#
2005 APS March Meeting

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Monday–Friday, March 21–25, 2005;
Los Angeles, CA

### Session B32: Focus Session: Superconductivity: Theory and Computation I

11:15 AM–2:03 PM,
Monday, March 21, 2005

LACC
Room: 507

Sponsoring
Units:
DCOMP DCMP

Chair: Jens Kortus, IPCMS

Abstract ID: BAPS.2005.MAR.B32.8

### Abstract: B32.00008 : Harmonic and anharmonic phonons in MgB$_2$

1:03 PM–1:39 PM

Preview Abstract
Abstract

####
Author:

Matteo Calandra

(Laboratoire Mineralogie-Cristallographie Paris, Universite Paris 6)

The discovery \footnote{ J. Nagamatsu, N. Nakagawa, T.
Muranaka,
Y. Zenitani,
and J. Akimitsu, Nature (London) {\bf 410}, 63 (2001).}
of a $39$ K critical superconducting temperature in MgB$_2$
has challenged our understanding of electron-phonon mediated
superconductivity. Several mechanisms have been proposed to
explain the large critical temperature, including a double gap
structure and anharmonic effects.
Much attention has been devoted to the study of the E$_{2g}$
phonon mode, an anti-phase vibration of the two boron atoms
parallel to the hexagonal plane.
In Raman spectra
\footnote{J. W. Quilty, S. Lee, A. Yamamoto, and S. Tajima,
Phys. Rev. Lett. {\bf 88}, 087001 (2002)} an E$_{2g}$
symmetry feature, commonly attributed to the E$_{2g}$ phonon
mode, is strongly damped, an effect which has been ascribed
to large electron-phonon coupling and large anharmonic effects
of the E$_{2g}$ mode.
The interpretation of the magnitude of each effect is, however,
very controversial, mostly because accurate phonon dispersion
measurements by neutron spectroscopy are not yet available
due to the small size of MgB$_{2}$ single crystals.\\
In this talk we show how the magnitude of anharmonic effects can
be determined using a joined experimental and theoretical
approach.
We measure, for the first time, the phonon dispersion and
lifetime
in MgB$_{2}$ single crystals with inelastic X-ray scattering
\footnote{A. Shukla, M. Calandra, M. d'Astuto, M. Lazzeri,
F. Mauri, C. Bellin, M. Krisch, J. Karpinski, S. M. Kazakov,
J. Jun, D. Daghero, and K. Parlinski,
Phys. Rev. Lett. {\bf 90}, 095506 (2003)}.
This experimental technique allows accurate determination of
phonon spectra even in the case of small single crystals.
By using first principles calculations we obtain the harmonic
phonon dispersion in MgB$_2$ (in agreement with previous
calculations \footnote{Y. Kong, O. V. Dolgov, O. Jepsen, and O.
K. Andersen, Phys. Rev. B 64, 020501(R) (2001)}).
We evaluate the magnitude of anharmonic effects by calculating
the
anharmonic contributions to the phonon self-energy. We consider
all the lowest order terms from three- and four-phonon vertices.
The scattering between different phonon modes at different
k-points in the Brillouin zone are included.
We use density functional theory and the (2n+1) theorem to
evaluate the three- and four-phonon vertices. The inclusion of
these terms is found to be crucial in determining the
anharmonic contribution to the phonon self-energy.
From the real and imaginary part of the phonon self
energy we extract anharmonic phonon frequency shifts and
linewidths (the inverses of the lifetime) at the special k-
points
$\Gamma$, A, M.
We find the anharmonic linewidth of the E$_{2g}$ mode to be
negligible compared to that due to electron-phonon coupling.
Thus the measurement of the phonon linewidth of the
E2g mode allows the experimental determination of the
electron-phonon coupling. For the anharmonic
phonon frequency shift of the E$_{2g}$ mode we find a
cancellation between the contributions of the three- and
four-phonon vertices \footnote{M. Lazzeri, M. Calandra and F.
Mauri, Phys. Rev. B 68, 220509(R) (2003).}.
The total anharmonic shift of the E$_{2g}$ mode at Gamma is
$+3.5$ meV, corresponding to a relative frequency shift of
$+5.4\%$.
The resulting anharmonic phonon frequencies are in good
agreement
with the phonon dispersion measured with inelastic X-ray
scattering.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2005.MAR.B32.8