The 1st-year II level Course in Physics "Laurea Magistrale Interateneo" (from the collaboration between the Universities of Trieste and Udine) is open in the academic year 2016/17. The academic year is divided in two terms, with a 2 months interval between terms dedicated to individual study and exams.

The "Condensed Matter Physics I" Course is given in the first term (28 Sept. 2016 - 16 Jan. 2017), for a total number of 48 hours (6 credits). It is suggested for all the training tracks.
The course will provide theoretical concepts fundamental to understanding the behaviour of electrons in crystals and the basic tools to treat them, both in problems solvable with classical methods and those requiring a quantum treatment. Main topics: models for non-interacting electrons; crystalline lattices and structures; independent electrons in a periodic potential (Bloch electrons) and energy bands; semiconductors; magnetism.

Timetable: Wed., 9:00-11:00, and Thu., 11:00-13:00, Room 3B, III floor, Building H2bis, via Valerio 12/1.
Staring from Oct. 18, the teacher is available for questions and doubts on Wed., 12:00-13:00, in Room 205 of Building F, via Valerio 2; for other appointments, contact by e-mail.

  • Lectures
  • Textbooks and other material
  • Exams

  • Lectures:

    Lecture Date Argument Details
    1-2 27/9/2016 Transport of noninteracting electrons: Drude model Introduction to the Course; references. Basic assumptions of the Drude model for metals (noninteracting and free electrons; collisions, damping term, relaxation time; application of the kinetic theory of gases); DC electrical conductivity; Hall effect. (Ashcroft-Mermin, Ch. 1, first part)
    3-4 28/9/2016 Transport of noninteracting electrons: Drude model AC electrical conductivity; dielectric function and plasma frequency. Thermal conductivity and Wiedemann-Franz law. (Ashcroft-Mermin, Ch. 1) [Seebeck effect: not explained in class, to be done]. Homework: EXERCISES on the Drude model from the textbook (2, 3 of Ch. I); other exercises
    5-6 5/10/2016 Transport of noninteracting electrons: Sommerfeld model Fermi-Dirac distribution. Ground state of free and indep. electron gas; Fermi momentum; energy; temperature; prediction for the pressure exerted by electrons, bulk modulus and comparison with experiments. [Ashcroft-Mermin, Ch. 2 (not section 2: derivation of the FD distribution)];
    7-8 6/10/2016 Transport of noninteracting electrons: Sommerfeld model Integrals in energy and k space: density of states (see also these notes). Chemical potential. Use of Sommerfeld expansion; electronic contribution to the specific heat. Comparison between predictions of Drude and Sommerfeld model. [Ashcroft-Mermin, remaining parts of Ch. 2]
    See also lecture notes from a course at UCSD summarizing Ch. 1 and 2 of A&M book. Note: for the derivation of the Sommerfeld expansion see Course of Statistical Mechanics by prof. Senatore (e.g., see Landau, Course of Theoretical Physics, Pergamon, volume 5, Statistical Physics, Part I (in the 3rd edition: p. 169-170).
    9-10 13/10/2016 " EXERCISES on the free independent electrons models. In particular: ex. 1.1 (first two points), 1.2, 1.3, 2.1, 2.3 from A&M book.
    11-12 14/10/2016 " EXERCISES on the free independent electrons models. In particular: 1D electron gas in the Sommerfeld model; 1D electron gas with periodic boundary conditions and with hard walls ( figure of the solution); ex. 2.4 from A&M book.
    13-14 19/10/2016 Lattices and crystalline structures Introduction to lattice structures: Bravais lattices and crystalline structures in real space. Lattices with basis (generalities; examples about the conventional cells of the cubic lattices; other relevant examples: diamond, graphene, graphite). Packing fraction [Ch. 4]. (some slides)
    15-16 20/10/2016 " Other examples of Bravais lattices with basis: zincblende, rocksalt, wurzite (one slide). Wigner-Seitz cells. Reciprocal lattices. Families of lattice planes (some slides) . [Ch. 5] .
    17-18 26/10/2016 " Miller indices. Brillouin zone. X-ray diffraction: Bragg and von Laue (one slide) (NO: Experimental geometries suggested by the Von Laue condition) [Ch. 6].
    19-20 27/10/2016 11:20-12:45 " Structure factor; example of diamond as a Bravais with basis (some slides). EXERCISES on crystalline lattices.
    21-22 4/11/2016 Independent electrons in a periodic potential: exact results and approximations [Ch. 8, D, F, 9, 10]. Periodic potential: Bloch theorem, I and II proof (Ch. 8).
    23-24 9/11/2016 Exercises on the first part of the course
    25-26 11/11/2016 " Consequences of the Block theorem: quasi-crystalline momentum; velocity; energy bands. (Ch. 8)
    27-28 16/11/2016 "" Fermi surfaces. Density of states; different approaches. Derivation of the DOS using the properties of the delta-function (one slide) Band index and folding. Van Hove singularities in 1D, 2D, 3D. EXERCISES on Bloch electrons.
    29-30 17/11/2016 " Brillouin zones, band folding and band indices, band plots in reduced zone / periodic / extended representation. Fermi surfaces [Ch. 9]. Exercises on Bloch electrons: bands of free electrons in FCC structure (problem with solution; pdf file). (figure with Brillouin zones and high symmetry points). (Homework: bands of free electrons in other 2D and 3D structures and along high symmetry directions.)
    31-32 23/11/2016 " Effects of a weak perturbing potential (nearly free electrons): non degenerate case; degenerate case (two-levels system) (summary (two slides)). [Ch 9 excluding: The geometrical structure factor in monoatomic lattices with bases; Importance of spin-orbit splittig].
    33-34 24/11/2016 " Exercises on the weak potential. The tight-binding approach: introduction, general formulation; the simplified case of s-band arising from a single atomic s-level.
    35-36 30/11/2016 " Tight-binding in crystals with inversion symmetry; band dispersion. Exercises on tight-binding: s-band arising from a 1D linear chain of atoms, density of states; s-band in 2D square lattice: band dispersion along some high symmetry directions, energy isosurfaces in the Brillouin zone, half filling of bands.
    37-38 1/12/2016 Semiclassical dynamics of the electrons [Ch. 12] Validity of semicl. dynamics. Equations of motions. Filled bands. Holes. [first part of Ch. 12]
    39-40 2/12/2016 " Orbits in r and k space. Motion of electrons in uniform and static electric fields. Motion of electrons in uniform and static magnetic fields (and related exercise). [Ch. 12]
    41 7/12/2016 " More on motion of electrons in a magnetic field: electron orbits, hole orbits and open orbits. Period of close orbits. Fermi surfaces of real metals (examples from
    42-43 7/12/2016 Transport, Boltzmann equation [Ch. 13 and 16] Boltzmann eq.: Ch. 13 only Introduction; Ch. 16: Sect. IV (The Boltzmann eq.); Sect. I (Source of el. scattering); Ch. 16: Sect. II (Scattering prob. and relaxation time); Sect. III (Rate of change of the distribution function due to collisions). ( lecture notes, see parts 1-4). Ch. 13 Sect. IV (DC and AC Electric conductivity); transport in anisotropic materials ( lecture notes, see parts 5-6) ( lecture notes).
    44-45 14/12/2016 Semiconductors [Ch. 28] Homogeneous semiconductors: materials (elemental and compounds), typical bandstructures, intrinsic and extrinsic semiconductors. Intrinsic case: number of carriers in thermal equilibrium. Extrinsic semiconductors: donor and acceptor levels.
    46 14/12/2016 Exercises: correction of the I written partial test
    47-48 15/12/2016 Exercises on Bloch electrons and semiclassical model
    49 21/12/2016 Magnetism [Ch. 31] Few concepts about Magnetism in solids: Larmoor diamagnetism; Pauli paramagnetism. (this lecture is not part of the exam program)
    50 21/12/2016 Exercises on Bloch electrons.
    51-52 11/1/2017 Exercises
    WRITTEN TEST ON THE II PART OF THE COURSE (2h) and FINAL WRITTEN TEST (3h) (Dept. Physics, via Valerio 2, Building F, Room A)
    FINAL WRITTEN TEST (Dept. Physics, via Valerio 2, Building F, Room B)
    ORAL EXAMS (Cond Matt curriculum) (Miramare campus, Leonardo Building, Room 204) for 5 candidates (register on esse3 system!)
    ORAL EXAMS (other curricula) (Miramare campus, Leonardo Building, Room 204) for 5 candidates (register on esse3 system!)
    ORAL EXAMS (other curricula) (Miramare campus, Leonardo Building, Room 204) for 5 candidates (register on esse3 system!)
    ORAL EXAMS (other curricula) (Miramare campus, Leonardo Building, Room 204) for 8 candidates (register on esse3 system!)
    FINAL WRITTEN TEST (Dept. Physics, via Valerio 2, Building F, Room B)
    ORAL EXAMS (Miramare campus, Leonardo Building, Room 204)
    ORAL EXAMS (Miramare campus, Leonardo Building, Room 204)
    FINAL WRITTEN TEST (Dept. Physics, via Valerio 2, Building F, Room B) (register on esse3!)
    ORAL EXAMS (Miramare campus, Leonardo Building, Room 204) (register on esse3!)
    9:00-12:00 CORRECT! (esse3) (wrong, old schedule: 14:00-17:00)
    FINAL WRITTEN TEST (Dept. Physics, via Valerio 2, Building F, Room B) (register on esse3!)
    FINAL WRITTEN TEST (Miramare Campus, Leonardo Building, Room 204) (register on esse3! "prova parziale")
    FINAL WRITTEN TEST (Dept. Physics, via Valerio 2, Building F, Room D) (register on esse3! "prova parziale")

