Physics Research International

VolumeΒ 2011Β (2011), Article IDΒ 505091, 5 pages

http://dx.doi.org/10.1155/2011/505091

## Spin Polarized Transport in an AC-Driven Quantum Curved Nanowire

^{1}Faculty of Engineering, Ain-Shams University, Cairo 11517, Egypt^{2}Higher Technological Institute, Ramadan Tenth City 44629, Egypt

Received 17 September 2010; Accepted 20 April 2011

Academic Editor: NeilΒ Sullivan

Copyright Β© 2011 Walid A. Zein et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Using the effective-mass approximation method, and Floquet theory, we study the spin transport characteristics through a curved quantum nanowire. The spin polarization, , and the tunneling magnetoresistance, TMR, are deduced under the effect of microwave and infrared radiations of wide range of frequencies. The results show an oscillatory behavior of both the spin polarization and the tunneling magnetoresistance. This is due to Fano-type resonance and the interplay between the strength of spin-orbit coupling and the photons in the subbands of the one-dimensional nanowire. The present results show that this investigation is very important, and the present device might be used to be a sensor for small strain in semiconductor nanostructures and photodetector.

#### 1. Introduction

In the rapidly growing field of semiconductor spintronics, the spin degree of freedom is used for information processing [1, 2]. Devices concepts have been proposed which offer lower power consumption and a higher degree of functionality [3]. Among the research area of spintronics, the spin-orbit coupling (SOC) creates another way to manipulate spins by means of an electric field [4]. The Rashba spin-orbit coupling effect [4] is found to be very pronounced in semiconductor heterostructure, for example, quantum dots, quantum wires, and quantum rings [5], and its strength can be controlled by gate voltage. The spin polarization in two-dimensional electron gas (2DEG) systems with spin-orbit coupling (SOC) has been attracted extensive attention by many authors [6β9]. Spin-orbit coupling (SOC) has been investigated in parallel quantum wires [10, 11], where universal conductance fluctuations are suppressed. More recently, ballistic spin resonance due to an intrinsically oscillating spin-orbit field has been realized experimentally in a quantum wire [12]. The observation of the one-dimensional spin-orbit gap in quantum wires has also been reported in [13] and also recently in [14].

The aim of the present paper is to investigate the spin transport characteristics through a curved quantum nanowire under the effect of microwave (MW) and infrared (IR) radiations. The main difference between the straight nanowire and curved one is that the spin rotation is characterized by certain angles, as it will be shown below.

#### 2. The Model

We will now derive an expression for both the spin polarization for spin injection current in the curved nanowire and the corresponding tunneling magnetoresistance (TMR) for a curved nanowire under the effect of induced photons of wide range of frequencies. This nanowire is connected to two metallic leads. The effective Hamiltonian for spin-injected electrons through one-dimensional nanowire can be written as three parts according the geometrical design of the curved nanowire as [15, 16]

where is the effective mass of the electron, is the barrier height at the interface with the leads, is the gate voltage, and is the arc length along the curve. The second part of the curved nanowire including the Rashba spin-orbit coupling effect is given by

Also, the third part of the curved nanowire is

In (1), (2), and (3), the parameter represents the arc length along the curved part of the nanowire, is the polar angle, is the angle between two rectilinear parts of the nanowire and is the amplitude of the induced photons with frequency . The spin operators in (1), (2), and (3) are represented as follows [17]:

The energy spectrum and the unnormalized eigenstates for the two parts of the straight line of the nanowire are given by [18β20]

where the symbol corresponds to the spin up and spin down , and which corresponds to the direction of motion along the nanowire. The eigenstate function and the energy eigenvalue for the curved section of the nanowire are given as [18β20]

where is the orbit quantum number

The spinors , and in (6), (10), and (7) are given by

In (8), we have the frequency associated with spin-orbit coupling and the parameter which are defined as where is the strength of the spin-orbit coupling and is the radius of curvature.

The eigenfunctions corresponding to the spin transport through a curved wire are given by [18β20]
where is the th order Bessel function. The solutions of (11) must be generated by the presence of different subbands, , in a quantum nanowire, which come with phase factor , where is the frequency of the induced photons. Now, the tunneling probability could be obtained by applying Griffith boundary conditions [20]. Accordingly, therefore, the expressions for the tunneling probabilities corresponding to spin-up and spin-down electrons, respectively, are given byAnd that for spin-down aswhere the parameters, in (12) and (13), *, **, **, *andβ *, *are expressed as
So, the spin polarization of the tunneled electrons [21] is
In order to investigate the spin injection tunneling through the curved nanowire, we could calculate the tunneling magnetoresistance (TMR) which is related to the spin polarization (15) as [21β23]:
where is the relaxation parameter and is given by [21β23]:
where is the normal-state density of electrons calculated for both spin-up and spin-down distribution function , which is expressed as [21β23]
where is the shift of the chemical potential, is the spin relaxation time, is the cross-sectional area of the nanowire, and is the resistance at the interface of the tunnel junction.

