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Hyperfine interactions in silicon quantum dots

Lucy V. C. Assali, Helena M. Petrilli, Rodrigo B. Capaz, Belita Koiller, Xuedong Hu, and S. Das Sarma
Phys. Rev. B 83, 165301 – Published 4 April 2011
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  • INTRODUCTION
  • THEORY AND FORMALISM
  • HYPERFINE INTERACTIONS FOR A CONDUCTION…
  • HYPERFINE INTERACTIONS FOR A CONDUCTION…
  • CONCLUSIONS
  • ACKNOWLEDGEMENTS
    • References

    Abstract

    A fundamental interaction for electrons is their hyperfine interaction (HFI) with nuclear spins. HFI is well characterized in free atoms and molecules, and is crucial for purposes from chemical identification of atoms to trapped ion quantum computing. However, electron wave functions near atomic sites, therefore HFI, are often not accurately known in solids. Here we perform an all-electron calculation for conduction electrons in silicon and obtain reliable information on HFI. We verify the outstanding quantum spin coherence in Si, which is critical for fault-tolerant solid state quantum computing.

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    • Received 31 December 2010

    DOI:https://doi.org/10.1103/PhysRevB.83.165301

    ©2011 American Physical Society

    Authors & Affiliations

    Lucy V. C. Assali1, Helena M. Petrilli1, Rodrigo B. Capaz2, Belita Koiller2, Xuedong Hu3, and S. Das Sarma4

    • 1Instituto de Física, Universidade de São Paulo, CP 66318, 05315-970 São Paulo, SP, Brazil
    • 2Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21941-972 Rio de Janeiro, Brazil
    • 3Department of Physics, State University of New York, Buffalo, New York 14260-1500, USA
    • 4Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA

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    Issue

    Vol. 83, Iss. 16 — 15 April 2011

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    Images

    • Figure 1
      Figure 1
      Electron spin density in a (100) plane for bulk Si with an extra electron in the conduction band minimum at kz. The vertical axis is z and the color scheme runs from red (high density) to violet (low density), following the rainbow sequence. The circular high density spots are the Si atomic sites.Reuse & Permissions
    • Figure 2
      Figure 2
      Squares give the calculated hyperfine parameters versus 1/N, where N is the number of Si atoms in the supercell. The asterisks give the interpolated values expected for natural Si (~5% of Si29), with a≈1.9 mT and b≈0.06 mT. Solid straight lines are aN=(37/N) mT and bN=(1.1/N) mT, and give good fits to the data points. These results are the basis of a local spin density approximation used in our quantum dot calculations, similar to LDA in electronic calculations.Reuse & Permissions
    • Figure 3
      Figure 3
      Calculated η for different supercell sizes (red squares). The average value and standard deviation are given by the lowest (red) asterisk and respective error bar. Experimental results are given by the upper (blue) horizontal dashed lines, following the average values of Refs. 23 and 24, labeled S&W (1956) and Wilson (1964), respectively. The error bar for Wilson was obtained as an upper limit of the error estimated from Ref. 24, where η Si is given in an expression related to η Ge. The horizontal position of the asterisks is arbitrary, as they represent average values. The estimated value of η≳300 in Ref. 25 is off the scale here.Reuse & Permissions
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