Theory and Computation of Transport in Materials and Nanostructures

This module presents an introduction to modern theoretical methods for calculating transport properties of materials and nanostructures using computers. We will focus on the transport of electrical charge carriers as well as of phonons. To describe these phenomena, this module will introduce and describe in particular those theoretical methods allowing for microscopic calculations of transport phenomena in real materials, such as atomic chains and molecular wires. To this end, the basic aspects of methods for electronic-structure calculations, lattice dynamics, and Green’s function techniques will be explained and discussed. Demonstrating the prospects and challenges of these approaches will provide a direct understanding of their advantages and limitations. The physical contents include topics such as:

• Regimes of transport in materials and nanostructures
• Electronic structure: tight binding and density functional theory
• Landauer formalism
• Basic notions of many-body perturbation theory: quasiparticle concept and self-energy
• Green’s functions
• Quantum transport of electrons
• Lattice dynamics and phonons
• Theoretical calculations of heat transport

After successful completion of the module the students are able to:

1. Understand and explain the fundamental physical aspects of modern computational transport methods for materials and nanostructures.
2. To illustrate the prospects, challenges and limitations of the discussed methods as well as explaining their connections.
3. To independently apply the discussed methods to simple materials and nanostructures and interpret the results.

No preconditions in addition to the requirements for the Master’s program in Physics.

The module includes a lecture and exercises.

The lecture will explain methods and calculation schemes in a thematically structured manner with a particular focus on their fundamentals and most important findings and implications. To demonstrate the prospects, challenges and limitations of these methods, literature examples of theoretical and experimental results will be illustrated in computer presentations. Students will be encouraged to participate in scientific discussions both during the lectures as well as after them, in order to strengthen their analytical skills.

The exercises focus, next to detailed discussions for deepening the understanding of the theoretical contents and methods, especially on obtaining the practical skillset to perform computer-based transport calculations on simple material and nanostructures. To this end, the students will also learn the required tools to employ the theoretical methods and analyze the results on the computer. Together with intensive scientific discussions regarding their findings, this will allow students to independently perform such calculations.

online videos, online notes, online forum, supporting website, exercises and examples, example programs, reference data

J. C. Cuevas, E. Scheer: Molecular Electronics: An Introduction to Theory and Experiment, World Scientific Series in Nanoscience and Nanotechnology
S. Datta: Quantum transport: atom to transistor, Cambridge University Press
R. M. Martin: Electronic Structure: Basic Theory and Practical Methods, Cambridge University Press

The achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using presentations independently prepared by the students. The exam of 30 minutes consists of the presentation and a subsequent discussion.

For example an assignment in the exam might be:

• Derive the Green’s function of a free electron in 1D
• Solve analytically the secular equation for a benzene molecule
• Use the variational principle to derive the Kohn-Sham equations
• Compute the current through an atomic chain
• Study the convergence behavior of phonon calculations

Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.

There will be a bonus (one intermediate stepping of "0,3" to the better grade) on passed module exams (4,3 is not upgraded to 4,0). The bonus is applicable to the exam period directly following the lecture period (not to the exam repetition) and subject to the condition that the student passes the mid-term of successful participation in the exercises, which means: active participation in at least at 10 exercises, reach at least 50 % of the exercise points, and the presentation of at least one solution in the exercises.