Description

When classical charged particles are subjected to a magnetic field B, they experience the Lorentz force which is perpendicular to their velocity. The resulting motion is a circular orbit perpendicular to the direction of B. When the magnetic field is strong, Quantum effects become important and the bound states are subject to quantisation conditions resulting to what is known as Landau levels.

When many Quantum Mechanical particles are brought together in a magnetic field, a new phase of matter is formed resulting to a set of phenomena collectively termed as The Quantum Hall Effect. The most prominent experimental signatures is the so called Hall conductivity. Conductivity is generically a macroscopic property of real materials which is itself quantised in such states of matter. The quantisation of a macroscopic property of a many body system is rather suprising and its origin is not directly linked to the quantisation conditions of the single particle problem. The explanation relies largely on ideas resulting from geometry and topology.

The students involved in the project will explore the original, microscopic explanation of the Quantum Hall Effect through the many body wavefunction. A more elegant approach to modeling such systems comes from ideas of effective field theory. As it turns out, Chern-Simons theory essentially captures the crucial physics underlying the Quantum Hall Effect. A third approach is the consideration of the so called edge modes. These are degrees of freedom that leave on the boundary of the sample but can tell you about everything that is going on inside the material.

Prerequisites:

• Mathematical Physics II

Co-requisites:

• Quantum Mechanics III

Resources:

• For a brief introduction to the concepts see the Wiki pages
• An excellent set of notes by D. Tong
• Another set of lectures by S. Grivin
• E. Witten's notes on topological phases of matter