Download Electron transmission through 1D mesoscopic structures

Electron transmission through 1D mesoscopic structures
in the presence of two entangled magnetic impurities
F. Ciccarello1, G.M. Palma2, M. Zarcone1
1CNISM
and Dipartimento di Fisica e Tecnologie Relative dell'Università degli Studi di Palermo,
Viale delle Scienze, edificio 18, I-90128 Palermo (Italy)
2 NEST and Dipartimento di Scienze Fisiche ed Astronomiche dell'Università degli Studi di
Palermo, Via Archirafi 36, I-90123 Palermo (Italy)
email address: [email protected]
In the theory of mesoscopic transport, magnetic impurities are well known to play against electron
coherence [1,2]. Indeed, unlike the case of static impurities, an electron scattering with a magnetic
impurity undergoes a not fixed phase shift due to the internal (spin) degree of freedom of such
scattering center. For instance, the presence of a spin-1/2 impurity on one arm of a mesoscopic ring
reduces the amplitude of the Aharonov-Bohm (AB) oscillations of the electron transmission due to
occurrence of spin-flip events [3]. The coupling between electron and impurity spins is usually
modeled via the exchange interaction and thus spin-flip can occur when the spins are initially antialigned. In the special case when the electron spin is aligned with the impurity spin, no spin-flip is
allowed and the impurity behaves as it was static.
In the present work we investigate electron transmission through mesoscopic systems where two
identical spin-1/2 magnetic impurities prepared in a maximally entangled state are embedded. To
this aim, a quantum waveguide approach [4] properly generalizing the technique used for a single
magnetic impurity [3,5] and based on the coupling of three angular momenta is used [6].
The case of a quantum wire where only the lowest electron subband is accounted for may be
regarded as the electron analogue of a Fabry-Perot (FP) interferometer with the impurities, whose
distance is denoted by x0 , playing the role of two mirrors with an internal degree of freedom: the
spin. A striking behavior is observed when the impurity spins are prepared in the maximally

entangled singlet state 
[6]. Perfect resonance (namely 100% of electron transmittivity) is
observed whatever the strength of the electron-impurity exchange coupling constant J is and for
electron wavevectors k n / x0 (n integer) not depending on J. Furthermore, this happens
regardless of the electron incident spin state (thus no constraint on electron spin polarization is
required) and without occurrence of spin-flip.
We have also investigated the AB oscillations of the electron transmission in a mesoscopic ring
with the two impurities each placed on one of the arms. Denoting by l the circumference of the ring,
we found that for low values of kl, when the impurities are embedded at equivalent positions on the
two arms, a relevant robustness against electron decoherence with negligible occurrence of spin-flip

is observed when the impurity spins are prepared in the state  . Again, this occur regardless of
the electron spin state.
All these behaviors, clearly due to quantum interference phenomena, are quantitatively analyzed
and explained in terms of constants of motion of the system.
References
[1] A. Stern, Y. Aharonov, and Y. Imry, Phys. Rev. A 41, 3436 (1990)
[2] S. Datta, Electronic Transport in Mesoscopic Systems, (Cambridge Univ. Press, Cambridge, 1995)
[3]
[4]
[5]
[6]
S. K. Joshi, D. Sahoo, and A. M. Jayannavar, Phys. Rev. B 64, 075320 (2001)
J.-B. Xia, Phys. Rev. B 45, 3593 (1992)
O. L. T. de Menezes, and J. S. Helman, Am. J. Phys. 53, 1100 (1985)
F. Ciccarello, G. M. Palma, M. Zarcone, Y. Omar, and V. R. Vieira, cond-mat/0603456