The developments of nanofabrication have enabled the design of electronic systems that exhibit spectacular signatures of quantum coherence. Basic concepts and analytical tools needed to understand nanophysics are presented in a series of theoretical fundamental courses.
Contents
Lecturers; Seminar speakers; Participants; Preface; Contents; Fundamental aspects of electron correlations and quantum transport in one-dimensional systems; Introduction; Non-Fermi liquid features of Fermi liquids: 1D physics in higher dimensions; Long-range effective interaction; 1D kinematics in higher dimensions; Infrared catastrophe; 1D; 2D; Dzyaloshinskii-Larkin solution of the Tomonaga-Luttinger model; Hamiltonian, anomalous commutators, and conservation laws; Reducible and irreducible vertices; Ward identities; Effective interaction; Dyson equation for the Green's function
Solution for the case g2 = g4Physical properties; Momentum distribution; Tunneling density of states; Renormalization group for interacting fermions; Single impurity in a 1D system: scattering theory for interacting fermions; First-order interaction correction to the transmission coefficient; Hartree interaction; Exchange; Renormalization group; Electrons with spins; Comparison of bulk and edge tunneling exponents; Bosonization solution; Spinless fermions; Bosonized Hamiltonian; Bosonization of fermionic operators; Attractive interaction; Lagrangian formulation; Correlation functions
Fermions with spinTunneling density of states; Transport in quantum wires; Conductivity and conductance; Galilean invariance; Kubo formula for conductivity; Drude conductivity; Landauer conductivity; Dissipation in a contactless measurement; Conductance of a wire attached to reservoirs; Inhomogeneous Luttinger-liquid model; Elastic-string analogy; Kubo formula for a wire attached to reservoirs; Experiment; Spin component of the conductance; Thermal conductance: Fabry-Perrot resonances of plasmons; Polarization bubble for small q in arbitrary dimensionality; Polarization bubble in 1D; Small q
Q near 2kFSome details of bosonization procedure; Anomalous commutators; Bosonic operators; Commutation relations for bosonic fields phi and nu; Problem with backscattering; References; Impurity in the Tomonaga-Luttinger model: A functional integral approach; Introduction; Functional integral representation; The effective action for the Tomonaga-Luttinger Model; The bosonized action for free electrons; Gauging out the interaction; Tunnelling density of states near a single impurity; Jacobian of the gauge transformation; References
Novel phenomena in double layer two-dimensional electron systemsIntroduction; Overview of physics in the quantum hall regime; Basics; Quantized hall effects; Integer QHE; Fractional QHE; Composite fermions; Double layer systems; Coulomb drag between parallel 2D electron gases; Basic concept; Experimental; Elementary theory of Coulomb drag; Comparison between theory and experiment; Tunneling between parallel two-dimensional electron gases; Ideal 2D-2D tunneling; Lifetime broadening; 2D-2D tunneling in a perpendicular magnetic field
