Schema della sezione

  • Introduction

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    The "Condensed Matter Physics I" Course is given in the first term, for a total number of 48 hours (6 credits). It is compulsory 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:
    Lectures are generally planned in these slots:
    Mon., 9:00-11:00
    Wed., 9:00-11:00

    in Room A and D, Building A (Piazzale Europa, 1)

    Students are kindly invited to check the announcements for possible changes/updates


    Textbooks:
    N. Ashcroft, N D. Mermin, Solid State Physics, Saunders College (1976) (main text).
    G. Grosso and G. Pastori Parravicini, Solid State Physics, Academic Press (2000)
    C. Kittel, Introduction to Solid State Physics, Wiley (1996).
    L. Mihaly e M.C. Martin, Solid State Physics: Problems and Solutions, Wiley (1996).

     

    Exams:

    The exam includes written & oral parts

    Six dates for the final written test are or will be scheduled  (2 dates in Jan/Feb 2021; 2 in June/July 2021; 2 in September 2021: see esse3.

    The oral exam must be done within few days after the written test (depending on the number of candidates).

    Typically 2 hours available for the written tests. Books and lecture notes can be used during the written exams.

    Starting from the Summer session and unless other info, the exams will be done in presence. Exceptionally will be done in remote under motivated and documented request, as explained in the UniTS guide lines reported on https://www.units.it/ateneo/emergenza-covid-19-indicazioni-e-aggiornamenti. The specific form of the written test will depend on the presence or not of candidates in remote mode: in such a case, the written part will include a multiple choice test for all the candidates.



  • Transport of noninteracting electrons: Drude model (5 and 7 Oct. 2020)

    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.

    AC electrical conductivity; dielectric function and plasma frequency. Thermal conductivity and Wiedemann-Franz law. Seebeck effect (Ashcroft-Mermin, Ch. 1) 

  • Transport of noninteracting electrons: Sommerfeld model (12, 14, 19, 21 Oct. 2020)

    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.

    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.

    Exercises.

    [Ashcroft-Mermin, Ch. 2 - Exercises n. 1, 3, 4]



  • Lattice and crystalline structures (Oct. 26, 28; Nov. 2, 4)

    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.

    Other examples of Bravais lattices with basis: zincblende, rocksalt, wurzite (one slide). Wigner-Seitz cells. Reciprocal lattices. Families of lattice planes

    Miller indices. Brillouin zone. X-ray diffraction: Bragg and von Laue.  Structure factor.

    [Ashcroft & Mermin, Ch. 4, 5, 6]


  • Exercises on free electrons models and crystalline structures (Nov. 9, 11))

    For the Ist partial written test, review of exercises of previous exams, e.g., 7/11/2018 (1st) + those uploaded here concerning the Drude & Sommerfeld models.

  • Independent electrons in a periodic potential: general aspects (Nov. 18, 21, 23, 25)

    Periodic potential: Bloch theorem, I and II proof (Ch. 8).

    Consequences of the Block theorem: quasi-crystalline momentum; velocity; energy bands. (Ch. 8)

    Fermi surfaces. Density of states (DoS): different approaches. Derivation of the DoS using the properties of the delta-function (see notes).

    Band index and folding. Van Hove singularities in 1D, 2D, 3D. (Ch. 8)

    Brillouin zones, band folding and band indices, band plots in reduced zone / periodic / extended representation. Fermi surfaces [Ch. 9].

  • Approximated treatment of electrons in a periodic potential: effects of a weak potential (Nov. 30)

    Effects of a weak perturbing potential (nearly free electrons): non degenerate case; degenerate case (two-levels system) (A&M, ch. 9; excluding The geometrical structure factor in monoatomic lattices with bases)

    Exercises on weak potential: simple cases in 1D

  • Approximated treatment of electrons in a periodic potential: tight-binding approach (Dec. 2, 5)

    The tight-binding approach: introduction, general formulation; the simplified case of s-band arising from a single atomic s-level. Tight-binding in crystals with inversion symmetry; band dispersion. (A&M, ch. 10).

    Exercise: tight-binding: s-band arising from a 1D linear chain of atoms, density of states; half filling of band.

    Suggested as homework: s-band in 2D square lattice: band dispersion along some high symmetry directions, energy isosurfaces in the Brillouin zone.

