Pure electron-electron dephasing in percolative aluminum ultrathin film grown by molecular beam epitaxy
Lin et al. Nanoscale Research Letters
Pure electron-electron dephasing in percolative aluminum ultrathin film grown by molecular beam epitaxy
Shih-Wei Lin 0 3
Yue-Han Wu 1 3
Li Chang 1 3
Chi-Te Liang 2 3 4
Sheng-Di Lin 0 3
0 Department of Electronics Engineering, National Chiao Tung University , 1001 University Road, Hsinchu 30010 , Taiwan
1 Department of Materials
2 Department of Physics, National Taiwan University , Taipei 10617 , Taiwan
3 Science and Engineering, National Chiao Tung University , Hsinchu 30010 , Taiwan
4 Geballe Laboratory for Advanced Materials (GLAM), Stanford University , Stanford, CA 94305 , USA
We have successfully grown ultrathin continuous aluminum film by molecular beam epitaxy. This percolative aluminum film is single crystalline and strain free as characterized by transmission electron microscopy and atomic force microscopy. The weak anti-localization effect is observed in the temperature range of 1.4 to 10 K with this sample, and it reveals that, for the first time, the dephasing is purely caused by electron-electron inelastic scattering in aluminum.
Weak anti-localization; Ultrathin metal films; Pure electron-electron dephasing
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Background
Weak localization (WL) is the quantum correction to
the conductance which occurs in weakly disordered
systems due to coherent backscattering of electrons (or
holes). As a results of spin-orbit coupling, weak
antilocalization (WAL) may be observed in a weakly
disordered electron (or hole) system [1]. The theoretic
derivation and experimental proof of WAL were extensively
developed since 1980s, and the investigation on various
materials in all dimensions has been a central topic in
condensed matter physics for decades. In particular, a
wide variety of experimental results of WAL were
obtained in two-dimensional (2D) systems. 2D system is
suitable for experimental study of WAL because of its
stronger WAL contribution than three-dimensional (3D)
ones and its easier sample fabrication than
onedimensional (1D) ones. Recently, due to its sensitivity to
the electron dephasing and spin dephasing, WAL has
been widely applied to studying the spin-orbit
interaction in new materials, such as graphene, topological
insulator, magnetic-doped semiconductor, and
narrowgap semiconductor, to evaluate the potential for
spintronics devices [2-7].
In addition, the interplay between superconducting
effect and WAL also attracts much attention and has been
investigated extensively. Ebisawa et al. derived the
relationship between the superconducting pair-breaking
parameter and the inelastic scattering rate i1 by = (/
8kBT)i1 [8]. Their results have been used to study
experiments of WAL in aluminum thin films [9-11].
However, it is a chanting challenge to grow an ideal 2D
superconducting metallic sample. As the thickness of
evaporated metal goes thinner, the discontinuity of the
metal film un-avoidably appears due to large lattice
mismatch between the template and metallic material as
well as the surface non-uniformity of the bottom
template. Previously, the reported metallic films were in the
thickness of ten to a few tens of nanometers [9-14].
Although plenty of the theoretic works of WAL in
twodimensional systems have been published in the past few
decades, the experimental proof toward WAL in an ideal
two-dimensional metallic system is still lacking. In this
work, we have used molecular beam epitaxy (MBE)
system as the deposition technique to prepare ultrathin Al
films. By using gallium-rich GaAs as the epi-template,
we are able to successfully deposit ultrathin percolated
Al film for studying WAL toward the 2D limit.
Interestingly, we have observed a pure electron-electron
dephasing in this sample over the whole temperature range
that WAL effect exists. Note that all of our
characterizations including structural and electrical assessments
were fulfilled ex situ, and the continuity of the Al film
remains even after the post-processing for the Hall
device fabrication. Even though our sample is not thin
enough to reach the ultimate two-dimensional limit such
as monolayer graphene, our results still provide an
experimental proof that Nyquist scattering becomes the
dominant inelastic scattering mechanism at all
temperatures when the system approaches an ideal
twodimensional one.
Theory
Magneto-resistance measurements are commonly used
to study WAL. The theoretical calculation of 2D WAL
in a perpendicular magnetic field was derived by Hikami,
Larkin, and Nagaoka [1]. The difference of conductance
induced by applied magnetic field can be expressed as:
where B is the applied magnetic field. Y(x) represents
(1/2 + x) ln(x), B2 = Bi + 3/4Bso, (x) is the digamma
function. Here, Bi and Bso represent the strength of
electron dephasing and spin-orbit interaction, respectively. For
a superconducting material near its critical temperature
Tc, superconducting fluctuations must be considered. Maki
has calculated the effect of superconducting fluctuations
in a 2D system ( (...truncated)