Enhanced spin-polarized transport through DNA double helix by gate voltage
aa r X i v : . [ c ond - m a t . m e s - h a ll ] S e p Enhanced spin-polarized transport through DNA double helix by gate voltage
Ai-Min Guo and Qing-feng Sun Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China (Dated: August 11, 2018)We report on a way to manipulate the spin transport through double-stranded DNA contactedby normal-metal electrodes. On the basis of an effective model Hamiltonian, the conductanceand the spin polarization are calculated in the presence of a gate voltage by using the Landauer-B¨uttiker formula. Our results indicate that the spin polarization presents strong dependence on themagnitude as well as the direction of the gate voltage. The spin polarization can be significantlyenhanced by tuning the gate voltage and shows oscillating behavior with increasing the DNA length.
PACS numbers: 87.14.gk, 85.75.-d, 87.15.A-, 85.35.-p
I. INTRODUCTION
The field of spintronics, which aims at using the elec-tron spin to store and process information, has triggeredextensive interest during the last two decades. Sincethe discovery of the giant magnetoresistance in 1988, much progress has been achieved on the spin transportthrough solid-state systems and a set of spintronic de-vices were proposed based on organic materials. Mag-netic tunnel junctions were fabricated from organic semi-conductor and spin injection across metal-organic inter-face was demonstrated. A supramolecular spin-valve de-vice was presented by coupling single molecule magnetsto a single-walled carbon nanotube quantum dot. Thespin transport properties of the DNA molecule were in-vestigated theoretically by connecting to ferromagneticelectrodes.
The spin effects of all these systems arisefrom magnetic materials and from heavy atoms withlarge spin-orbit interactions, and are not determined bythe organic molecules themselves.Recently, an efficient spin filter was reported by de-positing self-assembled monolayers of double-strandedDNA (dsDNA) on gold substrate or by sandwiching sin-gle dsDNA between two electrodes. The electrons arehighly polarized after transmitting through the dsDNAwith spin polarization up to 60% at room temperature.Moreover, the spin filtration efficiency increases with theDNA length, implying that the spin effects are dominatedby the dsDNA and do not depend on the interface be-tween the dsDNA and the gold surface. These resultsare surprising since the DNA molecule is nonmagneticand has weak spin-orbit coupling (SOC) that could notsupport such high spin polarization. Until now, severaltheoretical works have studied the spin-polarized trans-port through single-stranded DNA (ssDNA) based on thehelical chain-induced Rashba SOC.
Very recently, weproposed a model Hamiltonian to explain the experimentby combining the SOC, the dephasing, and the doublehelix structure of the DNA molecule. The results in-dicated that the spin polarization is significant for thedsDNA even in the case of small SOC and increases withits length, while no spin polarization occurs in the ss-DNA. These are in good agreement with the experimen- E g yxr x yz E g (a) (b) FIG. 1: (color online). (a) Schematic view of right-handeddsDNA with helix angle θ and cylindrical coordinate ϕ un-der external electric field E g . The left-handed dsDNA can bederived by replacing θ with π − θ and ϕ with − ϕ . (b) Projec-tion of bottom five base-pairs and the electric field into x - y plane. Here, r and φ are radius of the dsDNA and angle fromthe electric field to the bottommost (first) base-pair (negativedirection of x axis), respectively. The spin-selectivity of thedsDNA originates from the combination of the SOC, the de-phasing, and its double helix structure. Moreover, the spinfiltration efficiency could be considerably enhanced by adjust-ing the magnitude and the direction of E g (see text). tal results. The DNA molecule is a promising candidate for molec-ular electronics (see Refs. 12,13 for review), due to itsunique structural and self-assembling properties. Ascompared with conventional semiconductors and met-als, the DNA molecule preserves long spin relaxationtime which makes it attractive for building spintronicdevices. Meanwhile, it was reported that the dsDNAcould be a field-effect transistor in the presence of a gateelectrode.
