Tunable spin transport using zigzag MoS 2 nanoribbon

Transcription

1 Tunable spin ranspor using igag MoS nanoribbon Hamidrea Simchi,, Mahdi smaeiladeh, Hossein Maidabadi, Mohammad Noroui, Deparmen of Physics, Iran Universiy of Science and Technology, Narmak, Tehran 6844, Iran Semiconducor Technology Cener, Tehran Iran We consider a igag nanoribbon of MoS and sudy is spin-dependen conducance and spin-polariaion in presence (absen) of an exernal elecric field. The field is no only perpendicular o he molybdenum plane (called verical field ) bu also o he ranspor direcion of elecrons (called ransverse field ). I is shown ha, while in he absen of he exernal elecric field, wo bands of seven bands are spin spli in he valence band bu no spin spliing is seen a poin kx.. Under applying he elecric field we show, he ribbon behaves as a prefec spin up (down) filer if and only if he boh componens of he elecrical field are presen. Finally i is shown ha, by changing he srengh of, he ribbon acs as a spin inverer for fixed values of. Keywords: MoS nanoribbon, non-equilibrium Green s Funcion, Spin ranspor, Spin filer, Spin inverer

2 I. Inroducion Some bulk maerials are composed by sacks of srongly layers wih weak inerlayer aracion, allowing exfoliaion ino individual, aomically hin layers. Transiion meal dichalcogenides (TMDCs) wih formula MX, where M is a ransiion meal and X is a chalcogen, are examples of hese kinds of bulk maerials. -3 They are known as wo dimensional (D) maerials which shows a wide range of elecronic, opical, mechanical, chemical and hermal properies. -6 Molybdenum disulfide (MoS ) is a TMDC semiconducor wih an indirec band gap. 7 The MoS monolayer is a semiconducor wih he compued direc K K gap equal o.79 ev and he compued indirec Qgap equal o.3 ev. 8 The compued band gap is in good agreemen wih he experimenally measured emission energy a ev. 9, Cao e al., have shown ha, monolayer of MoS is an ideal maerial for valleyronics. I has been shown ha, inversion symmery breaking ogeher wih spin-orbi coupling leads o coupled spin and valley degree of freedoms in monolayer of MoS and oher group-vi dichalcogenides. I means ha, i is possible o conrol boh spin and valley in hese D maerials. Peelaers e al., have shown ha, srain allows engineering he magniude as well as he naure (direc versus indirec) of he band gap in MoS. 3 Also, i has been shown ha, wih increasing he srain he excion binding energy is nearly unchanged, while opical gap is reduced significanly in monolayer of MoS. 4 Kang e al., have sudied he band offses and he heerosrucures of monolayer and few-layer of MX and i has been shown ha some of he monolayers and heir heerosrucures are suiable for poenial applicaion in opoelecronics. 5 One dimensional (D) nanosrucures have been of boh fundamenal and echnological ineres due o he ineresing elecronic and physical properies inrinsically associaed wih heir low

3 dimensionaliy and quanum confinemen effec. Using spin-polaried firs principle densiy funcional heory (DFT) mehod, Li e al., have shown ha igag (armchair) nanoribbons of MoS show he ferromagneic (nonmagneic) and meallic (semiconducor) behavior. 6 Also, i has been shown ha, armchair nanoribbons of MoS could be meallic and exhibi a magneic momen; and, when passivaing wih hydrogen, hey become semiconducor. 7 Zigag nanoribbons of MoS are meallic and exhibi unusual magneic properies regardless of passivaion. 7 Someimes, he band gap of maerial can be uned by applying an exernal elecric field. Using firs-principle calculaion, Yue e al., have shown ha, he band gap of monolayer armchair MoS nanoribbons can be significanly reduced and be closed by applying a ransverse field, whereas he band gap modulaion is absen under perpendicular field. 8 I has been shown ha, ensile srain in he igag direcion of single-layer MoS igag nanoribbon produces reversible modulaion of magneic momens and elecronic phase ransiion. 9 The srain-induced modulaion can be enhanced or suppressed furher by applying an elecric field. 9 In his paper, we consider a monolayer igag naoribbon of MoS and sudy is spindependen conducance and spin-polariaion in presence (absen) of an exernal elecric field which is no only perpendicular o he molybdenum (Mo) plane (called verical field also o he ranspor direcion of elecrons (called ransverse field ) bu ). I is shown ha in he absen of he field, while wo bands of seven bands srucure are spin spli in he valence band bu no spin spliing is seen a poin kx.. We show ha, he spin spliing is happened in he lowes unoccupied molecular orbial (LUMO) region of ransmission curve under applying 3