#### 3. Result and Discussion

The nanowire is the semiconductor heterostructure InAs-InGaAs with characteristic values , βmeV, [14, 16, 17]. The features of our present results are the following.

(i) Figure 1 shows the variation of the spin polarization with the strength of the spin-orbit coupling, , at different values of the radius of the curvature of the nanowire. The results show periodic oscillations of the polarization. Also, the peak heights vary in a quantized form for the two values of a (radius of curvature).

(ii) Figure 2 shows the variation of the tunneling magnetoresistance (TMR) with the strength of the spin-orbit coupling, . As in Figure 1, periodic oscillations of the tunneling magnetoresistance (TMR) are observed. Also, peak heights vary in a quantized form for the two values of the radius of the curvature for nanowire. Such results show that the spin transport through curved nanowire is very sensitive to the geometrical shape of the nanowire. The strength of the spin-orbit coupling, , can be controlled by the gate voltage, the energy of the induced photons and the geometrical shape. Such results are found to be concordant with those in the literature [7, 11, 14].

(iii) Figure 3, shows the variation of polarization with the photon energy at different values of the strength of the spin-orbit coupling, . An oscillatory behavior of the polarization is observed. This is due to Fano-type resonance [24β27].

(iv) Figure 4 shows the variations of the tunneling magnetoresistance (TMR) with the photon energy at different values of the strength of SOC. Oscillations are observed as in the case of the spin polarization (Figure 3). These results show a good concordant with those in the literature [24β27]. These results show that the location and line shape of Fano-type resonance can be controlled by both the frequency of the induced photons and the strength of the spin-orbit coupling.

We can conclude that the present investigation is very important for devising a mesoscopic nanowire with controllable curvature. By this device, we can determine very minute strain in semiconductor heterostructure solids [28]. Also, this nanowire can be used as a photodetector [29].