    Textbooks and other material:

  • N. Ashcroft, N D. Mermin, Solid State Physics, Saunders College (1976)
  • G. Grosso and G. Pastori Parravicini, Solid State Physics, Elsevier
  • C. Kittel, Introduction to Solid State Physics, Wiley (1996).

  • L. Mihaly e M.C. Martin, Solid State Physics: Problems and Solutions, Wiley (1996).

  • Exams:
    Two partial written tests (partial: on the first and on the second half of the program) or one final written exam + final oral exam. Dates to be announced. Typically 2 - 3 hours available for the written tests. You can bring with you books, lecture notes...
    Examples of past written intermediate tests and final exams:

    Test.I 23-11-2010
    Test.II 12-01-2011
    Final exam 25-01-2010
    Test.II 16-01-2012
    Final exam 23-01-2012
    Final exam 24-02-2012
    Final exam 20-06-2012
    Final exam 11-07-2012
    Test.II 14-01-2013
    Final exam 28-01-2013
    Final exam 15-02-2013
    Final exam 11-06-2013
    Test.I 14-11-2013
    Test.II 19-12-2013
    Final exam 27-01-2014
    Final exam 17-02-2014
    Final exam 24-06-2014
    Final exam 14-07-2014
    Final exam 10-09-2014 (the same of 20-06-2012!)
    Test.I 18-11-2014
    Test.II 13-01-2015
    Final exam 23-01-2015
    Final exam 16-02-2015
    Final exam 25-02-2015
    Final exam 13-07-2015
    Test.I 20-11-2015
    Test.II 14-01-2016
    Final exam 19-01-2016
    Final exam 08-02-2016
    Final exam 04-07-2016
    Final exam 16-01-2017

    Last modified: August 2017