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Introduction
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Quantum dots are small devices that contain a tiny droplet of free electrons. They are fabricated in semiconductor materials and have typical dimensions between nanometres to a few microns. The size and shape of these structures and therefore the number of electrons they contain, can be precisely controlled; a quantum dot can have anything from a single electron to a collection of several thousands. The physics of quantum dots shows many parallels with the behaviour of naturally occurring quantum systems in atomic and nuclear physics. As in an atom, the energy levels in a quantum dot become quantized due to the confinement of electrons. Unlike atoms however, quantum dots can be easily connected to electrodes and are therefore excellent tools to study atomic-like properties. There is a wealth of interesting phenomena that have been measured in quantum dot structures over the past decade. Below are a few examples from our group. The next paragraph first discusses briefly the parallels between atoms and quantum dots.

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Artificial atoms
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The three-dimensional (3D) spherically symmetric potential around atoms yields degeneracies known as shells, 1s, 2s, 3s, 3p,... Each shell can hold a specific number of electrons. The electronic configuration is particularly stable when these shells are completely filled wih electrons, occurring at 'magic' atomic numbers 2, 10, 18, 36,... In a similar way, the symmetry of a two-dimensional (2D), disk-shaped quantum dot leads to a shell structure with magic numbers 2, 6, 12, 20,... The lower degree of symmetry in 2D results in a different sequence of magic numbers than in 3D. By measuring electron transport through quantum dots, a periodic table of artificial 2D elements can be obtained. For this purpose, dots are connected via potential barriers to source and drain contacts. If the barriers are thick enough enough, the number of electrons on the dot, N, is a well defined integer. This number changes when electrons tunnel to and from the dot. However, due to Coulomb repulsion between electrons, the energy of a dot containing N+1 electrons is larger than when it contains N electrons. Extra energy is therefore needed to add an electron to the dot. Consequently, no current can flow which is known as the Coulomb blockade. The blockade can be lifted by means of a third electrode closeby, known as the gate contact. A negative voltage applied to this gate is used to supply the extra energy and thereby change the number of free electrons on the dot. This makes it possible to record the current flow between source and drain as the number of electrons on the dot, and hence its energy, is varied. The Coulomb blockade leads to a series of sharp peaks in the measured current (see figure below). At any given peak, the number of electrons on the dot alternates between N and N+ 1. Between the peaks, the current is zero and N remains constant. The distance between consecutive peaks is proportional to the so-called addition energy, which is the difference in energy between dots with N+1 and N electrons. The magic numbers can be identified because significantly higher voltages are needed to add the 2nd, 6th and 12th electron. Quantum dots are 2D analogies for real atoms. But since they have much larger dimensions they are suitable for experiments that can not be carried out in atomic physics. It is especially interesting to observe the effect of a magnetic fieldd, B, on the atom-like properties. A magnetic flux-quantum in an atom requires typically a B-field as high as 10^6 T, whereas for dots this is of the order 1 T, which is experimentally accessible.

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Current research
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Current research focusses on the coherent manipulation of individual electron spins isolated in single and coupled quantum dots, with the goal of realizing an elementary quantum computer in the solid state. For more information, please visit the page of the Delft spin qubit project.

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Introductions and review articles
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**1. ***Quantum Dots*

L.P. Kouwenhoven and C.M. Marcus

Physics World vol.11 no. 6, 35-39 (1998)

PDF(680KB)

**2. ***Electron transport in quantum dots.*

L.P. Kouwenhoven, C.M. Marcus, P.L. McEuen, S. Tarucha, R.M. Westervelt,
and N.S. Wingreen

Proceedings of the NATO Advanced Study Institute on Mesoscopic Electron
Transport, edited by L.L. Sohn, L.P. Kouwenhoven, and G. Schön (Kluwer
Series E345, 1997) p. 105-214

PDF(3949KB)

**3.*** Few-electron Quantum Dots*

L.P. Kouwenhoven, D.G. Austing, S. Tarucha

Reports on Progress in Physics 64 (6), 701-736 (2001)

PDF(1352KB)

**4.***Electron transport through double quantum dots.*

W. G. van der Wiel, S. De Franceschi, J. M. Elzerman, T. Fujisawa, S. Tarucha and L. P. Kouwenhoven

Rev. Mod. Phys. 75 **75**, No.1, 1-22 (2003)

PDF(1.17MB)