#### References

- P. Ball, βMeet the spin doctorsβ¦,β
*Nature*, vol. 404, no. 6781, pp. 918β920, 2000. View at Google Scholar - S. A. Wolf, D. D. Awschalom, R. A. Buhrman et al., βSpintronics: a spin-based electronics vision for the future,β
*Science*, vol. 294, no. 5546, pp. 1488β1495, 2001. View at Publisher Β· View at Google Scholar Β· View at Scopus - I. Ε½utiΔ, J. Fabian, and S. D. Sarma, βSpintronics: fundamentals and applications,β
*Reviews of Modern Physics*, vol. 76, no. 2, pp. 323β410, 2004. View at Publisher Β· View at Google Scholar Β· View at Scopus - E. I. Rashba, βElectron spin operation by electric fields: spin dynamics and spin injection,β
*Physica E*, vol. 20, no. 3-4, pp. 189β195, 2004. View at Publisher Β· View at Google Scholar Β· View at Scopus - R. Winkler,
*Spin-Orbit Coupling Effect in Two Dimensional Electron and Hole Systems*, Springer, New York, NY, USA, 2003. - Z. Li and Z. Yang, βEffects of extended and localized states on spin Hall polarization in ballistic Rashba structures,β
*Physical Review B*, vol. 77, no. 20, Article ID 205322, 2008. View at Publisher Β· View at Google Scholar Β· View at Scopus - S. Bellucci and P. Onorato, βQuantum wires as logic operators: XNOR and NOR gate response in a ballistic interferometer,β
*Physical Review B*, vol. 81, no. 16, Article ID 165427, 2010. View at Publisher Β· View at Google Scholar - Q. Wang and L. Sheng, βCurrent induced local spin polarization due to the spin-orbit coupling in a two dimensional narrow strip,β
*International Journal of Modern Physics B*, vol. 19, no. 27, pp. 4135β4142, 2005. View at Publisher Β· View at Google Scholar Β· View at Scopus - M. Lee, M. O. Hachiya, E. Bernardes, J. C. Egues, and D. Loss, βSpin Hall effect due to intersubband-induced spin-orbit interaction in symmetric quantum wells,β
*Physical Review B*, vol. 80, no. 15, Article ID 155314, 2009. View at Publisher Β· View at Google Scholar Β· View at Scopus - V. A. Guzenko, A. Bringer, J. Knobbe, H. Hardtdegen, and T. SchΓ€pers, βRashba effect in GaInAs/InP quantum wire structures,β
*Applied Physics A*, vol. 87, no. 3, pp. 577β584, 2007. View at Publisher Β· View at Google Scholar Β· View at Scopus - Th. SchΓ€pers, V. A. Guzenko, A. Bringer, M. Akabori, M. Hagedorn, and H. Hardtdegen, βSpin-orbit coupling in GaxIn1-xAs/InP two-dimensional electron gases and quantum wire structures,β
*Semiconductor Science and Technology*, vol. 24, no. 6, Article ID 064001, 2009. View at Publisher Β· View at Google Scholar - S. M. Frolov, S. LΓΌscher, W. Yu, Y. Ren, J. A. Folk, and W. Wegscheider, βBallistic spin resonance,β
*Nature*, vol. 458, no. 7240, pp. 868β871, 2009. View at Publisher Β· View at Google Scholar Β· View at Scopus - A. Tsukernik, A. Palevski, V. J. Goldman, S. Luryi, E. Kapon, and A. Rudra, βQuantum magnetotransport in periodic V-grooved heterojunctions,β
*Physical Review B*, vol. 63, no. 15, Article ID 153315, 4 pages, 2001. View at Google Scholar Β· View at Scopus - C. H. L. Quay, T. L. Hughes, J. A. Sulpizio et al., βObservation of a one-dimensional spin-orbit gap in a quantum wire,β
*Nature Physics*, vol. 6, no. 5, pp. 336β339, 2010. View at Publisher Β· View at Google Scholar Β· View at Scopus - R. C. T. Da Costa, βConstraints in quantum mechanics,β
*Physical Review A*, vol. 25, no. 6, pp. 2893β2900, 1982. View at Publisher Β· View at Google Scholar Β· View at Scopus - B. K. NikoliΔ, L. P. ZΔrbo, and S. Welack, βTransverse spin-orbit force in the spin Hall effect in ballistic semiconductor wires,β
*Physical Review B*, vol. 72, no. 7, Article ID 075335, 6 pages, 2005. View at Publisher Β· View at Google Scholar Β· View at Scopus - X. Fu, W. Liao, and G. Zhou, βSpin accumulation in a quantum wire with Rashba Spin-Orbit coupling,β
*Advanced in Condensed Matter Physics*, vol. 2008, Article ID 152731, 5 pages, 2008. View at Google Scholar - W. A. Zein, A. H. Phillips, and O. A. Omar, βQuantum spin transport in mesoscopic interferometer,β
*Progress in Physics*, vol. 4, pp. 18β21, 2007. View at Google Scholar - W. A. Zein, A. H. Phillips, and O. A. Omar, βSpin-coherent transport in mesoscopic interference device,β
*NANO*, vol. 2, no. 6, pp. 389β392, 2007. View at Google Scholar - W. A. Zein, N. A. Ibrahim, and A. H. Phillips, βSpin-dependent transport through Aharonov-Casher ring irradiated by an electromagnetic field,β
*Progress in Physics*, vol. 4, pp. 78β80, 2010. View at Google Scholar - W. A. Zein, A. H. Phillips, and O. A. Omar, βSpin transport in mesoscopic superconducting-ferromagnetic hybrid conductor,β
*Progress in Physics*, vol. 1, pp. 42β46, 2008. View at Google Scholar - A. A. Awad Alla, A. H. Aly, and A. H. Phillips, βElectron spin dynamics through ferromagnetic quantum point contact,β
*International Journal of Nanoscience*, vol. 6, no. 1, pp. 41β44, 2007. View at Publisher Β· View at Google Scholar - S. Takahashi, T. Yamashita, H. Imamura, and S. Maekawa, βSpin-relaxation and magnetoresistance in FM/SC/FM tunnel junctions,β
*Journal of Magnetism and Magnetic Materials*, vol. 240, no. 1β3, pp. 100β102, 2002. View at Publisher Β· View at Google Scholar Β· View at Scopus - F. M. Souza, βSpin-dependent ringing and beats in a quantum dot system,β
*Physical Review B*, vol. 76, no. 20, Article ID 205315, 2007. View at Publisher Β· View at Google Scholar Β· View at Scopus - K. Kobayashi, H. Aikawa, S. Katsumoto, and Y. Iye, βTuning of the Fano effect through a quantum dot in an Aharonov-Bohm interferometer,β
*Physical Review Letters*, vol. 88, no. 25, Article ID 256806, 4 pages, 2002. View at Google Scholar Β· View at Scopus - K. Kobayashi, H. Aikawa, A. Sano, S. Katsumoto, and Y. Iye, βFano resonance in a quantum wire with a side-coupled quantum dot,β
*Physical Review B*, vol. 70, no. 3, Article ID 035319, 2004. View at Publisher Β· View at Google Scholar Β· View at Scopus - A. T. Tilke, F. C. Simmel, H. Lorenz, R. H. Blick, and J. P. Kotthaus, βQuantum interference in a one-dimensional silicon nanowire,β
*Physical Review B*, vol. 68, no. 7, Article ID 075311, 6 pages, 2003. View at Google Scholar Β· View at Scopus - S. S. Kwon, W. K. Hong, G. Jo et al., βPiezoelectric effect on the electronic transport characteristics of ZnO nanowire field-effect transistors on bent flexible substrates,β
*Advanced Materials*, vol. 20, no. 23, pp. 4557β4562, 2008. View at Publisher Β· View at Google Scholar Β· View at Scopus - W. Wu, S. Bai, N. Cui et al., βIncreasing UV photon response of ZnO sensor with nanowire array,β
*Science of Advanced Materials*, vol. 2, pp. 402β406, 2010. View at Google Scholar