Contains table of contents for Section 2, description of one research project and a list of publications.Joint Service Electronics Program Contract DAAL03-92-C-000

Altshuler, Boris L.

Ariel, Imadiel

Berkovits, Richard

Bowring, Kristine M.

Faas, Michael

Szafer, Aaron

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Section 2 Quantumew-Effect OovllcosChapter 1, Statistical Mechanit-8 of-',Odahturb DotsChapter 2 Single Electroa TiahS'WorsChapter 3, Differential ResistanIce, Tbrou'gh';a., Quantum Dot-,Signature of Kond'o.*Corre'lation',';'.',''.'Chapter. 4 Submicron'and- Nahlo iate $,tfU M ro's- Tech blogyand Researd h38 RLE Progress Report Number 135Chapter 1. Statistical Mechanics of Quantum DotsChapter 1. Statistical Mechanics of Quantum DotsAcademic and Research StaffProfessor Boris L. Altshuler, Dr. Richard Berkovits, Dr. Aaron SzaferGraduate StudentsMichael FaasTechnical and Support StaffImadiel Ariel, Kristine M. Bowring1.1 Project DescriptionSponsorJoint Service Electronics ProgramContract DAAL03-92-C-0001We are continuing to study equilibrium properties ofquantum dots-isolated metallic systems with sizessmaller than a typical length of an electrondephasing. In contrast with the transport propertiesof these systems, their thermodynamics was rela-tively neglected by both theorists andexperimentalists.We are investigating theoretically the dielectricproperties of quantum dots. We have considered aneutral grain with a positive uniform backgroundand conduction electrons which are scattered bydisordered impurity centers. Due to the fact that thegrain is disordered, one should expect a nonuniformdistribution of charge inside the grain. The electricfield outside a grain is determined by the chargedistribution inside the sample. Therefore, in prin-ciple, it is possible to measure electric field outsidethe grain, although the grains net charge is equal tozero. This means that a neutral quantum dotwithout any external electric field possesses a finitedipole moment as well as higher-order multipolemoments.We have calculated the mean square electricpotential far from the grain surface and determinedits temperature and magnetic field dependence.1We have also considered the response of quantumdot to an external electric field and determinedmesoscopic (sample to sample) fluctuations of theelectric polarizability.2 The zero field (spontaneous)dipole moment, as well as the polarizability,depends significantly on the temperature and themagnetic field manifesting the quantum nature ofthe phenomena. Due to screening of the chargefluctuations in the bulk of the grain, both effects arerather weak, so that only the surface charge fluctu-ations are important. Nevertheless, for systems withrelatively low-electron density (such as semiconduc-tors), both effects are well within current exper-imental capabilities.Modern experimental technique allows us to resolvesingle-electron energy levels in a quantum dot.3 Inmost cases the electrons within a dot are scatteredirregularly by impurities and the surface. Even for a"clean" quantum dot with a size much smaller thanthe mean free path, the motion of electrons can bechaotic rather than integrable due to the particularshape of the grain. The electron energy spectrum ofthese chaotic systems turns out to be rather irreg-ular.We have started to develop a statistical approach tothe description of chaotic energy spectra in thepresence of external fields. First, we have consid-ered a disordered mesoscopic ring with Aharonov-Bohm flux D. The energy of a given electron stateE, (we will measure ,, in units of mean energy levelspacing A) is a periodic function of (, with a periodo = hc/e. At the same time, on the interval0 < ( < (o, this function E,(O) can be considered asa random one. We have found that the autocor-relation function of the derivatives dE,/d( (i.e., of1 R. Berkovitz and B.L. Altshuler, "Electric Field Outside a Neutral Mesoscopic Grain," Europhys Lett. 19: 115 (1992).2 R. Berkovitz and B.L. Altshuler, "Fluctuations of the Electrical Polarizability of a Thin Mesoscopic Film," Phys. Rev. B 46: 12526(1992).3 R.C. Ashoori, H.L. Stormer, J.S. Weiner, L.N. Pfeiffer, S.J. Pearton, K.W. Baldwin, and K.W. West, "Single-Electron CapacitanceSpectroscopy of Discrete Quantum Levels," Phys. Rev. Lett. 68: 3088 (1992).Chapter 1. Statistical Mechanics of Quantum Dotsthe currents carried by the level a at differentfluxes) is determined asOa(4 1) deg(acV +c(D) - de 1  d DIn the interval gl/2 0o < < o (where g > > 1 is theconductance of the system in units e2/h ), this cor-relation function is universal, i.e., independent onthe disorder and particular characteristics of thequantum dot:C(4)- 1 022 0This result, though derived for the quantum dotswith sufficiently strong disorder, is probably alsovalid for clean quantum dots with chaotic shape andperhaps also for much broader classes of quantumsystems including, for example, Rydberg atoms inan external magnetic field.1.2 PublicationsAltshuler, B.L., and L.B. loffe. "Motion of Fast Parti-cles in Strongly Fluctuating Magnetic Fields."Phys. Rev. Lett. 69: 2979 (1992).Berkovitz, R., and B.L. Altshuler. "Electric FieldOutside a Neutral Mesoscopic Grain." Euro-phys. Lett. 19: 115 (1992).Berkovitz, R., and B.L. Altshuler. "Fluctuations ofthe Electrical Polarizability of a Thin MesoscopicFilm." Phys. Rev. B 46: 12526 (1992).Szafe, R., and B.L. Altshuler. "Universal Corre-lations in the Spectra of Chaotic Systems Withan Aharonov-Bohm Flux." Phys. Rev. Lett.Forthcoming.40 RLE Progress Report Number 135

Statistical Mechanics of Quantum Dots

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Statistical Mechanics of Quantum Dots

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