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
10/11/2016
11:15-13:15 WRITTEN TEST ON THE I PART OF THE COURSE
(Room 2A, Building H3)
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 www.phys.ufl.edu/fermisurface)
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
16/1/2017
14:00-17:00 WRITTEN TEST ON THE II PART OF THE COURSE (2h)
and FINAL WRITTEN TEST (3h)
(Dept. Physics, via Valerio 2, Building F, Room A)
30/1/2017
14:00-17:00 FINAL WRITTEN TEST
(Dept. Physics, via Valerio 2, Building F, Room B)
2/2/2017
9:00-17:00 ORAL EXAMS (Cond Matt curriculum)
(Miramare campus, Leonardo Building, Room 204)
for 5 candidates (register on esse3 system!)
6/2/2017
14:00-19:00 ORAL EXAMS (other curricula)
(Miramare campus, Leonardo Building, Room 204)
for 5 candidates (register on esse3 system!)
9/2/2017
9:00-14:00 ORAL EXAMS (other curricula)
(Miramare campus, Leonardo Building, Room 204)
for 5 candidates (register on esse3 system!)
10/2/2017
9:00-18:00 ORAL EXAMS (other curricula)
(Miramare campus, Leonardo Building, Room 204)
for 8 candidates (register on esse3 system!)
22/2/2017
14:00-17:00 FINAL WRITTEN TEST
(Dept. Physics, via Valerio 2, Building F, Room B)
23/2/2017
9:00-17:00 ORAL EXAMS
(Miramare campus, Leonardo Building, Room 204)
24/2/2017
14:00-18:00 ORAL EXAMS
(Miramare campus, Leonardo Building, Room 204)
12/6/2017
14:00-17:00 FINAL WRITTEN TEST
(Dept. Physics, via Valerio 2, Building F, Room B)
(register on esse3!)
15/6/2017
9:00-12:00 ORAL EXAMS
(Miramare campus, Leonardo Building, Room 204)
(register on esse3!)
7/7/2017
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!)
5/9/2017
9:00-12:00 FINAL WRITTEN TEST
(Miramare Campus, Leonardo Building, Room 204)
(register on esse3! "prova parziale")
20/9/2017
9:00-12:00 FINAL WRITTEN TEST
(Dept. Physics, via Valerio 2, Building F, Room D)
(register on esse3! "prova parziale")
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