4 he field, and igag MoS nanoribbon behaves as a prefec spin up(down) filer. Also i is shown ha, he device acs as a prefec spin filer if and only if boh componens of he field are presen. Finally, we show ha, he ribbon behaves as a spin inverer by changing he ransverse elecric filed, for fixed value of verical elecric field,. The organiaion of paper is as follow. In secion II, he calculaion mehod is presened. The resuls and discussion are presened in secion III and conclusion and summary are provided in secion IV. II. Calculaion mehod Differen igh binding Hamilonians have been inroduced for monolayer of MoS before. -4 When he exernal elecric field is presen, here is no symmery beween wo sulfur (S) aoms and he relevan orbials accouning for he band srucure are he 4d orbials of he Mo, d x y, d xy and d, and wo 3p orbials of S, px, p y. The 77Hamilonian ( H ) and overlap ( S ) marices of MoS is wrien as: H H H a ( ) b H H ' b H k H H, S S S S S () wih he on-sie energy Hamilonian, H a, H b, H ' and hopping marix b i f ( k, ) e f ( k, ) H f ( k, ) f ( k, ) i f ( k, ) e f ( k, ) () 4

5 where is hopping inegral beween orbial d of Mo-aom and orbial px ipy, px ipy of S- aom. Also, is hopping inegral beween orbial d id x xy ( d id x xy ) of Mo-aom and orbial px ipy( px ipy ) of S-aom. Finally, is hopping inegral beween orbial y y d id ( d id x y xy ) of Mo-aom and orbial px ipy ( px ipy) of S-aom. x y xy. i( k. ) i( k. 3 ) i k f ( k, ) e e e is he srucure facor wih / 3, in plane momenum k ( k, k ), and in-plane componens of he laice vecor i ( i,,3 ). The x y overlap marix S id defined similar o H bu wih hopping inegral s.. The spin-orbi Mo coupling erm (SOCT) H diag, s, s SO, where.8 ev is he spin-orbi coupling consan and s. I should be noed ha he mos imporan conribuion of Mo aoms is considered in SOCT. The values of on-sie energies and hopping inegrals and also vecors i have been given in Ref. and hus we do calculae hem in he presen sudy. For calculaing he spin-dependen conducance and spin polariaion, we consider a linear chain of uni cells (in x-direcion), including 8 Mo-aoms and 6 S-aoms such ha, he uni cells of lef lead (L) are placed a posiions..-3, -, -,, he ranspor channel (C) is placed a posiions,,..,n-,n, and he uni cells of righ lead (R) are placed a posiions n+, n+,n+3,. (see Fig.). The wide of ribbon is in he y-direcion and -direcion is perpendicular o he Mo-plane. The ranspor channel is composed by en uni cells and includes 4 aoms oally. The ransverse elecric field ( ) creaes a poenial difference beween aoms wih differen y-value. The verical elecric field ( ) creaes a poenial difference beween up and down sulfur aoms. The boh poenial differences are added o he 5