  • The semiclassical model of electron dynamics (Dec. 9, 14)

    Validity of semicl. dynamics. Equations of motions. Filled bands. Holes. [first part of Ch. 12]

    Orbits in r and k space. Motion of electrons in uniform and static electric fields. Motion of electrons in uniform and static magnetic fields; electron orbits, hole orbits, open and closed orbits. Period of closed orbits. Fermi surfaces of real metals (examples from www.phys.ufl.edu/fermisurface)

  • The Boltzmann equation (Dec. 16)

    Issues discussed in class and requested for the exam:

    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 Electrical conductivity) ( lecture notes, see part 5)

    Issues not discussed in class, optional, not requested for the exam:

    AC Electric conductivity (Ch. 13 Sect. IV); transport in anisotropic materials (lecture notes, see parts 5-6)

  • Semiconductors (Dec. 21)

    Homogeneous semiconductors: materials (elemental and compounds), typical band structures, intrinsic and extrinsic semiconductors.  Intrinsic case: number of carriers in thermal equilibrium.  Extrinsic semiconductors: donor and acceptor levels.  (Ch. 28; excluding: population of impurity levels in thermal equilibrium, eqs. 28.30-28.34)


  • Exercises (Dec 23, Jan 11)

    Jan. 11, 2021:

    ·      20/12/2019 Esercizio 3 (punti 3),4),5)).

    ·      20/09/2018 Esercizio 3 (in particolare il punto 3)

    ·      30/01/2017 es3 ( distorsioni di Peierls ) => vedere soluzione completa

    ·      16/01/2017 es2 punto 6 (ampiezza dell'oscillazione per γ ed E tipici).

    ·      16/01/2017 Esercizio 1  (dubbi sulle richieste); 

    ·      8/02/2016 Esercizio 2 => vedere soluzione completa

    ·      16/02/2015 Esercizio 2

    ·      19/12/2013  Esercizio 3, punti 5 e 6 (condizione sul termine di damping).

    ·      11/07/2012 esercizio 3





  • prova parziale intermedia (16 Nov)

    • Quiz - Elettroni liberi
      Accesso consentito fino al 16 novembre 2020, 09:50
    • Problemini strutture cristalline Compito
      Accesso consentito fino al 16 novembre 2020, 11:10
    • struttura β-Sn File PNG
    • testo quiz e risposte corrette File PDF
    • soluzione problemini File PDF

  • seconda prova parziale (13 genn. 2021)

    • Quiz II prova parziale

      Ci sono 15 domande a risposta multipla.  Una sola risposta è esatta.

      Ogni domanda vale 2 punti: +2 risposta esatta, -1 risposta errata, 0 non risposto.

      Quindi il punteggio del Quiz è normalizzato a 30. Sufficienza con almeno 18/30.

      Tempo 15 minuti.

      Accesso consentito fino al 13 gennaio 2021, 09:35
    • Compito della II prova parziale

      Il compito consta di 10 domande. E' richiesto di farle tutte. Il tempo di consegna potrà costituire elemento di valutazione.

      Accesso consentito fino al 13 gennaio 2021, 10:45

  • Test utilizzo strumento quiz per le prove scritte on line

    • quiz di prova
      Accesso consentito fino al 18 gennaio 2021, 18:15

  • prova scritta (20 gennaio 2021)

    • Quiz 20/1/2021

      Ci sono 15 domande a risposta multipla.  Una sola risposta è esatta.

      Ogni domanda vale 2 punti: +2 risposta esatta, -1 risposta errata, 0 non risposto.

      Quindi il punteggio del Quiz è normalizzato a 30.

      Tempo 15 minuti.


      Accesso consentito fino al 20 gennaio 2021, 09:30
    • compito 20/1/2021
      Accesso consentito fino al 20 gennaio 2021, 10:55

  • prova scritta (22 febbraio 2021)

    • Quiz 22/2/2021

      Ci sono 15 domande a risposta multipla.  Una sola risposta è esatta.

      Ogni domanda vale 2 punti: +2 risposta esatta, -1 risposta errata, 0 non risposto.

      Quindi il punteggio del Quiz è normalizzato a 30.

      Tempo 15 minuti.


      Accesso consentito fino alla fine del 26 febbraio 2021
    • Compito 22/2/2021
      È possibile svolgere il compito su fogli e poi scansionarli; in alternativa, usare qualsisi editor di note, testi e documenti in uso sul proprio pc.
      In ogni caso, alla fine fare un UNICO FILE PDF nominato COGNOME.pdf e caricarlo (limite 20 Mb).
      Il tempo per lo svolgimento è 1h 15'. Altri 15' extra sono concessi SOLO per il caricamento. ATTENZIONE: NON VERRANNO CONCESSE PROROGHE (IL SISTEMA CHIUDERÀ AUTOMATICAMENTE), QUINDI NON UTILIZZARE I MINUTI EXTRA PER TENTARE DI COMPLETARE LO SVOLGIMENTO.

  • prova scritta (15 giugno 2021)

    • Quiz

      Ci sono 15 domande a risposta multipla.  Una sola risposta è esatta.

      Ogni domanda vale 2 punti: +2 risposta esatta, -1 risposta errata, 0 non risposto.

      Quindi il punteggio del Quiz è normalizzato a 30.

      Tempo 15 minuti.


      Accesso consentito fino al 17 giugno 2021, 23:55
    • Compito
      Accesso consentito fino al 15 giugno 2021, 11:00