Consequently, one may ask the followingquestions: (1) will the gate voltage affect the spin trans-port of the dsDNA? (2) can the gate voltage be used tocontrol its spin transport? Besides, the components ineach integrated circuit have different electric potentials.It is thus important to illustrate how these potentials willinfluence the spin transport of the dsDNA-based devices.In this paper, we investigate the spin-selective tunnel-ing of electrons through the dsDNA contacted by non-magnetic electrodes in the presence of an external electricfield, which is perpendicular to the helix axis of the ds-DNA, as illustrated in Fig. 1. On the basis of an effectivemodel Hamiltonian, the conductance and the spin po-larization are calculated by using the Landauer-B¨uttikerformula. We find that the spin polarization strongly de-pends on the magnitude as well as the direction of thegate field. The dsDNA could be a very efficient spin filterand the spin polarization is considerably large under thegate voltage. Furthermore, the spin polarization exceeds70% for long dsDNA by properly tuning the gate voltage.The rest of the paper is organized as follows. In Sec. II,the model is presented. In Sec. III, the spin polarizationand the conductance are shown in the presence of the gatevoltage. Finally, the results are summarized in Sec. IV.
II. MODEL
The spin transport through the dsDNA can be simu-lated by the Hamiltonian: H = X j ( X n ε jn c † jn c jn + N − X n =1 t j c † jn c jn +1 + H . c . )+ X n ( λc † n c n + H . c . )+ X jn { it so c † jn [ σ ( j ) n + σ ( j ) n +1 ] c jn +1 + H . c . } + X jnk ( ε jnk b † jnk b jnk + t d b † jnk c jn + H . c . )+ X jk ( t L a † Lk c j + t R a † Rk c jN + H . c . )+ X k,β = L,R ε βk a † βk a βk . (1)Here the first two terms are the Hamiltonian of usualtwo-leg ladder model including the spin degree of free-dom. c † jn = ( c † jn ↑ , c † jn ↓ ) is the creation operator of thespinor, with j = 1 , n ∈ [1 , N ] de-noting a base-pair of the dsDNA. ε jn is the on-site energy, t j is the intrachain hopping integral, and λ is the inter-chain hybridization interaction. The third term is theSOC Hamiltonian, arising from the double helix shapeof the electrostatic potential of the dsDNA. t so is theSOC and σ ( j ) n +1 = σ z cos θ − ( − j [ σ x sin ϕ − σ y cos ϕ ] sin θ ,with σ x,y,z the Pauli matrices, θ the helix angle, ϕ = n ∆ ϕ the cylindrical coordinate, and ∆ ϕ the twist angle. Thefourth one denotes the B¨uttiker’s virtual electrodes, which are introduced to simulate the phase-breaking pro-cesses by attaching each base to a virtual electrode, because of the inelastic scattering from the phonons andother inelastic collisions with the counterions. The lasttwo terms describe the coupling between the real non-magnetic electrodes and the dsDNA, and the real elec-trodes, respectively. When the dsDNA is subjected to a perpendicular elec-tric field (Fig. 1), the on-site energy at each base site willbe modulated into following form: ε jn = ε (0) jn − ( − j eV g cos[( n − ϕ + φ ] , (2)where ε (0) jn is the on-site energy of the base at zero elec-tric field and e is the elementary charge. V g = E g r is thegate voltage across the dsDNA with E g the perpendic-ular electric field and 2 r the effective distance betweenthe complementary bases. The phase φ , being the an-gle between the electric field and the first base-pair, re-flects the orientation of the gate voltage with respect tothe dsDNA, as seen in Fig. 1. φ could be changed byrotating the dsDNA with the direction of its helix axisfixed. Besides the gate electrode, the gate voltage mayalso originate from the voltage drop across the left andright real electrodes. One notices from Eq. (2) that thegate voltage tunes the on-site energies harmonically alongeach strand and introduces disorder within each pitch ofthe dsDNA, due to the intrinsic double helix structureof the dsDNA. Such modulation will definitely modifythe electronic structure of the DNA molecule and thusinfluences its transmission ability as well as the spin po-larization (see below). Finally, the gate voltage is chosento be the order of 0 . q th real or virtual electrode withspin s = ↑ , ↓ can be obtained from the Landauer-B¨uttikerformula I qs = ( e /h ) P m,s ′ T qs,ms ′ ( V m − V q ), where V q isthe voltage in the q th electrode and T qs,ms ′ is the trans-mission coefficient from the m th electrode with spin s ′ tothe q th electrode with spin s . By applying a small biasbetween the real electrodes with V L = V b and V R = 0, V q can be derived for the virtual electrodes, since the netcurrent flowing through each of them is zero. Then theconductances for spin-up and spin-down electrons can becalculated G s = ( e /h ) P m,s ′ T Rs,ms ′ V m /V b . The spinpolarization is P s = ( G ↑ − G ↓ ) / ( G ↑ + G ↓ ).The values of aforementioned parameters are the sameas those in Ref. 11, i.e., ε (0)1 n = 0, ε (0)2 n = 0 . t = 0 . t = − .
