2 r Home page of Xavier Blase
Solid State, Electrons and Phonons - 3 ECTS - September-December 2020

Master Nanosciences and Nanotechnology, Grenoble Alpes University

Contact: xavier.blase_at_neel.cnrs.fr (http://perso.neel.cnrs.fr/xavier.blase/)

Lectures will take place mostly on Thursdays at 8 am.

Goal: This solid-state physics class aims at providing the basics theories that allow to understand the properties of materials, and in particular their electronic and vibrational properties. Why are some solids metallic and other semiconducting ? Can we calculate their specific heat ? What is their velocity of sound ? Applications to low-dimensional systems (including graphene and nanotubes) will serve as a bridge to nanosciences.

Content: The historical Drude model of conductivity / Introducing quantum mechanics : non-interacting electrons in a box / Density of states in several dimensions / Translational properties and Bloch theorem : reducing the complexity / Reciprocal space and Brillouin zone / Tight-binding approximation and band structures / Examples : graphene, Peierls distortion, the minimal cuprate, s-p and s-d hybridization, etc. / Phonons ; acoustic and optical modes.

Bibliography:

  • Introductory chapters of a basic book on Quantum mechanics

  • Introduction to Solid-State Physics, Charles Kittel

  • Solid-State Physics, Ashcroft and Mermin

  • Electronic structure of materials, Adrian P. Sutton

    UE "Practicals" Two "mini-exams" will be given this fall consisting in 2 exercices picked from the compilation you should have received.

    Lectures and Documents (exact schedule will be updated continuously):

  • Lecture 1 : The historical Drude model of conductivity (September 3, 8-10 am, room A019). Associated Document

  • Lecture 2 : Non-interacting quantum electrons in a box (September 10, 8-10 am, room A019). Associated Document     Lecture notes chapters 1 and 2

    BOOKS for Lecture 2 : Kittel, Chapter 6 : "Free electrons Fermi gas"; Ashcroft, Chapter 2 : "The Sommerfeld Theory of Metals".

  • Exercises session (September 17, 8-10 am, room A019). Notes for correction

  • Lecture 3 : Chemical bonding and the tight-binding method. The H2+ molecule. (September 24, 8-10 am, room A019). Lecture notes chapter 3

  • Lecture 4 : Bloch theorem. The 1D chain with 1-atom/cell. The tight-binding formalism. (October 1, 8-10 am, room A019).

  • Lecture 5 : Brillouin zone, discretization of k-vectors and the band structure. (October 8, 8-10 am, room A019). Lecture notes chapter 4

  • Lecture 6 : The tight-binding formalism. The 1D chain with 2-atoms/cell. Band folding. (October 15, 8-10 am, room A019). Lecture notes with Exercises 17, 19, 23 and 24

             UE "Practicals 1" October the 20th (Exercises 1 to 15 from Exercises booklet)     Notes for correction

  • Exercises session on the tight-binding formalism (where we understand 3 Nobel prizes in 2 hours !) (October 22nd, 8-10 am, room A019). Exercises 17, 23, 24 again     Corrections (again)

  • Lecture 8 : Phonons (1 atom/cell). Dispersion. Einstein model for the specific heat. Phonons first chapter

    BOOKS for Lectures 8-9 : Kittel, Chapters 4 and 5 on phonons.

  • Lecture 9 : Phonons. Acoustic and optical modes. Band folding. Phonons second chapter with exercises 25 and 27     Phonons second chapter : zoom lecture pdf

             UE "Practicals 2" November the 17th : Exercises 19 and 24

  • Zoom seminar November 19 Corrections Exercises 19 and 29

  • Zoom seminar December 3 : indirect gap, photovoltaics, defects (Exercise 21), surface states Zoom seminar December 3 pdf


    • Last update: December 2020