Scientia Iranica F (2017) 24(6), 3448{3451

Sharif University of Technology Scientia Iranica Transactions F: www.scientiairanica.com

Spintronics in nano scales: An approach from DNA polarization

S. Behnia and S. Fathizadeh

Department of , Faculty of Science, Urmia University of Technology, Urmia, Iran.

Received 8 August 2016; received in revised form 28 September 2016; accepted 5 December 2016

KEYWORDS Abstract. DNA nanotechnology is a purist approach to biomolecular engineering. The eld is aimed to create molecular structures and devices through the exclusive use of DNA DNA nanowire; as an engineering material. On the other hand, DNA Spintronics, as a DNA nanotechnology Spintronics; eld, uses the spin to store and process information. In this work, we have Pure spin current; used the Peyrard-Bishop-Holstein model combined with spin-orbit interaction for studying ; the spin transfer mechanism in DNA nanowires. In this work, the electrical currents Spin-orbit coupling. corresponding to the spin-up and spin-down are obtained directly using the Hamiltonian equations of system. We can obtain the best functional ranges for external agents, such as magnetic and electrical elds, and surroundings temperature to use in spintronics applications. By considering the simultaneous e ects of parameters, we have determined the islands with pure spin current. However, the considerable result is where we have applied the time periodic magnetic eld and observed the characteristic peaks in polarization diagram. These peaks can be used for information coding as zero-one codes. Therefore, one could construct DNA nanowires that lter the spin current, create the nearly pure spin currents, and act as a spintronics device for processing and transferring information. © 2017 Sharif University of Technology. All rights reserved.

1. Introduction motors or circuits that can autonomously move or process information. In the last 30 years, the DNA DNA as a molecule that carries the genetic informa- nanotechnology community has gone from an initial tion of a living organism is diverse in structure and wave of making static structures of di erent shapes function. In nature, this complementary base pairing and sizes to a second wave of creating increasingly contributes to DNA's helical structure and the way sophisticated and dynamic structures capable of car- genetic information is stored and retrieved. Because rying drugs, interacting with cell surface proteins, and of its programmability, DNA has also earned itself a performing certain functions inside cells [1,2]. In the reputation as a versatile engineering material. The case of dynamic structures, such as those that can move well-characterized nature of DNA base pairing provides or perform computational tasks, strand displacement is an easy means to control DNA interactions; this used, whereby the nanodevice is programed to respond `sequence programmability' has allowed the rational to an incoming DNA strand that displaces an existing design of precisely de ned structures, and molecular one on the nanodevice [3]. The ability to program these structures to fold a certain way to carry information *. Corresponding author. Fax: +98 4433554184 and recon gure themselves means that DNA nanode- E-mail address: [email protected] (S. Behnia) vices can be designed to do many things. They can, for example, carry drugs and deliver them to targets doi: 10.24200/sci.2017.4421 in clever ways [4], or can be designed to have movable S. Behnia and S. Fathizadeh/Scientia Iranica, Transactions F: Nanotechnology 24 (2017) 3448{3451 3449 parts that can sense and/or amplify signals, or even where: perform logic functions like a . On the other hand, the ability of DNA for charge transfer makes it Dn;n+1 =itso sin fsin[n] + sin[(n + 1)] a suitable candidate for any design of nanoelectronical devices, , nanocercuits, and nanowires [5]. + i cos[n] + i cos[(n + 1)]g; Moreover, the spin transport properties of the DNA, as an organic molecule, make it applicable as a spintronic and tso is the spin-orbit coupling constant,  is the device [6]. Spintronic systems exploit the fact that the twisting angle of DNA, and ' = n is the cylindrical electron current is composed of spin-up and spin-down coordinate angle. carriers, which carry information encoded in their spin HLead is the Hamiltonian corresponding to the left state and interact di erently with magnetic materials. and right leads written as follows: Rich physics behind the organic materials and speci c X X +  +   functions, such as switchability with light and electrical HLead = "kak ak +t fak (c1 +cN )+H:c:g; (4) or magnetic elds, are two important motivations for k k; using the organic materials such as DNA. where " is the on-site energy of leads, and t is the In the current study, we have tried to investigate k hopping constant between leads and DNA. the electron transfer in DNA nanowires by consider- It is clear that the Hamiltonian terms are complex ing the electron spin. We have taken into account and dealing with them is hard. Then, considering the the electron-lattice interaction through the Peyrard- nonlinear dynamics tools could open a new horizon Bishop-Holstein (PBH) model by considering the spin in understanding the spin transfer mechanism and its degree of freedom. On the other hand, spin-orbit e ects on DNA. In this way, we have obtained the interaction is combined with the PBH model. evolution equations of the system as follows:

