Recent highlights include: the discovery of the conditions for electron confinement in single layer graphene quantum dots, an effective mass theory of semiconducting carbon nanotube dots and a theory of wave-function imaging by scanning tunnelling microscopy (STM).

To find out more, please contact Professor Peter Maksym, or look at the introduction to our work below.

Background

Semiconductor quantum dots are artificial atoms in which the Coulomb field of a nucleus is replaced by an artificial confining potential. Dots can be made to confine a few electrons and holes, ranging from one upwards, leading to semiconductor analogues of hydrogen, helium and so on.

Image: Atomic resolution STM image of a stack of self assembled quantum dots (50 x 50 nm). PM Koenraad et al Physica E 17 (2003)

Typical dot sizes vary from 10nm to 100nm, at least 100 times larger than a real atom. The largest dots are made by using lithographic techniques to engineer a spatially modulated gate that generates an electrostatic confining potential. The smallest dots self-assemble naturally during growth of materials like InAs on GaAs.

Sophisticated experimental techniques based on the Coulomb blockade allow the numbers of electrons and holes in a dot to be manipulated at will and it is even possible to study optical spectra of individual dots.

Introduction to work at Leicester

We are interested in many types of semiconductor nanostructure including graphene quantum dots, quantum dots on carbon nanotubes and both self assembled and lithographically produced semiconductor quantum dots.

	Carbon nanotube connected to a gold contact. A single electron transistor can be built from a carbon nanotube connected between source and drain contacts. The behaviour of this device is controlled by a quantum dot which is created by confining carriers electrostatically in the centre of the nanotube.
	Schematic of an InGaAs self assembled quantum dot and wetting layer (blue) surrounded by a GaAs matrix (green). The InGaAs alloy in the dot has a higher indium concentration toward the centre (red).
	Schematic of a lithographically produced gated dot. Electrons are confined vertically within the thin layer of InGaAs inside the 500nm wide pillar. The lateral confinement can then controlled by varying the potential on the gate electrode. Image from: L. P. Kouwenhoven et al., Rep. Prog. Phys, 64,701 (2001)

Carbon nanotube quantum dots

Nanotube quantum dots lie at the heart of a new generation of molecular electronic devices. A quantum dot engineered into a carbon nanotube device confines carriers on a length scale of about 10nm or less - about an order of magnitude smaller than the smallest conventional semiconductor devices. Room temperature single electron transistors based on nanotube dots have already been made and it has been proposed that a nanoscale field effect transistor with novel electrically tunable characteristics could be made from a nanotube dot.

Our research program is focused on understanding the interacting few-electron states in a nanotube quantum dot. We are developing theoretical models which can be used to predict device performance and explore spin-dependent phenomena that could be exploited to make new and exotic devices.

Recently we have performed the first calculation of the interacting states for a few (2-6) electrons in a semiconducting nanotube quantum dot. We have investigated the dot addition energy and the quantum states as a function of the parameters of the dot-device and observe examples of both strongly and weakly correlated electron behaviour in the dot.

The figure shows the 6-electron density in a 35,0 nanotube quantum dot. With a large confinement potential (red) the system is weakly correlated and the electrons are forced close together. In the strongly correlated regime (blue) the electrons separate and form Wigner molecule-like states.

Self-assembled quantum dots

We are currently studying self-assembled dots which will have important applications in optoelectronics and optical quantum information technology. As part of our ambitious program we are collaborating with experimental groups in the UK and abroad to develop a reliable dot model which will have the predictive power needed to design dot-based optoelectronic devices.

A crucial part of the work is understanding the physical structure of the dot. A combination of cross-sectional STM imaging, and modelling can be used to obtain information on the shape, size and composition profile of the highly strained quantum dots. We calculate the strain with a continuum finite element model and use it to find the strained confinement potential and position dependent effective masses which appear in the dot effective mass Hamiltonian.

	Atomic resolution STM image of a cleaved InGaAs quantum dot grown at Sheffield. The image contains detailed information on the shape and composition profile of the self assembled quantum dot. The dot was imaged at the Technical University of Eindhoven (D Bruls et al, Appl. Phys. Lett. ,81, 1708, 2002).
	When it is cleaved, the highly strained quantum dot system relaxes outward. We model the strain and deformation with a finite element, continuum model. The deformation, which can be measured in STM experiments, is strongly dependent on the composition profile of the dot.
	Slice planes through the calculated electron confinement potential of the self assembled InGaAs quantum dot shown left. Colour indicates the confinement energies: from red (-0.42 eV) at the top of the InGaAs dot through green to blue to pink (0 eV) in the GaAs matrix.

We find the single particle electron and hole states by exact diagonalisation of the effective mass Hamiltonian.

Isosurfaces of first 4 bound electron (top) and hole (bottom) wavefunctions are shown left to right below. Isosurfaces at 30%. Electrons- positive:red, negative:blue . Holes- positive:copper, negative:aquamarine.

Recently we have investigated a new material system: InAs quantum dots in an AlAs matrix. These dots are of interest because of their large confinement potential and their consequent suitability for resonant tunnelling devices. The figure shows the measured PL for an ensemble of InAs/AlAs dots (Braunschweig) together with 2 calculated energies. The PL energies are calculated (Leicester) from structural information obtained by STM (Eindhoven) on the smallest (S) and largest (L) dots in the sample. (Phys. Rev. B. 72 165332 (2005)).

Electrostatically confined quantum dots

TEM image of a lithographically produced pillar dot.

Our work on electrostatically confined quantum dots centres on correlation effects in a magnetic field. We have developed software for calculating correlated electron and hole states and applied it to study strong correlation in electrostatically confined systems. Our work has shown that confined electrons in a strong magnetic field behave like an electron molecule that rotates and vibrates inside the quantum dot and we have found that this picture is able to predict electron energies to an accuracy of about 1 part in 10,000.

Recently we have performed calculations of spin relaxation effects in gated dots. Importantly we have shown that the dephasing times are long enough to allow quantum computing in systems where the qbits are manipulated with ultrafast optical pulses.