modes in the lattice and in the continuum
• First encounter of charge fractionalization

3. Evaluation of the induced charge using various methods
• Supersymmetry and the Witten index
• The gradient expansion
• The adiabatic expansion
• Fractionalization from Abelian bosonization
• Rational vs. irrational charges in 1D

4. Fractionalization in one-dimensional superconductors
• Bogoliubov-de-Gennes Hamiltonians
• The Kitaev chain
• Majorana zero modes

5. 2D systems – Dirac fermions
• Graphene and the Dirac fermions in 2D
• Classification of masses for 2D Dirac fermions
• Vortices in mass order parameters
• Zero-modes tied to vortices
• Confinenement and deconfinement – axial gauge fields
• Rational vs. irrational charges in 2D – confinement vs. deconfinement

6. 2D systems – fractional quantum Hall systems
• Quantized Hall effect
• Laughlin gauge argument
• Flux insertion and fractional charge quantization
• Chern-Simons theory and electromagnetic response
• Wire construction of 2D fractional quantum Hall states
Lecture notesRequired Texts:
• C. Chamon and C. Mudry, manuscript on Fractionalization of Particles in Physics. These notes will be made available to students in the course.
LiteratureRecommended Texts:
There are many helpful references available to complement the notes, including:
• E. Fradkin, Field Theories of Condensed Matter Physics, 2nd edition (Cambridge Univ. Press)
• A. Tsvelik, Quantum Field Theory in Condensed Matter Physics, 2nd edition (Oxford univ. Press)
• C. Mudry, Lecture notes on field theory in condensed matter physics (World Scientific Publishing)
• B. A. Bernevig with T. L. Hughes, Topological Insulators and Topological Superconductors (Princeton Univ. Press)
Prerequisites / NoticeContact: Link
402-0888-00LField Theory in Condensed Matter Physics
Does not take place this semester.
W6 credits2V + 1U
AbstractThe topics covered in this class are: superfluidity in weakly interacting Bose gas, the random phase approximation to the Coulomb interaction in the Jellium model, superconductivity within the random phase approximation, the renormalization group analysis of non-linear-sigma models and of the Kosterlitz-Thouless transition.
ContentIn this class I will show, by examples, how field theory can describe some important phenomena in condensed matter physics. The transition from a discrete to a continuum description is illustrated with the one-dimensional Harmonic chain both in classical and quantum mechanics in Lecture 1. Spontaneous symmetry breaking is introduced with the phenomenon of superfluidity for a weakly interacting Bose gas in Lecture 2. Lectures 3 and 4 deal with the physics of screening in the Jellium model for electrons at the level of the random phase approximation. Superconductivity is described within the mean-field and random-phase approximation in Lectures 5 and 6. The Caldeira-Leggett model for dissipation, in the context of a Josephson junction, is treated in Lectures 7 and 8. Classical non-linear-sigma models are introduced in Lecture 9 and their beta functions are calculated explicitly for the O(N)/O(N-1) target manifold in the 2+epsilon expansion in Lectures 9 and 10. The Kosterlitz-Thouless phase transition is discussed in a one-loop renormalization group analysis in Lecture 11. Lecture 12 is devoted to bosonization in (1+1)-dimensional space time.
LiteratureLecture Notes on Field Theory in Condensed Matter Physics,
Christopher Mudry,
World Scientific Publishing Company,
ISBN 978-981-4449-09-0 (Hardcover),
978-981-4449-10-6 (paperback)]
402-0604-00LMaterials Analysis by Nuclear Techniques Information W6 credits2V + 1UM. Doebeli
AbstractMaterials analysis by MeV ion beams. Nuclear techniques are presented which allow to quantitatively investigate the composition, structure and trace element content of solids.
ObjectiveStudents learn the basic concepts of ion beam analysis and its different analytical techniques. They understand how experimental data is taken and interpreted. They are able to chose the appropriate method of analysis to solve a given problem.
ContentThe course treats applications of nuclear methods in other fields of research. Materials analysis by ion beam analysis is emphasized. Techniques are presented which allow the quantitative investigation of composition, structure, and trace element content of solids:
- elasic nuclear scattering (Rutherfor Backscattering, Recoil detection)
- nuclear (resonant) reaction analysis
- activation analysis
- ion beam channeling (investigation of crystal defects)
- neutron sources
- MeV ion microprobes, imaging surface analysis

The course is also suited for graduate students.
Lecture notesLecture notes will be distributed in pdf.
Literature'Ion Beam Analysis: Fundamentals and Applications', M. Nastasi, J.W. Mayer, Y. Wang, CRC Press 2014, ISBN 9781439846384
Prerequisites / NoticeIf possible, a practical lab demonstration is organized as part of lectures and exercises.

The course is also well suited for graduate students.
It can be held in German or English, depending on participants.
402-0710-00LDoctoral Student Seminar in Nuclear and Particle PhysicsW1 credit2SA. Rubbia, G. Dissertori, M. Dittmar, C. Grab, K. S. Kirch, R. Wallny, University lecturers
AbstractSeminar for PhD students
Lecture notesSeminar for PhD students
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