6 on-sie energy of aoms. Of course i is assumed ha, he exernal elecric field acs only on he channel region and does no ac on he lef and righ leads. The surface Green s funcion of lef ( L g ) and righ ( g ) leads are calculaed by suing he Sancho s algorihm. 5 The self energies, R, and he coupling marices, L( R), can be calculaed by using he surface Green s L( R) funcion. 6-8 The Green s funcion of he ribbon can be calculaed by using 6 (( i) I H ) ( ) ( ) C L R (3) where is elecron energy, is an infiniesimal number, I is he uni marix, and for spin up (down ). 6-8 sands Now, he spin dependen conducance can be calculaed by using 6-8 G G Im( Trace( L R )), Im( Trace( L R )), (4) where, Im denoes he imaginary par. The spin-polariaion is defined by 6,7,8 P S ( G G ) ( G G ) (5) III. Resuls and discussion Fig. shows a monolayer igag nanoribbon of MoS. The channel includes 8 Moaoms and 6 S-aoms (oally 4 aoms). Mo-aoms and S-aoms are shown in blue and yellow color, respecively. Fig. (a) shows he seven band srucure of monolayer of MoS for 6

7 boh spins up and down which is found by using q. () and q. () when he elecric field is absen. I is in good agreemen wih he five band srucure of Ref.. As he figure shows, he spin spliing is seen in he valence band. Of course a poin kx., no spin spliing is seen in he valence band and energy band gap g ev. I should be noed ha, a acos( ) where, a.43 A, and 4.7 degree. a is he Mo-S bond lengh and is he angle beween he bond and he Mo s plane. Fig. (b) shows he conducance versus elecron energy of he igag MoS nanoribbon a poin kx. when he exernal elecric field is absen. As i shows, no spin spliing is seen and ransmission gap is equal o 5.6 ev which is a order of poin. g a his Fig.3 shows he conducance versus elecron energy when V/nm and V/nm. As i shows, spin spliing is happened in he lowes unoccupied molecular orbial (LUMO) region. I is happened since ransmission gap is closed by elecric fields a leas for one of wo componens of spin for some values of elecron energy. For example, when.48 ev hen G. G and G.48 G while when.7 ev hen G 3.3( G ) and G. G. Fig.4 shows spin polariaion versus elecron energy when V/nm and V/nm. As i shows, he device can habi as a prefec spin down (up) filer i.e., P ( ) when.48(.7 ) ev. I is happened due o he gap closing by applying he S elecric field. Fig.5 (a) shows he hree dimensional graph of spin polariaion versus elecron energy and ransverse field when V/nm. Also, Figs. 5(b) and (c) show he conducance of spin 7

8 up, G and spin down G versus elecron energy and ransverse field when V/nm. By aenion o hese figures, i can be concluded ha PS for a wide range of and elecron energy when V/nm. Also as Fig.5 (a) shows, when.5v/nm PS. when.48(.7 ) ev. Les us o focus on he wo elecron energies.48 ev and.7 ev and sudy he effec of verical and ransverse elecric fields on he spin polariaion a hese poins. We assume ha, no only bu also changes and sudy he effec of heir variaions on he spin polariaion when.48 ev and.7 ev. Fig.6 shows spin polariaion versus ransverse elecric field for differen values of perpendicular elecric field,,.,, V/nm when elecron energy.48 ev. As i shows, when. V/nm no spin polariaion is seen for all values of (solid line in green color). Therefore, boh elecric fields are necessary for creaing he spin polariaion. Also as i is seen, when and V/nm and and.95 V/nm, he spin polariaion P, approximaely. Bu, when and.7 V/nm and S and.76 V/nm, he spin polariaion P, approximaely. Therefore, by changing and fixing S one can inver spin polariaion perfecly. Fig.7 is similar o Fig.6 bu here, he elecron energy.7 ev. Alhough, boh elecric field s are necessary for creaing he spin polariaion, bu here, he prefec spin inversion is no seen. 8

