Spin-orbit coupling and electron-phonon scattering - Fachbereich ...
Spin-orbit coupling and electron-phonon scattering - Fachbereich ...
Spin-orbit coupling and electron-phonon scattering - Fachbereich ...
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
108 Coupled quantum dots in a <strong>phonon</strong> cavity<br />
The energy that limits the current spectrum is given by the source-drain voltage<br />
V SD since ε = E L −E R ≤ eV SD . For V SD = 140µV as in [146], 16 <strong>phonon</strong> subb<strong>and</strong>s<br />
contribute to the current.<br />
Since every real experimental system is finite, we expect structures in the current<br />
which were derived for an infinitely extended system to be broadened due the<br />
finite area of the cavity A. This broadening should be on an energy scale c l /L,<br />
where A = L 2 . Thus, for a setup with c l /L ≈ 0.1ω b ≈ 1µeV (L ≈ 10b) the broadening<br />
is negligible. Finite temperatures yield a similar effect. Since Eq. (6.16) is<br />
strictly valid only at T = 0, structures in the I–V characteristic should be broadened<br />
on a scale of ω ≈ k B T ≈ 2µeV (at 20 mK). In addition, <strong>phonon</strong> absorption<br />
may become relevant at higher temperatures.<br />
Besides the transport that is mediated by the DP, there is also an influence<br />
of the PZ <strong>electron</strong>-<strong>phonon</strong> <strong>coupling</strong>. In a <strong>phonon</strong> cavity, the PZ effect couples<br />
all mode families, shear <strong>and</strong> Lamb waves, to the dot <strong>electron</strong>s. Moreover, the<br />
anisotropy of the piezo-electric tensor leads to a highly non-trivial q ‖ dependence<br />
of the matrix elements [176], <strong>and</strong> thus to anisotropic transport properties. However,<br />
this anisotropy is expected to be a minor correction since the PZ <strong>coupling</strong><br />
yields only a small contribution to the inelastic <strong>scattering</strong> rate in small FSQWs.<br />
From the above arguments we conclude that there is no fundamental obstacle to<br />
measure the predicted features of <strong>phonon</strong> confinement in <strong>electron</strong> transport.<br />
Recently, the <strong>electron</strong> transport through a Coulomb blockaded quantum dot<br />
in a free-st<strong>and</strong>ing 130nm thick GaAs/AlGaAs membrane was measured [170].<br />
At zero bias, a complete suppression of single-<strong>electron</strong> tunnelling was found.<br />
The authors attributed the associated energy gap in the transport spectrum to<br />
the excitation of a localised cavity <strong>phonon</strong>. The observed energy gap of ε 0 ≈<br />
100µeV matches reasonably well with the lowest dilatational (73µeV) or flexural<br />
(145µeV) van–Hove singularity in the DOS of a 130nm thick planar cavity. Although,<br />
a detailed microscopic explanation of the experimental findings is to our<br />
knowledge still missing, this experiment clearly highlights the feasibility to built<br />
artificial structures with well controlled electro-mechanical properties.