Quantum dots

The number of electrons in atoms can be tuned by ionization, while in QGs – by changing the confinement potential. This is similar by a replacement of nucleus ...
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Quantum dots

Quantum dot (QD) is a conducting island of a size comparable to the Fermi wavelength in all spatial directions. Often called the artificial atoms, however the size is much bigger (100 nm for QDs versus 0.1 nm for atoms). In atoms the attractive forces are exerted by the nuclei, while in QDs – by background charges. The number of electrons in atoms can be tuned by ionization, while in QGs – by changing the confinement potential. This is similar by a replacement of nucleus by its neighbor in the periodic table.

Quantum dots


Comparison between QDs and atoms Parameter


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Level spacing

1 eV

0.1 meV

Ionization energy

10 eV

0.1 meV

Typical magnetic field

104 T

1-10 T

QDs are highly tunable. They provide possibilities to place interacting particles into a small volume, allowing to verify fundamental concepts and foster new applications (quantum computing, etc). Quantum dots


Phenomenology of quantum dots


AFM micrograph of the gates structure to define a QD in a Ga[Al]As heterostructure.

The Au electrodes (bright) have a height of 100 nm. The two QPCs formed by the gate pairs F-Q1 and F-Q2 can be tuned into the tunneling regime, such that a QD is formed between the barriers. Its electrostatic potential can be varied by changing the voltage applied to the center gate Lateral quantum dot Quantum dots


Conductances of all QPCs can be tuned by proper gate voltages. The F-Q1 and F-Q2 pairs behave as perfect quantized QPCs The contact F-C cannot be pinched off, but still shows depletion The central gate is designed to couple well to the dot, but with a weak influence on QPCs. Blue arrow shows the working point. Quantum dots


Gate voltage characteristics Pronounced oscillations The reason of the oscillations was not clear in the beginning: Coulomb blockade? Resonant tunneling?

The usual way to find the answer is to study magnetotransport

Quantum dots


The position of 22 consecutive conductance resonances as function of the gate voltage and the magnetic field. The QD has an approximately triangular shape with a width and height of about 450 nm. The upper inset shows peak spacings at B=0 as a function of QD’s occupation. They are consistent with theory (FockDarwin- model) center gate Quantum dots


Why the peaks are not equidistant? • There is a smooth dependence on the gate voltage, just because of change in the geometry (and consequently, in capacitances); • In addition to a smooth dependence there are pronounced fluctuations – a rather rich fine structure. This fine structure is shown in the next slide, where the smooth part is subtracted

Quantum dots


One can discriminate between three main regimes: 1. Weak magnetic fields – the spacings fluctuate, with a certain tendency to bunch together for small occupation numbers; 2. Intermediate regime – quasiperiodic cusps; 3. High magnetic fields Level fine structure for up to 45 electrons on the dot

The observed structure needs an interpretation! Quantum dots


What one would expect for a QB device? SET

Diamond stability diagram

V=10 μV

Quantum dots


Stability diagram for a Quantum Dot Resembles diamond structure for Coulomb blockage (SET) system. However, size of diamonds fluctuates. At low bias – resembles usual CB oscillations; At larger bias a fine structure emerges, which is absent in SETs

Quantum dots


Finally, the amplitude of resonances can be tuned by magnetic field: Here we see amplitudes of five consecutive resonances versus magnetic field. The peak positions fluctu