Biomedical Engineering Reference
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Fig. 7.1 Interference in a
single electron transistor
(SET). The dynamics is
governed by equivalent paths
that involve two (or more)
degenerate states in the
many-body spectrum.
From [ 22 ]
decoherence introduced by the leads, in such devices, that we called interference
single electron transistors [ 20 ] (I-SET), interference effects show up even in the
Coulomb blockade regime.
In the present chapter we develop a general theory of interference blockade. We
give in fact an apriori algorithm for the detection of the interference blocking states
of a generic I-SET. As concrete examples, we analyze the triple dot and the benzene
I-SET. The first is chosen as the simplest structure exhibiting interference blockade
and in the second we emphasize the crucial role of the coupling geometry in the
interference phenomena. In both cases we further analyze the blockade that involves
orbitally and spin degenerate states and we show how to realize all electrical
preparation of specific spin states. Thus we obtain an interference mediated control
of the electron spin in quantum dots, a highly desirable property for spintronics
[ 23 - 25 ] and spin-qubit applications [ 26 - 30 ]. Similar blocking effects have been
found also in multiple quantum dot systems in dc [ 31 ]andac[ 32 ] magnetic
fields. The method of choice for the study of the dynamics in those systems is the
generalized master equation approach for the reduced density matrix (RDM), where
coherences between degenerate states are retained [ 19 - 21 , 33 - 43 ]. Such coherences
give rise to precession effects and ultimately cause interference blockade.
The chapter is organized as follows: in Sect. 7.2 we introduce a generic model
of I-SET. In Sect. 7.3 we set the necessary and sufficient conditions which define
the interference blocking states and a generic algorithm to detect them. In Sects. 7.4
and 7.5 we apply the theory to the benzene and to the triple dot molecule I-SET.
Section 7.6 is dedicated to the implications on spin transport of the interference
effects in presence of ferromagnetic leads. In Sect. 7.7 we analyze the robustness
of the interference phenomena upon relaxation of the exact orbital degeneracy
condition. Section 7.8 closes the chapter with a summary of the results and
conclusive remarks.
7.2
Generic Model of I-SET
Let us consider the interference single electron transistor (I-SET) described by the
Hamiltonian:
H
=
H sys +
H leads +
H tun ,
(7.2)
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