2. Materials and methods 2aD  y = eayn eayn 1 n m We have considered DNA spin-charge lattice with the h following Hamiltonian: kb 2 + eb(yn+yn1) (y y ) 2m n n1 H = HPBH + Hso + HLead; (1) i b(yn+1+yn) 2 where HPBH is the Hamiltonian of PBH model for +e (yn+1 yn) the description of DNA lattice and charge carriers   dynamics by considering the spin degree of freedom. " 2 # 2 cn + cn ; (5) HPBH is written as follows [7]: m   X 1 n   2 " i " " " HPBH = my_ + V (yn) + W (yn; yn+1) c_ = (" + y )c V c + c 2 n n n n n n;n+1 n1 n+1 n ~ o X X " # " +  +  +  +Dn:n+1c Dn1;nc + t a ; (6) + f"ncn cn Vn;n+1(cn cn+1 +cn+1cn) n+1 n1 k n; k;n=1 n   +  i # # + yncn cng; (2) c_# = (" + y )c# V c + c n ~ n n n n;n+1 n1 n+1 ay 2 where V (yn) = D(e n 1) as Morse poten- o X tial describes the hydrogen binding between the D c" + D c" + t a#; (7) k n;n+1 n+1 n1;n n1 k complementary base pairs, W (yn; yn+1) = 2 (1 + k b(y +y ) 2 e n+1 n )(yn+1 yn) is the stacking interaction h  i +  i in a DNA chain, cn (cn) is the creation (annihilation) " " " " a_ k = "kak + t c1 + cN ; (8) operator for a spinor with spin , Vn;n+1 is the hopping ~ constant, and is the charge-lattice coupling. i h  i H is the spin-orbit coupling Hamiltonian ex- # # # # so a_ k = "kak + t c1 + cN : (9) pressed by the second quantization method as follows: ~ X h "+ #  #+ " 3. Results and discussion Hso = Dn;n+1cn cn+1 Dn;n+1cn cn+1 n For analyzing the spin transfer mechanism in DNA and i investigating the a ected parameters, we have tried to +D c#+c" D c"+c# ; (3) n1;n n n1 n1;n n n1 obtain the electrical current for spin-up and spin-down 3450 S. Behnia and S. Fathizadeh/Scientia Iranica, Transactions F: Nanotechnology 24 (2017) 3448{3451

electrons, directly from eld equations. These currents where B is the Bohr magneton, and B is the magnetic are written as follows: eld in the direction of DNA helix axes. This Hamil- " # i " i # ( tonian term modi esc _n(_cn) by BBcn( BBcn). ie X h   ~ ~ I" = V c"+c" + c"+c" Figure 1 shows the regions in magnetic eld values ~ n;n+1 n n1 n n+1 in which the minimum charge current exists; as a result, n the maximum spin current ows through DNA. These i +D c"+c# D c"+c# regions are the best values for spintronics applications. n;n+1 n n+1 n1;n n n1 For examining the e ect of external magnetic eld ) over the time, we have considered the time series of Xh   i +t c"+ +c"+ a"+ a"+ c"+ +c"+ ; one of the spin currents (spin-up current) versus the 1 N k k 1 N variation of external magnetic intensity (see Figure 2). k (10) It is clear in a 3D scheme that in low eld values, ( the spin-up current is almost zero, but after about B = ie X h   I# = V c#+c# + c#+c# 0:2 mT, the current increases in time. ~ n;n+1 n n1 n n+1 n On the other hand, by applying a time variable i eld with frequency !, one could obtain the best in-  #+ #  #+ " terval in frequency domain with maximal spin ltering. Dn;n+1cn cn+1 + Dn1;ncn cn1 To this end, we have considered external magnetic eld ) Xh   i B = B0 cos !t, where B0 and ! are the eld intensity #+ #+ #+ #+ #+ #+ and frequency, respectively. +t c1 +cN ak ak c1 +cN : k (11) It is clear in Figure 3 that spin polarization shows the characteristic peaks in certain frequencies. The Using the above relations, we could de ne the net maximal peak appears in ! = 0:7 THz. By considering charge (Ic) and the net spin currents; as a result, the this result, one could design an information coder based spin polarization relation is as follows: on zero-one codes for information transfer aims.