9 Fig.8(a) shows hree dimensional graph of spin polariaion and Figs.8 (a) and (b) show hree dimensional graph of spin up conducance G and spin down conducance G versus ransverse and perpendicular elecric fields when elecron energy.48 ev, respecively. As Figs.8 (b) and (c) show, only for some resriced values of one of he wo componens of spin up and down conducance is no ero and herefore only for hese values of conducance he spin polariaion canno be ignored. Fig.9 (a) is similar o he Fig. 8 bu here, he elecron energy.7 ev. Similar o.48 ev,for some resriced values of one of he wo componens of spin up and down conducance is no ero and herefore only for hese values of conducance he spin polariaion canno be ignored. IV. Conclusion and summary We have considered a monolayer igag ribbon of MoS and sudied is spin-dependen conducance and polariaion by using he igh binding non-equilibrium Green s funcion mehod in presence (absen) of and exernal elecric filed. The field was no only perpendicular o he Mo-plane (verical filed) bu also o he ranspor direcion of elecrons (ransverse field). In absence of he elecric filed, i has been shown ha, while he wo bands of seven bands srucure are spin spli in he valence band bu no spin spliing is seen in ransmission curve a poin kx.. We have shown ha, under applying he elecric field, he MoS ribbon behaves as a prefec spin up (down) filer duo o he ransmission gap closing by he elecric field. Also, i has been shown ha, he device can habis as a prefec spin filer if and only if boh ransverse and verical elecric field is presen. Finally, we have shown ha under fixed value of 9

10 verical elecric field he MoS nanoribbon could ac as spin inverer by changing he srengh of he ransverse elecric field.

11 References [] K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booh, V. V. Khokevich, S. V. Moroov, and A. K. Geim, PNAS,, 453 (3). [] L. F. Maheis, Phys. Rev. B, 8, 379 (973). [3] J. A. Wilson and A. D. Yoffe, Adv. Phys. 8, 93 (969). [4] A. D. Yoffe, Annu. Rev. Maer. Sci. 3, 47 (993). [5] A. D. Yoffe, Adv. Phys. 4, 73 (993). [6] Q. H. Wang, K. Kalanar-Zadeh, A.. Kis, J. N. Coleman, and M. S. Srano, Naure nanoech. 7, 93 (). [7] A. D. Yoffe, Chem. Soc. Rev. 5, 5 (976). [8]. S. Kadansev and P. Hawrylak, Soli. Sa. Commu. 5, 99 (3). [9] K. F. Make, C. Lee, J. Hone, J. Shan, and T. F. Hein Phys. Rev. Lr. 5, 3685 (). [] A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C. Y. Chim, G. Galli, and F. Wang, Nano le., 7 (). [] T. Cao, G. Wang, W. Han, H. Ye, C. Zhu, J. Shi, Q. Niu, P. Tan,. Wang, B. Liu, and J. Feng, Naure Commu. 3, 887 (). [] D. Xiao, G. B. Liu, W. Feng, X. Xu, and W. Yao, Phys. Rev. Le. 8, 968 (). [3] H. Peelaers and C. G. Van de Walle, Phys. Rev. B 86, 44(R) ().

12 [4] H. Shi, H. Pan, Y. W. Zhang, and B. I. Yakobson Phys. Rev. B 87, 5534 (3). [5] J. Kang, S. Tongay, J. Zhou, J. Li, and J. Wu Appl. Phys. Le., (3). [6] Y. Li, Z. Zhou, S. Zhang, and Z, Chen J. Am. Chem. Soc. 3, 6739 (8). [7] A. R. Boello-Mende, F. Lope-Urias, M. Terrones and H. Terrones IOP Nanoech., 3573 (9). [8] Q. Yue, S. Chang, J. Kng, X. Zhang, Z. Shao, S. Qin, and J. Li, J. Phys. Condens. Ma. 4, 3355 (). [9] L. Kou, C. Tang, Y. Zhang, T. Heine, C. Chen, and T. Frauenheim, J. Phys. Chem. Le. 3, 934 (). [] A. C. Gome, R. Roldan,. Cappellui, M. Buscema, F. Guinea, H. S. J. van der Zan, and G. A. Seele, Nano Le. 3, 536 (3) (and is supporing informaion). []. Cappellui, R. Roldan, J. A. Silva_GUillen, P. Ordejon, and F. Guinea Phys. Rev. B 88, 7549 (3). [] H. Rosami, A. G. Moghaddam, and R. Asgari, Phys. Rev. B 88, 8544 (3). [3] F. Parhigar, H. Rosami, and R. Asgari Phys. Rev. B 87, 54 (3). [4] G. B. Liu, W. Y. Shan, Y. Yao, W. Yao, and D. Xiao, Phys. Rev. B 89, 399 (4). [5] M. P. Lope Scancho, J. M. Lope Sancho, and J. Rubio, J. Phys. F: Me. Phys., 4, 5 (984).

