Notes on steady state current through a noninteracting quantum dot

Abstract

A pedagogical introduction to matrix Green's function, focusing on its application to steady state transport through discrete-level quantum systems. Topics covered in the notes: 1. Retarded Green's function, spectral function and density of states 2. LCR system 3. Green's function and spectral function of LCR systems 4. Landauer formula and transmission coefficient 5. Semi-infinite tight-binding leads and wide-band limit 6. Linear conductance at zero temperature 7. Steady state current in a quantum dot: resonance and coherence 8. Steady state current across a tight-binding chain: metal-insulator transitions 9. Steady state current along the edge of a two-dimensional lattice: topologically quantized transport