1, and λ = − .
3, which are determined fromfirst-principles calculations and the unit is eV.Other parameters are t so = 0 . θ = 0 .
66 rad, and ∆ ϕ = π , indicating that there are ten base-pairs within thepitch of the dsDNA. For the real electrodes, the linewidthfunctions are Γ L/R = 1; for the virtual ones, the dephas-ing is small with Γ d = 4 × − or 4 × − , becausethe DNA length is shorter than the persistence length and the DNA molecule is rigid. When Γ d = 4 × − ,the phase coherence length is L φ = 16, at which the co-herent conductance is equal to the incoherent one. Forshort dsDNA of
N < L φ , the coherent conductance islarger than the incoherent one and the charge transportis determined by quantum mechanism; for the dsDNAof N > L φ , the coherent conductance is smaller and the -0.3 -0.2 -0.1 0.5 0.60.00.30.60.00.51.0 Energy d =4 10 -3 V g =0.06 =1.1(b) G ( e / h ) , G ( e / h ) , P S (a) d =4 10 -4 FIG. 2: (color online). Energy-dependent conductances G ↑ (solid line), G ↓ (dotted line), and spin polarization P s (dashedline) in the presence of the gate voltage for (a) Γ d = 4 × − and for (b) Γ d = 4 × − with N = 30. incoherent charge transport mechanism becomes domi-nant, in accordance with previous results. The effectsof the gate voltage on the spin transport through the ds-DNA can be observed in both coherent and incoherentcharge transport regime (see below), and are generic fordifferent model parameters. In what follows, we mainlyfocus on right-handed dsDNA except for Fig. 3(a), wherethe spin polarization is shown for both right-handed andleft-handed dsDNA.
III. RESULTS AND DISCUSSIONS
Although the gate voltage is employed, no spin po-larization could appear also in the ssDNA and in thedsDNA if any factor of the SOC, the dephasing, and thechirality is absent, regardless of the strength and direc-tion of the gate field. It is well known that the SOC willgive rise to spin precession as the charges move. For thessDNA, the charges can transport from one base to an-other along only single channel. In this case, the Hamil-tonian can be transformed into a spin-independent oneby using a unitary transformation, which is equivalentto choosing a space-dependent spin-rotating frame. Inthis spin-rotating frame which follows the spin precession,the spin is invariant. Accordingly, the Hamiltonian doesnot depend on the spin after the transformation and nospin polarization could be obtained in the ssDNA. Never-theless, the dsDNA presents a fundamental distinction.There are many channels for the charges to propagatebetween two bases, and one cannot find a spin-rotatingframe to follow the spin precession. As a result, theHamiltonian cannot be altered into a spin-independentone and the spin polarization will appear.Figures 2(a) and 2(b) plot the conductances G ↑ / ↓ andthe spin polarization P s under the gate voltage with V g =0 .
