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Thermometry and Refrigeration using Quantum Dots

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The two-dimensional electron gas in GaAs/AlGaAs heterostructures has diverse applications at cryogenic temperatures, but is heated by noise in the measurement set up. Our work involves the fabrication of a quantum dot refrigerator which can cool the electron gas to below the ambient lattice temperature1.

Lithographically defined Ti/Au gates patterned on the surface of a GaAs/AlGaAs heterostructure define three quantum dots (left, right, and top) of radius 150 nm, tunnel-coupled to an enclosed, macroscopic, two-dimensional reservoir of electrons 100μm2 in area. The QDR uses the discrete energy levels of two quantum dots to cool the central electron reservoir. The third quantum dot (the ‘thermometer’) probes the temperature of the two dimensional reservoir being cooled.

Our temperature measurement scheme consists of monitoring the charge distribution of the thermometer dot. This dot is open only to the enclosed reservoir whose temperature we want to extract. Changing the energy level of the dot through the Fermi-Dirac energy distribution of the enclosed reservoir results in the occupation probability of the dot being described by the same distribution. This is reflected in the current flowing through an adjoining quantum point contact. Fitting a Fermi-Dirac distribution to the measured current thus yields the temperature of the two-dimensional reservoir. Electronic temperatures between 120 and 951 mK are measured with an accuracy of better than 1 mK in the best case, and agree with the lattice temperature measured by a resistance thermometer. The thermometer is non-invasive and does not pass a current through the electron system being measured. The tuning is independent of temperature, and the device is robust in a magnetic field up to 5.6T3. Using this scheme, we have also investigated the variation in the electron temperature as a function of the voltages on the top and right plunger gates. This variation is produced because the changing voltages on the plunger gates move the energy level of the entrance dot down through the Fermi level of the source while moving the level of the exit dot up through the Fermi level at the drain, thus changing the energy extracted from the reservoir. Our results agree qualitatively with the model of electron cooling developed by Edwards2.

References [1] J. R. Prance, C. G. Smith, J. P. Griffiths, S. J. Chorley, D. Anderson, G. A. C. Jones, I. Farrer, and D. A. Ritchie 2009 Phys. Rev. Lett. 102 146602 [2] H. L. Edwards, Q. Niu, G. A. Georgakis, and A. L. de Lozanne 1995 Phys. Rev. B 52 5714 [3] A. Mavalankar,a) S. J. Chorley, J. Griffiths, G. A. C. Jones, I. Farrer, D. A. Ritchie, and C. G. Smith 2013 Appl. Phys. Lett. 103, 133116

This talk is part of the Semiconductor Physics Group Seminars series.

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