**(Course description last updated for academic year 2020-21)**.

##### Prerequisites

The Part II Quantum Condensed Matter Physics course would be useful but is not vital.

##### Learning Outcomes and Assessment

This course aims to introduce students to the transport and optical physics of a range of systems where electrons are confined within less than about 100 nm in one or more dimensions. Familiarity with some solid-state physics in assumed (the Part II Quantum Condensed Matter Physics course would be useful but is not vital). On completion of the course, students should be able to appreciate the physics of low-dimensional systems, to describe experiments to measure such systems, and to calculate straightforward problems related to the field.

##### Synopsis

**Introduction to low dimensional systems:** length and energy scales, overview of fabrication techniques and possibilities, applications of low-dimensional physics, *examples, top-down vs bottom-up*.

**Electronic properties in low-dimensional systems:** band engineering; heterostructures, 2D electron gas.

Ballistic motion, collimation, experiments.

Quantum transport in 1D wires: eigenstates, conductance, saddle-point potential, d.c. bias.

Electrons in high magnetic fields: Hall effects, Landau levels, the oscillation of the Fermi energy. Landauer-Büttiker formalism, integer quantum Hall effect, edge states.

Electron-electron interactions, quasiparticles. Fractional quantum Hall effect, composite fermions.

Transport through 0D quantum dots, Coulomb blockade, resonant tunnelling, charge detection, single-electron dots, artificial atoms, antidots. Surface-acoustic-wave current source.

**Optical properties.** Optical transitions, excitons. Semiconductor lasers as example of effects of confinement. S-K growth, self-assembled quantum dots, microcavities, coupled modes. Single and entangled photon sources for quantum cryptography.

**Spintronics:** Giant magnetoresistance (briefly), tunnelling magnetoresistance (spin-valve) in layered structures. Spin injection from a ferromagnet to a semiconductor.

**Quantum computation (briefly).** Spin in a quantum dot as a qubit for quantum computation. Detection and manipulation of single spins – charge-to-spin conversion, electron spin resonance.

**Molecular systems.** Self-assembly. Conjugated polymers – electronic structure and devices. Transport in carbon nanotubes and graphene. Single-molecule transport. Nanocrystals, nanorods.

BOOKS

A comprehensive set of notes will be given out. No book covers the whole course. Background material may be found in semiconductor textbooks such as Kittel, and Ashcroft and Mermin.

*Low-dimensional Semiconductors: Materials, Physics, Technology, Devices, *Kelly M J (Clarendon Press 1996).

*The physics of low-dimensional semiconductors: an introduction, *Davies J H (CUP 1997).

*Nanophysics and Nanotechnology*, E. L. Wolf (Wiley-VCH 2007).