Quantum Mesoscopic Physics and Topological Matter
Lecturer : Mark Oliver Goerbig
These lectures introduce recent developments and fundamental questions in condensed matter physics, revealed by the miniaturisation of electronic circuits. We shall explore the world of mesoscopic physics, situated at an intermediate scale between the atoms and the macroscopic objects. Numerous developments are stimulated by the rapid evolution of integrated-circuit industry, lithographic methods and the synthesis of novel materials. As an example, it is now possible to fabricate samples in which the electrons propagate in strictly one or two spatial dimensions, almost without collisions.
We shall present the basic mechanisms of electronic transport at the mesoscopic or nanoscopic scales, where the macroscopic laws no longer apply and where new concepts related ton quantum mechanics are necessary. In particular, we shall describe the following phenomena : effects of quantum interferences on electronic transport, quantisation of the conductance, quantum Hall effect, and the quite recent physics of graphene, a purely two-dimensional crystal where the dynamics of the electrons is the dynamics of massless particles (Nobel Prize 2010). Beyond its interest in the physics of two-dimensional materials, graphen has given birth to a new research field in condensed-matter physics : topological matter. We introduce the description of topological insulators and semi-metals possessing "ultra-relativistic" electrons in two and three spatial dimensions as well as the so-called bulk-edge correspondence. The latter states that in spite of the bulk insulating properties, a topological insulator reveals conducting edges or surfaces that are topologically protected. We equally discuss the different technological applications associated with these phenomena.
Outline
New materials and low dimensions
Limitations of the classical description
The field of mesoscopic physics
How to describe electric conduction on the meso- and nanoscopic scales ?
From ballistic to diffusive transport
Electric conduction viewed as a transmission coefficient for electrons :
Landauer-Büttiker formalism, analogies between electronics and optics
Electrons in a strong magnetic field : the quantum Hall effect and its applications
Topological matter in two dimensions : from graphene to the quantum spin Hall effect
Three-dimensional topological insulators ans Weyl semimetals
Course language: English
ECTS credits: 5
- Teaching coordinator: Goerbig Mark Oliver