Device and Measurement Set-up 5
5.2 Device Working Principle
The metal split-gates provide a large degree in flexibility of the operational modes of the device. With no bias applied to the gate electrodes the 2DES underneath will not be depleted. This offers the possibility by using just a single out of the three vertical finger-gates countering the etched groove to create a quantum point contact rather than a quantum dot.
5.2 Device Working Principle
Two contact terminals to the 2DES are situated on the right and left hand side of the device serving as source and drain contact, respectively. The combination of the etched groove with the metal top-gates set to a negative bias forms two parallel constrictions where the electrons transverse the device. The influence of this two-path arrangement on the electric transport properties shall be studied by a variable Aharonov-Bohm phase introduced by a magnetic field applied perpendicularly to the 2DES.
The operational situation of the device with the split-gates set to a negative voltage and with two connections to the 2DES is shown in figure 5.2a. The air-bridge structures are not drawn for a better lucidity. Inside the constriction of the device two quantum dots (dark blue ellipses) reside that are tunnel coupled to both the common source and drain reservoir on either side. The side-gates deplete the 2DES underneath them. The electric transport through the device can only occur by single-electron tunneling via the quantum dots. The Coulomb repulsion prohibits that each quantum dot is occupied by more than one electron that contributes to the transport. In consequence single-particle contributions become a dominant feature. The two parallel quantum dots mimic a double-slit experiment for single electrons in a solid state device. In the quantum mechanical consideration the electron passes either quantum dot with a certain probability amplitude and they will interfere with their own partial waves as they pass the arrangement. The discrete tunneling events should give rise to an interference contribution that is observable in the electrical current as an ensemble averaged value over many single tunneling events.
But unlike the interference fringes seen on a screen in an optical interference experiment, here the electrical current in the device only gives a single value for a fixed phase relation determined by the device arrangement. One therefore needs a tunable phase in order to observe any interference effects.
The measurement set-up allows to apply an out-of-plane magnetic field. This will in-troduce a tunable phase Φ =B·Ain between the two different paths an electron can use to transverse the device, where B is the magnetic flux density and A the enclosed area between the two possible paths indicated by the red ellipse in figure 5.2a. The voltage applied to the side-gates at the etched groove thereby determines the size of the depleted area underneath in the 2DES. By changing the applied bias to the side-gates the depletion can be varied in size, as it is shown in figure 5.2b. With a more negative bias the depleted area increases. This offers the possibility to investigate the influence of the magnetic flux on the conductance of the device for both parameters independently from each other on the same device. Changing either parameter of the enclosed magnetic flux should allow to observe interference patterns in the conductance of the device.
At high magnetic fields the 2DES forms a quantum Hall system. The 2DES is no longer uniform but decomposed into compressible and incompressible strips. The strip pattern follows the contour of the depletion areas at the central groove and at the biased metal
5 Device and Measurement Set-up
A B
quantum dot
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Figure 5.2 A top view sketch of the device. A magnetic field is applied out of plane.
(a) The Aharonov-Bohm phase Φ =B·Adepends on magnetic flux densityB and the effective area A (red ellipse) that is enclosed in between the two-paths available for an electron (black dot). (b) The bias applied to the side-gates defines the depleted area underneath the side-gates in the 2DES. For a more negative bias it grows in size.
B
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Figure 5.3 Schematic view of the compressible/incompressible strip pattern evolving at a high magnetic field. Compressible and incompressible strips are marked in dark and light blue, respectively. The external Hall currentIHis indicated by the black arrows. The compressible strips at the sample edge and the antidot are (a) spatial fully separated in case of a shallow confinement potential rise or (b) overlap in case of a steep potential rise. Both cases yield the same conductance value. Regions of higher filling factors may be present in the bulk of the leads, but they are not connected throughout the device. This renders the details of the strip pattern in the leads to be unimportant (shaded area).
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5.2 Device Working Principle
B
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B
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Figure 5.4 (a) Schematic view of the compressible/incompressible strip pattern evolving at a high magnetic field. Compressible and incompressible strips are marked in dark and light blue, respectively. Both quantum dots are tunnel coupled to the same compressible strips on either side of the device. (b) The compressible strips act as connection and can be tuned in length with varying depletion around the central groove.
top-gates, likewise it seams the edges of the Hall bar. An expected distribution of the strip pattern is displayed in figure 5.3 for the case of only slightly biased vertical split-gates without the definition of quantum dots. The external Hall current (black arrows) flows dissipation-less through the incompressible strips (light blue) of the 2DES. The electro-chemical potentials of the source and drain contact are carried by the compressible strips (dark blue) following the top and bottom device edge, respectively. The steepness of the electrostatic potential at the edge of the device determines whether the compressible strips are spatially fully separated or merged (compare figures 5.3a and 5.3b). In the electrical measurement both situations cannot be distinguished from one another as they yield the same conductance value.
The strip pattern in the 2DES changes with the split-gates defining two quantum dots, rather than narrow channels, as depicted in figure 5.4a. Here, both quantum dots are coupled to the same compressible strip in each reservoir, seaming the depleting gates and etched groove next to the quantum dots. Within each lead, the path along the compress-ible strip in between the two quantum dots can be thought of as an effective distance between the dots, that can be tuned in-situ via the side-gates. The stronger the side-gate deplete the 2DES, the larger is the effective distance electrons have to travel in the com-pressible strip from one quantum dot before reaching the other, see figure 5.4.
In the electrical transport measurements the current flowing through the device as well as the differential conductance are investigated with the main focus of attention on the variation of magnetic flux density and the area change induced by the side-gate voltage.
Furthermore the source-drain bias as well as the temperature dependence are investigated.
I have used all three different operational configurations the device geometry offers: the combination of two quantum point contacts (chapter 6), the operation mode with two quantum dots (chapter 7 to chapter 9) and the intermediate combination of a quantum dot and a quantum point contact (chapter 10).
5 Device and Measurement Set-up