Contains description of one research project.Joint Services Electronics Program Contract DAAL03-89-C-0001Joint Services Electronics Program Contract DAAL03-92-C-000

Ariel, Imadiel

Kinaret, Jari M.

Lee, Patrick A.

Meir, Yigal

Wingreen, Ned S.

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Chapter 3. Transport Through a Quantum DotChapter 3. Transport Through a Quantum DotAcademic and Research StaffProfessor Patrick A. Lee, Dr. Yigal Meir, Dr. Ned S. WingreenGraduate StudentsJari M. KinaretTechnical and Support StaffImadiel Ariel3.1 Project DescriptionSponsorJoint Services Electronics ProgramContract DAAL03-89-C-0001Contract DAAL03-92-C-0001We continue the study of electron transportthrough a quantum dot. It is now well establishedboth experimentally' and theoretically2 thatCoulomb blockade plays a key role in this problemand is responsible for the conductance peakswhich have been observed to be periodic as afunction of gate voltage. Each of these conduc-tance peaks occurs at a gate voltage where theenergy of N and N+1 electron state are degenerateand each peak corresponds to the addition of asingle electron to the quantum dot. In the pastyear, the general formalism developed by Meir etal.2 has been extended and applied to the casewhere a strong magnetic field is applied to thesystem. The field is strong enough so that onlythe lowest two Landau levels are occupied, i.e.,the system would be in the integer quantum Hallregime in the bulk. The advantage of this systemis that the single particle states are well known tobe edge states, and the energy of these states arewell understood as a function of magnetic field.Thus, the successful application of the theory toexplain the experimental data3 provides strongsupport for the general theory 2 of Coulombblockade in resonant tunneling.Experimentally it was found that in the presence ofa strong magnetic field, the location in gatevoltage of each conductance peak exhibits smallperiodic fluctuation. At the same time, the magni-tude of each conductance peak goes through deepminima. This can be explained based on a modelwhere the low lying states are the edge states ofthe first and second Landau levels. For a givenconductance peak, the number of electrons on thequantum fluctuates between N and N+1.However, as the magnetic field is increased, the Nelectrons are distributed between the two Landaulevels in a different way, and electrons are trans-ferred from the second Landau level to the first.The transfer occurs when the edge state of the firstLandau level crosses the edge state of the secondLandau level. Thus, as a function as of a magneticfield, we are watching the transfer of electronsfrom the second to the first Landau level, one elec-tron at a time. Furthermore, since the dependenceof the energy of the edge state on magnetic field isunderstood, the periodic fluctuation of the reso-nant energy with magnetic field can be under-stood. The dips in the magnitude of theconductance peak can also be explained as beingdue to the fact that the edge state of the secondLandau level is more tightly bound, and its cou-pling to the leads is much smaller so that a dipoccurs every time the second Landau level movesthrough the chemical potential of the leads. Basedon this picture, quantitative calculation of the tem-perature dependence of the peak position wasmade and successfully compared with the exper-iment. Indeed, we now have sufficient confidencein the model that the problem can be turnedaround, and we can use the experiment as a spec-troscopy of the single particle level, i.e., we can1 U. Meirav, M.A. Kastner, and S.J. Wind, Phys. Rev. Lett. 65: 771 (1990).2 Y. Meir, N.S. Wingreen, and P.A. Lee, "Transport through a Strongly Interacting Electron System: Theory of Peri-odic Conductance Oscillations," Phys. Rev. Lett. 66: 3048 (1991).3 P.L. McEuen, E.B. Foxman, U. Meirav, M.A. Kastner, Y. Meir, N.S. Wingreen, and S.J. Wind, "Transport Spectro-scopy of a Coulomb Island in the Quantum Hall Regime," Phys. Rev. Lett. 66: 1926 (1991).Chapter 3. Transport Through a Quantum Dotextract the dependence of the edge state energylevel as a function of magnetic field.PublicationsFeng, S., and P.A. Lee. "Mesoscopic Conductorsand Correlations in Laser Speckle Patterns."Sci. 251: 633 (1991).Kinaret, J., and P.A. Lee. "Conductance of a Dis-ordered Narrow Wire in a Strong MagneticField." Phys. Rev. B. Forthcoming.Lee, P.A. "Small Structures: A Laboratory forStudying Strongly Interacting Systems," Pro-ceedings of the Taniguchi Symposium onMesoscopic Physics 1991. Shima, Japan.Forthcoming.McEuen, P.L., E.B. Foxman, U. Meirav, M.A.Kastner, Y. Meir, N.S. Wingreen, and S.J. Wind."Transport Spectroscopy of a Coulomb Islandin the Quantum Hall Regime." Phys. Rev. Lett.66: 1926 (1991).Meir, Y., N. Wingreen, and P.A. Lee. "TransportThrough a Strongly Interacting ElectronSystem: Theory of Periodic Conductance Oscil-lations." Phys. Rev. Lett. 66: 3048 (1991).62 RLE Progress Report Number 134

Transport Through a Quantum Dot

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Transport Through a Quantum Dot

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