Biomedical Engineering Reference
In-Depth Information
2.8
SEM micrographs of (a) series-coupled and (b) parallel-coupled
DQDs.
experiment, when the ratio t/
1, this problem maps onto the two-
impurity Kondo problem discussed by Jones and co-workers [157, 158],
characterized by the antiferromagnetic coupling J and Kondo scale T
K
, but
with an additional term due to the tunnel-coupling, which breaks the
symmetry in the even and odd channels. The basic behavior is similar to the
scenario in the two-impurity Kondo problem where competition between
Kondo and antiferromagnetic correlations leads to a continuous phase
transition (or crossover) at a critical value of the coupling ratio, J/T
K
≈
G
<
2.5.
However, the non-Fermi liquid quantum critical point at J/T
K
~
2.5 is not
accessible due to breakage of the symmetry between the even and odd
channels, and a crossover behavior is expected instead.
If t is tuned to t
before the antiferromagnetic transition point can be
reached, the system undergoes a continuous transition from a separate
Kondo state of individual spins on each dot (atomic-like) to a coherent
bonding-antibonding superposition of the many-body Kondo states of the
dots (molecular-like). Both the antiferromagnetic state and coherent
bonding state exhibit a double-peaked Kondo resonance in the differential
conductance versus source-drain bias and involve entanglement of the dot
spins into a spin-singlet. Therefore they are likely to be closely related.
The parallel-coupled case has only recently been analyzed in a model
without inter-dot tunnel coupling where the antiferromagnetic coupling
occurs via electrostatic coupling, yielding a discontinuous transition. Two
DQD geometries were studied: series-coupled and parallel-coupled.
Whereas the series-coupled geometry is more likely to be relevant for
quantum computation applications, the parallel-coupled geometry is well
suited for studying the quantum phase transition (crossover) in the two-
impurity Kondo problem.
Figure 2.8 shows the device patterns for the series- and parallel-coupled
DQDs. The devices are basically complex, multi-gate field effect transistors,
which are operated in the quantum regime. The bright lines in the electron
>
G
