Introduction to Quantum Transport in Nanoscience

(3 Credit Hours) · Undergraduate

The flow of heat, light, spin and electrical current on a nanometer-scale has revealed evidence of quantum mechanical effects for which classical physics cannot account. So, to equip the student with the tools required to invent future technologies in electronics, photonics, spintronics, quantum computing, quantum biology, sensing and metrology, this course tackles quantum transport on a nanometer-scale. With the introduction of the Schrodinger's and Maxwell's equations, the concept of a band structure and energy dispersion relations will be developed. In this context, compelling examples such as: quantum mechanical tunneling in a scanning tunneling microscope; Landau levels, edge states and Chern numbers in quantum Hall effect; conductance quantization in an electron wave-guide; flux-quantization in the Aharanov-Bohm effect and the Berry phase; photonic waveguides that bend light around corners; and metamaterials that scatter light in non-classical ways will be scrutinized through a variety of methods including the Boltzmann transport equation, perturbation theory and Fermi's Golden rule, the Landauer formula, non-equilibrium Green's functions (NEGF). This course does not require a background in quantum mechanics, but assumes only knowledge of basic concepts of vector algebra and some facility for solving differential equations. This course is intended for advanced undergraduates and graduate students in electrical engineering and biology, in particular, and engineering generally. Intro to Linear Algebra and Differential Equations ( MATH 20580 ) OR Differential Equations ( MATH 30650 ) recommended but not required.