Effective Hamiltonian theory for condensed matter systems (PW)5 ECTS
(englische Bezeichnung: Effective Hamiltonian theory for condensed matter systems)
(Prüfungsordnungsmodul: Physics elective courses)

Lehrveranstaltungen:

• • Effective Hamiltonian theory for condensed matter systems
    (Vorlesung mit Übung, 5 SWS, Sam Shallcross, Mo, 15:00 - 17:00, SR 02.779; Mi, 11:00 - 13:00, SR 02.729)

Inhalt:

Contents
1. Introduction to the idea with examples; the Dirac-Weyl Hamiltonian in graphene, the Dirac Hamiltonian in the IV-VI topological insulators.
2. General method for obtaining effective Hamiltonians: high symmetry systems, perturbative and non-perturbative lattice deformations to high symmetry systems, general multilayer systems. Example of the method: the Dirac-Weyl operator as the linear in momentum term in a general expansion, the graphene twist bilayer as an example of a non-perturbative deformation.
3. Minimal coupling of electric and magnetic fields. The chiral Landau spectrum of bilayer graphene.
4. Gauge fields in deformed graphene: the 3 hermitian fields.
5. Down-folded Hamiltonians. The example of the 2-band approximation to Bernal stacked bilayer graphene.
6. Description of IV-VI semi-conductors by the effective Hamiltonian approach. How strain distorts the bulk spectrum. Derivation of an effective Dirac equation.
7. Super-symmetric solution to the interface problem: a topological surface state. Role of the work function and role of the bulk electronic structure in surface spin-momentum locking.
8. Complex carbon allotropes. How simple low energy Hamiltonians can emerge from complex materials.
9. Dislocations in low dimensional materials - an interlayer stacking order field in an effective Hamiltonian approach. Impact of structural perturbations that cannot be avoided by charge carriers.
10. Plasmons in low dimensional materials; plasmon spectra and plasmon lifetimes. Methods of calculation: the random phase approximation and going beyond the random phase approximation.

Lernziele und Kompetenzen:

Learning goals and competences:
Students

• explain the relevant topics of the lecture

• apply the methods to specific examples

Verwendbarkeit des Moduls / Einpassung in den Musterstudienplan:

1. Physics (Master of Science)
   (Po-Vers. 2015s | NatFak | Physics (Master of Science) | Master examination | Master examination | Physics elective courses)
2. Physics (Master of Science)
   (Po-Vers. 2015s | NatFak | Physics (Master of Science) | Master examination | Master examination - Elite study program | Physics elective courses)

Studien-/Prüfungsleistungen:

Theoretical Quantum Optics (Prüfungsnummer: 168076)

(englischer Titel: Theoretical Quantum Optics)

Prüfungsleistung, mündliche Prüfung, Dauer (in Minuten): 30, benotet, 5 ECTS

Anteil an der Berechnung der Modulnote: 100.0 %

weitere Erläuterungen:
Masterstudierende mit Studienbeginn ab Sommersemester 2015 können Prüfungen in deutscher Sprache nur mit Genehmigung des Prüfungsausschussvorsitzenden ablegen.

Prüfungssprache: Englisch

Erstablegung: WS 2016/2017, 1. Wdh.: WS 2016/2017 (nur für Wiederholer)

1. Prüfer:

Sam Shallcross