" # " # We could examine the simultaneous e ects of Is = I I ;Ic = I + I ;P = Is=Ic: In spintronics, the pure spin current plays an important role in information processing, storage and transfer. A pure spin current is the ow of electron spin without the ow of electric charge at the same time. Our main aim is the studying of the pure spin current and its a ected parameters. We have tried to examine the e ect of an external magnetic eld on the formation of the spin currents in DNA (see Figure 1). In this regard, we have de ned the external magnetic eld Hamiltonian as follows: X  "+ " #+ # Figure 2. The spin-up time series with respect to the HB = BB cn cn cn cn ; (12) n external magnetic eld.

Figure 1. The spin currents with respect to the external Figure 3. The spin polarization with respect to the magnetic eld. frequency of external magnetic eld (B = 0:3 T). S. Behnia and S. Fathizadeh/Scientia Iranica, Transactions F: Nanotechnology 24 (2017) 3448{3451 3451

simultaneous e ects of electrical and magnetic elds can determine the pure spin islands in parameters in- tervals. Therefore, one could choose the best functional regions in parameters values in which DNA plays the role of a spin polarizable nano material. In addition, by considering the DNA wires in di erent temperatures, we have de ned some temperatures as critical ones in which spin polarization has maximum peaks. The simultaneous variations of external elds could specify the intervals with nearly pure spin currents.

Figure 4. The net spin current with respect to the References simultaneous e ects of external electrical and magnetic 1. Jones, M.R., Seeman, N.R. and Mirkin, C. \Pro- elds. grammable materials and the nature of the DNA bond", Science, 347(6224), p. 1260901 (2015). external electrical and magnetic elds and determine the region in these parameters in which the maximal 2. Pinheiro, A.V., Han, D., Shih, W.M. and Yan, H. net spin current ows through DNA. Therefore, we \Challenges and opportunities for structural DNA have used the external electrical eld Hamiltonian nanotechnology", Nat. Nanotech., 6(12), pp. 763-772 (2011). written as follows: X 3. Zhang, F., Jiang, S., Wu, S., Li, Y., Mao, C., Liu, +  Y. and Yan, H. \Complex wireframe DNA origami HE = eEd nc c ; (13) n n nanostructures with multi-arm junction vertices", Nat. n; Nanotech., 10(9), pp. 779-784 (2015). where e is the electron charge, E is the electrical eld 4. Chen, Y.J., Groves, B., Muscat, R.A. and Seelig, G. in helix direction, and d is the distance between the \DNA nanotechnology from the test tube to the cell", base pairs in the chain. According to the Hamiltonian Nat. Nanotech., 10(9), pp. 748-760 (2015). i " terms, Eqs. (6) and (7) are modi ed by ~ eEndcn and 5. Venkatesan, B.M. and Bashir, R. \Nanopore sensors i # ~ eEndcn, respectively. for nucleic acid analysis", Nat. Nanotech., 6(10), pp. There are the islands in Ic in which the net 615-624 (2011). current is zero; therefore, the maximal spin current 6. Gohler,B., Hamelbeck, V., Markus, T.Z., Kettner, M., ows through DNA (Figure 4). Hanne, G.F., Vager, Z., Naaman, R. and Zacharias, However, we have studied the e ect of the DNA H. \Spin selectivity in electron transmission through surroundings temperature together with external elds. self-assembled monolayers of double-stranded DNA", This work determines the temperatures with which Science, 331(6019), pp. 894-897 (2011). DNA could appear as the maximal spin polarization. 7. Komineas, S., Kalosakas, G. and Bishop, A.R. \E ects In addition, DNA sequence and its length as two of intrinsic base-pair uctuations on charge transport in uential factors alter the spin polarization of DNA. in DNA", Phys. Rev. E, 65(6), p. 061905 (2002).

4. Conclusions Biographies Organic spintronics combines the spin degree of free- Sohrab Behnia is currently an Associate Professor in dom of electron with its charge for application in Basic Science Department of Urmia University of Tech- nano electronics, information process or transfer. In nology. His research interests is analysis of nonlinear this regard, DNA as an organic material acts as a dynamical systems using the chaos and quantum chaos spin lter material. We could show a nearly pure theories. spin current through DNA in the presence of external magnetic eld. Appling the time variable magnetic Samira Fathizadeh is a PhD student of Fundamental eld, distinguished among the spin polarization e ects Physics in Urmia University of Technology. Her in DNA nanowires and used for information coding, can research area is analysis of dynamical systems using be the innovation of our work. On the other hand, the the chaos and quantum chaos theories.