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Quantum Transport

Course objective: To convey the basic concepts of electronic structure and electron transport to graduate students with little or no background in these subjects.

Brief course description: In recent decades, progress in experimental techniques has made it possible control matter on the atomic scale. One consequence of this nanoscale electronics is that a new transport regime became accessible in which the device size is smaller than the electron mean free path. The properties of such nanostructures cannot be described in terms of macroscopic parameters like mobility and diffusion coefficient. When the electron traverses the device without scattering a new quantum treatment of transport is necessary to keep track of the phase of the electron. Another consequence of nanoelectronics is the appearance of new essentially spin phenomena which require going beyond Mott's two current model of transport. The purpose of this course is to review some of the theoretical tools that are available for describing spin-dependent transport phenomena in nanostructures. The course will cover the necessary quantum mechanics and non-equilibrium statistical mechanics required for understanding of electron transport. In addition, elementary introduction to the electronic structure of solids and the methods for calculating it will be given. Some of the most popular modern methods for calculating transport properties, such as the Landauer and Keldysh formalisms, will be discussed.

Prerequisite: Matrix algebra, familiarity with MATLAB (or equivalent)

Text: S. Datta, Quantum Transport: Atom to Transistor, Cambridge (2005), ISBN 0521631459; S. Data, Electronic Transport in Mesoscopic Systems, Cambridge (1997), ISBN 0521599431.

Tentative Course Outline:

Week 1: Preliminary conceptsWeek 2-7: Electronic structure: Schrodinger equation; wavefunctions; self-consistent field; basis functions; band structure; density of statesWeek 8-15: Electron transport: coherent transport; transmission function; S-matrix; Green functions; self-energy; non-equilibrium Green functions; transport formalisms (Boltzmann, Landauer, Kubo, Keldysh); Coulomb blockade