13 [6] Supriyo Daa, Quanum ranspor: Aom o Transisor (Cambridge, 5). [7] H. Simchi, M. smaeiladeh, and M. Heydarisaani, Phys. Saus Solidi B 49, 9, (). [8] H. Simchi, M. smaeiladeh, and H. maidabadi, Physica, 54, (3). 3

14 Uni cell Lef lead Transpor channel Righ lead Fig. A igag monolayer of MoS nanoribbon. ach uni cells includes 8 Mo-aoms and 6 S-aoms and herefore, ranspor channel is composed by 4 aoms. The channel is conneced o semiinfinie monolayer nano-ribbons of MoS as lef and righ leads. Mo-aoms and S-aoms are shown in green and yellow color, respecively. 4

15 k - VBM (ev) Spin up is in solid curve (blue color) Spin down is in dashed line (red color) k x (4/a ) (a) 4 T = 5.6 ev G(G ) (ev) (b) Fig. (Color online) (a) Band srucure of monolayer of MoS consising of seven bands in which wo are spin spli in he valence band. (b) Conducance versus elecron energy of monolayer of igag nanoribbon of MoS a kx. (he number of uni cells in each super cell is N 8 ). a acos( ) where, a.43 A, and 4.7 degree. a is he lengh of Mo-S bond and is he angle 5 beween he bond and he xy plane.

16 8 7 6 = - V/nm = V/nm G G 5 G(G ) (ev) (a) 6 5 = - V/nm = V/nm =.7 ev G = 3.3 (G ) G =. (G ) G G 4 =.48 ev G(G ) 3 G =.89 (G ) G =. (G ).5.5 (ev) (b) Fig. 3 (Color online) Conducance versus elecron energy of monolayer igag anaoribbon of MoS when perpendicular elecric field and ransverse elecric field 6 are presen.

17 = - V/nm = V/nm. P s (ev) (a) P s =.48 ev P S = -.99 =.7 ev P S = (ev) (b) Fig. 4 (Color online) Spin polariaion versus elecron energy of monolayer igag anaoribbon of MoS when perpendicular elecric field and ransverse elecric field are presen. 7

18 =.48 ev = - V/nm P S = -.99 =.7 ev = - V/nm P S = (ev) (a) (ev) 3 (b) 8

19 (ev) (c) 3 Fig. 5 (Color online) (a) Spin polariaion, (b) conducance of spin up, G and (c) conducance of spin down, G elecrons versus elecron energy and ransverse elecric field, elecric field V/nm. when perpendicular 9

20 =.48 ev. P s = - V/nm = - V/nm =. V/nm = V/nm = V/nm (a) =.48 ev. P s = - V/nm = - V/nm =. V/nm = V/nm = V/nm Fig. 6 (Color online) Spin polariaion versus ransverse elecric field, (b) for differen values of perpendicular elecric field,,.,, V/nm, when elecron energy.48 ev.

21 =.7 ev = - V/nm = -V/nm =. V/nm = V/nm = V/nm P s (a).8.6 =.7 ev.4. P s = - V/nm = -V/nm =. V/nm = V/nm = V/nm (b) Fig. 7 (Color online) Spin polariaion versus ransverse elecric field, for differen values of perpendicular elecric field,,.,, V/nm, when elecron energy.7 ev.

22 =.48 ev (a) =.48 ev (b)

23 .5.5 =.48 ev (c) Fig. 8 (Color online) (a) Spin polariaion, (b) conducance of spin up, G and (c) conducance of spin down, G elecrons versus ransverse elecric field, elecron energy.48 ev. and perpendicular elecric field when 3

24 =.7 ev (a) =.7 ev (b) 4

25 =.7 ev (c) Fig. 9(Color online) (a) Spin polariaion, (b) conducance of spin up, G and (c) conducance of spin down, G elecrons versus ransverse elecric field, elecron energy.7 ev. and perpendicular elecric field when 5