06 and φ =1 . π for two dephasing strength Γ d , asa function of the energy E . One notes that the energy -0.18 -0.15 0.45 0.48 0.510.00.30.6 P S Energy =0.8 =1.3 =1.8(b) V g =0.06-0.30.00.3 P S V g =0.02V g =0.08V g =0.14(a) =1.1 FIG. 3: (color online). P s vs energy for (a) three values of V g with φ = 1 . π and for (b) different φ by fixing V g = 0 . d = 4 × − and N = 30. The black and red curves inFig. 3(a) refer to the right-handed and left-handed dsDNA,respectively. spectrum consists of HOMO and LUMO bands which aredivided by an energy gap, irrespective of Γ d . In compar-ison with the case of V g = 0 (see Fig. 2(a) in Ref. 11),it clearly appears that both bands become fragmented inthe presence of the gate voltage, because the periodicityof the system extends to ten base-pairs due to the har-monic variation of the on-site energies. Besides, severaltransmission peaks are observed in both bands and aremore distinct in the regime of smaller Γ d [Fig. 2(a)], ow-ing to the stronger coherence of the system. The conduc-tances G ↑ and G ↓ are declined by increasing Γ d , becausethe inelastic scattering of the electrons becomes strongerfor larger Γ d . On the other hand, one notices a peak orbell-shaped configuration in the curve of P s vs E . Thewidth of P s - E is enhanced by increasing Γ d , while itsheight is reduced.Figure 3(a) shows P s vs E with different values of V g by fixing φ = 1 . π for the right-handed dsDNA (blackcurves) and the left-handed one (red curves), which canbe obtained by employing the replacement θ → π − θ and ϕ →− ϕ . By increasing V g , one can see the followingfeatures: (1) the peak in the HOMO (LUMO) bandis shifted towards lower (higher) energies, since bothbands move away from the energy gap; (2) the widthand the magnitude of the peak are varied; (3) a newpeak will emerge in the LUMO band and locates at theposition of the one of V g = 0. In addition, the state-ment that only the sign of the spin polarization will bechanged if the chirality of the dsDNA is reversed, i.e., P s ( π − θ, − ϕ ) = − P s ( θ, ϕ ), does not hold in the case ofthe gate voltage. We consider P s at E = 0 . P s is 39%, 8 . V g = 0 .
02, 0 .
08, and 0 .
14, respectively; for the left-handed one, P s is changed to − − . − P S (a) V g =0 V g =0.03 V g =0.06 V g =0.11 P S N(b) E=0.488 P S (c) E=0.4916 G ( e / h ) N(d)
FIG. 4: (color online). Length-dependent (a) h P s i , (b) P s at E = 0 . P s at E = 0 . h G ↑ i for severalvalues of V g with φ = 1 . π and Γ d = 4 × − . symmetry between the right-handed dsDNA system andthe left-handed one due to the existence of identical gatefield. However, this symmetry will be recovered by prop-erly modulating the direction of the gate field applied onthe left-handed dsDNA that the angle between this newfield and the first base-pair of the left-handed dsDNAis altered to be − φ . In this situation, we obtain therelation P s ( π − θ, − ϕ, − φ ) = − P s ( θ, ϕ, φ ). We then in-vestigate the spin polarization by fixing V g , as illustratedin Fig. 3(b). A different behavior is observed that theposition of the peak remains still, while its magnitudedramatically depends on φ . In other words, the spinpolarization could be enhanced by adjusting the direc-tion of the gate field with respect to the dsDNA. Thisarises from the fact that the positions of both HOMOand LUMO bands are unchanged and the details of theenergy spectrum are modified due to the rearrangementof the on-site energies. As a result, the conductances willbe changed, which leads to the variation of P s .In the following, we calculate the averaged spin polar-ization h P s i , where h P s i ≡ ( h G ↑ i − h G ↓ i ) / ( h G ↑ i + h G ↓ i )with h G s i averaged over the LUMO band. Figure 4(a)plots h P s i vs N for several values of V g with the lengthup to N = 150. In comparison with the case of V g = 0that h P s i increases monotonically with N , the depen-dence of h P s i on N is complicated under the gate voltage.For V g = 0, h P s i oscillates between two envelopes, corre-sponding to the local maxima and minima of h P s i withineach pitch of the dsDNA. We find that h P s i usually in-creases with N if ( N − ϕ + φ ∈ [2 mπ, (2 m + 1) π ] anddecreases with N if ( N − ϕ + φ ∈ [(2 m − π, mπ ] inevery pitch with m the integer, because of the differentquantum interference properties in specific length regiondue to the gating effects. The values of both envelopesand the oscillating amplitude of h P s i increase with N .Besides, the oscillating amplitude of h P s i is considerablyenhanced by V g . These imply that the spin filtration ef-ficiency can be improved significantly by implementing a P S d =4 10 -4 (a) N P S d =4 10 -3 =0.8 =1.3 =1.8(b) P S d =4 10 -4 E=0.4916(c) G ( e / h ) N(d) d =4 10 -4 FIG. 5: (color online). Length-dependent (a) and (b) h P s i ,(c) P s at E = 0 . h G ↑ i for several values of φ and Γ d by fixing V g = 0 . perpendicular electric field to long dsDNA.A similar oscillating behavior can be also observed inthe curve of P s vs N for single Fermi energy, as illus-trated in Figs. 4(b) and 4(c). It can be seen that P s isvery sensitive to V g and E . For instance, when E = 0 . N = 92, P s is 31%, 59%, 18%, and 21%, respec-tively, by increasing V g from 0 to 0 .
