Introduction and Overview- classical, semi-classical and quantum transport, diffusive and ballistic transport, different length scales, near-equilibrium and high-field transport, transport in magnetic fields

Classical diffusive transport- continuity and drift-diffusion equation, scattering and Poisson process, random walk model of drift-diffusion, master equation/rate equation

Smoluchowski's formulation of transport phenomenon, charge and spin transport, master equation for quantum states and corresponding Boltzmann H-theorem, entropy and thermodynamics

Thermodynamics, equilibrium vs non-equilibrium, maximum entropy principle,equilibrium distributions - Maxwell-Boltzmann, Fermi-Dirac andBose-Einstein distributions

Lattice vibrations and phonon, quantum mechanics and Schrodinger equation,operator method and quantization of phonon energy, Plank's law,Debye-Einstein theory of specific heat, anharmonic effects

Free electron theory, Sommerfeld theory of electrons in metals, metals vssemiconductors, classical Hamiltonian mechanics, Heisenberg equation ofmotion, wave vs particle viewpoint

Liouville's theorem, Boltzmann transport equation (BTE) and collisionintegral for classical particle, electron and phonon transport,equilibrium and non-equilibrium

Boltzmann transport equation: relaxation time approximation,linearization, spherical harmonic expansion, momentum dependent scatteringand effect of backscattering

Boltzmann transport equation: moment equations, drift-diffusion equationand energy transport equations, coupled charge and heat transport,ballistic limit, quantum correction

Periodic potential and Bloch's theorem, band-structure calculation,effective mass approximation, Bloch oscillations, semi-classical transport

Stern-Gerlach experiment and spin, angular momentum, Pauli Hamiltonian,spin-orbit coupling, spin Hamiltonian for ferromagnet, Graphene andTopological Insulator (TI)

Fermi Golden Rule (FGR), Bardeen's transfer Hamiltonian, FGR and collisionintegral of BTE, applications in ferromagnet and TI heterostructures

Quantum ballistic transport- Landauer-Buttiker formalism, ballistic conductance and conductance quantization, quantum size effect, energy dispersion relation and density of states in 3D, 2D and 1D

Conductance from transmission, transmission modes in 3D, 2D and 1D, coherent and non-coherent transport, ballistic to diffusive limits, localization

Quasi-Fermi levels, voltage drop and heat dissipation, elastic and inelastic scattering, multi-terminal measurement and reciprocity

Spin transport and spin dependent resistance, Julliere formula, Giant magnetoresistance and tunnel magnetoresistance, spin-torque, quantum transport in magnetic fields, emerging spin-orbit devices

Fluctuation-dissipation theorem, Onsager reciprocity, thermoelectric effects, Maxwell demon

Nanoscale device applications:resonant tunneling diode, quantum capacitance and nano-transistor, Summary and Outlook

Recommended Reading

1. Datta, S., Lessons from nanoelectronics- a new perspective on transport, Vol. 1. World Scientific publishing company, 2012.
2. Lundstrom, M., Fundamentals of carrier transport, Cambridge University press, 2009.
3. Datta, S., Electronic transport in mesoscopic systems, Cambridge University press, 1997.
4. Van K., Nicolaas G., Stochastic processes in physics and chemistry, Vol. 1. Elsevier, 1992.