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Superconductivity: Charge Distribution in the Superconductor Magnesium Diboride
J. Zheng, J.W. Davenport, Y. Zhu, and L. Wu
MgB2 has
recently been found to display superconductivity at the surprisingly high
temperature of 39K [1]. This fact has stimulated a large research effort to
determine the cause of the high transition temperature, as well as other
properties of this otherwise unremarkable material. We have utilized first
principles density functional theory to calculate the charge density in
MgB2 and compare
it with transmission electron microscope and synchrotron x-ray measurements
carried out at Brookhaven. We used the full potential linear augmented plane
wave (FLAPW) method to solve the density functional equations [2]. The
calculated lattice constants are in good agreement with previous
calculations and with experiments. The same technique had been used earlier
to study the distribution in energy of the occupied and empty states
[3].
MgB2 forms in a hexagonal crystal structure, with the boron
atoms arranged in a honeycomb fashion in planes that are structurally the
same as graphite. The magnesium atoms are located in the hollow positions in
parallel planes above and below.
Figure 1 shows a contour plot of the
difference charge density in the boron plane [4]. The difference de nsity is obtained by subtracting the
density of isolated atoms from that of the compound. The red areas between
the atoms show clearly the build up of the bond charge.
Experiments measure the structure factors of the charge distribution,
which are related to the Fourier transform of the density. The calculations
described here agree with the experiments to within 3%. Calculations using
only the atomic density, which are typically used in diffraction
experiments, disagree with the data by up to 28%, clearly showing the
importance of quantum mechanical calculations of x-ray diffraction. We have
also studied the details of the electron energy loss spectra, finding excellent
agreement with experiments [5,6].
We note that electron scattering is more sensitive than x-rays to the low
Fourier coefficients of the charge density [6]. This fact has enabled
the accurate comparisons of charge density described here.
References
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[1] Nagamatsu, J., Nakagawa, N., Muranaka, T., Zenitani, Y., and
Akimatsu, J. Superconductivity at 39K in magnesium diboride. Nature 410:
63 (2001).
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[2] Blaha, P., Schwarz, K., Madsen, G., Kvasnicka, D., and Luitz, J.
WIEN2k, an augmented plane wave + local orbitals program for calculating
crystal properties (Karlheinz Schwarz, Techn. Universitat Wien,
Austria), 2001. ISBN 3-9501031-1-2.
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[3] Zhu, Y., Moodenbaugh, A. R., Schneider, G., Davenport, J. W., Vogt,
T., Li, Q., Gu, G., Fischer, D. A., and Tafto, J. Unraveling the
symmetry of the hole states near the Fermi level in the MgB2
superconductor. Phys. Rev. Lett. 88: 247002 (2002).
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[4] Wu, L., Zhu, Y., Vogt, T. Su, H., Davenport, J. W., and Tafto, J.
Valence electron-distribution in MgB2 by accurate diffraction
measurements and first-principles calculations. Phys. Rev. B 69: 064501
(2004).
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[5] Klie, R.F., Su, H., Zhu, Y., Davenport, J.W., Idrobo, J.-C.,
Browning, N., and Nellist, P.D. Measuring the hole-state anisotropy in
MgB2 by electron energy-loss spectroscopy. Phys. Rev. B 67:
144508 (2003).
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[6] Zheng, J-C., Zhu, Y., Wu, L., and Davenport, J. W. On the
sensitivity of electron and X-ray scattering factors to valence charge
distributions. J. Appl. Cryst. 38: 648 (2005).
Last Modified: January 31, 2008
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Claire Lamberti
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