11; when N = 92 and V g = 0 . P s is increased from 18% at E = 0 .
488 to 69%at E = 0 . h G ↑ i vs N . The behavior of h G ↑ i on N has almostthe same trend in Fig. 4(a), i.e., the specific dependenceof the physical quantity on N in different length region.For V g = 0, h G ↑ i oscillates between two envelopes corre-sponding to the local maxima and minima of h G ↑ i in eachpitch of the dsDNA, due to the harmonic modulation ofthe on-site energies. Both envelopes and h G ↑ i of V g = 0are declined by increasing N and h G ↑ i decreases with V g , since larger N or V g will strengthen the scattering ofthe electrons. However, h G ↑ i remains quite large even for N = 150 and V g = 0 .
11, because of the incoherent chargetransport mechanism. Therefore, the dsDNA could bea better spin filter by modifying the magnitude of thegate voltage.We then study the influence of φ on the length-dependent spin polarization by fixing V g . Figures 5(a)and 5(b) plot h P s i vs N with three values of φ and V g = 0 .
06 for Γ d = 4 × − and 4 × − , respectively.Although a similar behavior is found that h P s i oscillatesbetween two envelopes, the positions of the local maxima(minima) are shifted towards smaller N by increasing φ ,independent of Γ d . For instance, one local maximum forlong dsDNA is decreased from 92 to 88 by increasing φ from 0 . π to 1 . π . The values of both envelopes increasewith N in a wider range of N in the case of extremelysmall Γ d , and increase with N at first and are then sup-pressed by further increasing N for relatively large Γ d ,because the electron loses its phase and spin memoryfaster by increasing Γ d . Moreover, the magnitude of V g / -0.0400.0650.17 FIG. 6: (color online). Two-dimensional plot of h P s i vs V g and φ π with Γ d = 4 × − and N = 100. It is clear that h P s i is independent of φ if V g = 0 and has the same value for φ and φ + 2 π . both envelopes can be enhanced by varying φ (see thecurves of φ = 1 . π ), due to the quantum interferenceproperties. Figure 5(c) shows P s vs N for single Fermi en-ergy, where one notes that P s is larger than 70% for longdsDNA [see also Fig. 4(c)] and is almost the same as thatobserved in the photoelectrons emitted from strained In-GaAs layers. In addition, Fig. 5(d) shows h G ↑ i vs N .One can see that the conductance remains quite large for N = 120. Accordingly, the dsDNA is a very efficient spinfilter in the presence of the gate voltage. Let’s further study the spin effects of the dsDNA byvarying the magnitude and the direction of the gate fieldin a wider parameter’s range, as plotted in Fig. 6. Itclearly appears that h P s i increases with V g at first andis then declined by further increasing V g . h P s i is about11% at V g = 0 and is larger than 16% by increasing V g within the range [0 . , . h P s i is very small in theregime of V g > .
2, where the conductance is also quitesmall, because of the strong gating effects. On the otherhand, the behavior of h P s i on φ is more complex andwill have multi-turning points in the curve of h P s i - φ byfixing V g . For small V g ( V g < . h P s i decreases with φ at first, then increases with φ , and is finally decreasedby further increasing φ ; while for large V g ( V g > . h P s i will oscillate with increasing φ . IV. CONCLUSIONS
In summary, we investigate the quantum spin trans-port through the dsDNA contacted by nonmagnetic elec-trodes under the gate voltage. This dsDNA-based devicecould be a very efficient spin filter and the spin filtrationefficiency can be improved significantly by modulatingthe magnitude and the direction of the gate voltage. Ourresults could be readily checked by further experiments.
Acknowledgments
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