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)

• Conventional Superconductivity

  Unconventional Superconductivity

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

• The Kondo effect in metals I

• • • • Local moments in metals: first experimental puzzles.
      • Anderson and Kondo models.
      • Quenching of local moments: Kondo’s calculation.
      • Anderson’s poor man scaling

• The Kondo effect in metals II

• • • • Non perturbative approaches
      • The Kondo resonance
      • The two impurity Kondo model
      • The Kondo lattice

• The Kondo effect in nanostructures

• • • • 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

• • Dirac materials  (Alberto Cortijo)

• • • •  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.

• Topological Insulators  (Alberto Cortijo)

• • • • Beyond Landau
      • Characterization of topological phases
      • TKNN theory. Berry connection and Berry curvature
      • Path integral formalism

      Topological Semimetals  (Alberto Cortijo)

 

• Topological Superconductors (Ramón Aguado)