Solid State Physics (P715), Spring 2021

Instructor: Romain Vasseur, Assistant Professor
office: Hasbrouck 405A
email: rvasseur[at]umass[dot]edu
office hours: email and zoom

Lectures: TuThu 10-11.15am, remote lectures on Zoom

Suggested reading materials: The lecture notes for this course are far from being original, and will rely heavily on the following references (in particular, David Tong’s notes for the band theory, phonons and dynamics chapters):

• The Oxford Solid State Basics by Steve Simon
• Solid State Physics by N.W. Ashcroft and N.D. Mermin
• David Tong’s lecture notes

Website: https://websites.umass.edu/rvasseur/teaching/. Course materials will also be made available on Moodle.

Grading: The course grade will be based on the problem sets (75%) and a final take-home exam (25%) 

Topics:

• Introduction
• The early days of solid state physics: specific heat of solids, electrons in metals, Drude theory, Sommerfeld theory.
• Crystal structure and band theory: electrons in one dimension, tight-binding model, electrons in a weak periodic potential; crystal structure, Bravais lattices, neutron and X-ray diffraction; Bloch’s theorem, reciprocal lattice, Brillouin zone.  
• Phonons: Monotonic and diatomic chains, optical and acoustic phonons, Peierls instability, continuum limit, quantization.
• Electron dynamics in solids: insulators, metals and semiconductors; semi-classical equations of motion, Bloch oscillations, magnetic fields, quantum oscillations.
• More advanced topics: Topology in solid state physics. Berry phase and Berry curvature, spin 1/2, Dirac Hamiltonian, Chern number. Anomalous velocity and semi-classical equations of motion revisited. Quantum anomalous Hall effect and Chern insulators. Graphene and Haldane model. SSH model and edge states.

Lecture Notes:

• Introduction
• Early days
• Band theory: part 1, part 2
• Phonons
• Dynamics of electrons in solids
• Topology in band theory

see also in-class Zoom notes here.

Problem Sets:

• Problem set #1: Early days
• Problem set #2: Band theory
• Problem set #3: Phonons
• Problem set #4: Transport

Final exam (on topology)

Solutions available on Moodle, or upon request by email.

Schedule:

week 1: Introduction. Early days: specific heat of solids, Einstein and Debye models. We also started discussing the Drude model.

week 2: Drude and Drude-Sommerfeld models. Fermi gases. HW1 posted.

week 3: Band theory: tight binding model in 1d, metals vs insulators, nearly free electrons in a weak periodic potential.

week 4: Translation invariance, Bloch’s theorem in 1d, crystal momentum. Bravais lattices, primitive cells, examples of non-Bravais lattices. Reciprocal lattice and Fourier series.

week 5: Wave scattering in solids, diffraction. Bloch’s theorem in 3d, nearly free electrons in a periodic potential in higher d.

week 6: Wannier functions, tight-binding approximation, LCAO. Phonons in 1d monoatomic and diatomic classical chains.

week 7: Peierls transition, quantization of phonons, field theory description.

week 8: Fermi surfaces, metals vs insulators, group velocity, electric and energy currents, semi-classical equations of motion of Bloch electrons.

week 9: Effective mass, Bloch oscillations, holes, Drude model revisited, motion of Bloch electrons in a magnetic field, cyclotron frequency.

week 10: Quantum oscillations, intro to topology in band theory. Berry phase and Berry curvature.

week 11: Spin 1/2 example, Dirac Hamiltonian, Chern number and Chern insulator. Semi-classical equations of motion revisited.

week 12: No lecture on Tuesday. Anomalous velocity, quantum anomalous Hall effect and Chern insulators. Graphene.

week 13: Graphene and Haldane model. Low energy Hamiltonians and phase diagram. SSH model and edge states.