Slides Ed. 2021

Introduction and Basic Concepts (Leni Bascones)

      • Emergence in condensed matter systems. Focus on electronic properties
      • Some basic concepts: Fermi statistics, screening, Hubbard model, quantum mechanics representations …

The Fermi liquid (Leni Bascones)

      • Adiabaticity and quasiparticles. Quasiparticle weight and the spectral function
      • The energy functional. Fermi liquid parameters. Renormalized mass and residual interactions
      • Measurable properties: specific heat, bands in ARPES, spin susceptibility, resistivity.

Mott physics in single orbital systems (Leni Bascones)

        • The Mott transition at half-filling and zero temperature.
        • Mott-Hubbard and Brinkmann-Rice approaches. DMFT description of the transition
        • Finite temperatures
        • Doping away from half-filling
        • Beyond single-site DMFT
        • Cuprates. Doping a Mott insulator in two dimension.

Mott and Hund physics in multi orbital systems     (Leni Bascones)

    • The Mott transition in multi-orbital systems
    • Hund metals
    • Iron superconductors.

Magnetism   (María José Calderón)

      • Free magnetic atoms
      • Environment
      • Magnetic order and susceptibility
      • Exchange between localized moments
      • Indirect exchange between itinerant electrons
      • Magnetism in metals
      • Excitations

Superconductivity (2 talks) (María José Calderón)

The Kondo effect in metals and nanostructures (Ramón Aguado).

        • Local moments in metals: first experimental puzzles.
        • Anderson and Kondo models.
        • Quenching of local moments: Kondo’s calculation.
        • Anderson’s poor man scaling
        • Non perturbative approaches
        • The Kondo resonance
        • The two impurity Kondo model
        • The Kondo lattice
        • Kondo in mesoscopic systems: quantum dots and nanotubes, non-equilibrium effects.
        • New developments: hybrid systems (competition between superconductvity and Kondo), Shiba states, etc.

Topological materials

        •  The Dirac equation: Originis, definition and the concept of spin.
        • Bloch theorem. Symmetries with and without spin.
        •  Dirac equation on a lattice: graphene, stanene, TMDC,
        • the BHZ model, Bi2Se3…
        •  Edge/surface states: Jackiw/Rebbi construction.
        • Beyond Landau
        • Characterization of topological phases
        • TKNN theory. Berry connection and Berry curvature
        • Path integral formalism

      Topological Semimetals  (Alberto Cortijo)




Instituto de Ciencia de Materiales de Madrid, CSIC