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Optical and electric control of charge and spin-valley transport in ferromagnetic silicene junction
Accepted Manuscript Optical and electric control of charge and spin-valley transport in ferromagnetic silicene junction
Xuejun Qiu, Zhenzhou Cao, Jiemei Lei, Jian Shen, Chaochao Qin PII:
S0749-6036(17)30713-9
DOI:
10.1016/j.spmi.2017.05.059
Reference:
YSPMI 5040
To appear in:
Superlattices and Microstructures
Received Date:
22 March 2017
Revised Date:
08 May 2017
Accepted Date:
09 May 2017
Please cite this article as: Xuejun Qiu, Zhenzhou Cao, Jiemei Lei, Jian Shen, Chaochao Qin, Optical and electric control of charge and spin-valley transport in ferromagnetic silicene junction, Superlattices and Microstructures (2017), doi: 10.1016/j.spmi.2017.05.059
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
1
Optical and electric control of charge and spin-valley
2
transport in ferromagnetic silicene junction
3 4 5 6 7
Xuejun Qiua,*, Zhenzhou Caoa, Jiemei Leia, Jian Shena, Chaochao Qinb aCollege
of Electronics and Information, Hubei Key Laboratory of Intelligent Wireless
Communications, South-Central University for Nationalities, Wuhan 430074, China bCollege
of Physics and Electronic Engineering, Henan Normal University, Xinxiang, 453007,
8
China
9 10
Abstract: We theoretically investigate the charge and spin-valley transport in a
11
normal/ferromagnetic/normal silicene junction, where the ferromagnetic region is
12
exposed to an off-resonant circularly polarized light and perpendicular electric field.
13
We show that one wider transport gap can be produced by the optical field than the
14
electric field, which provides a simple way to fabricate an optical controlled on/off
15
switch. On the other hand, in the presence of a proper optical field and ferromagnetic
16
exchange field, the spin-polarized conductance is enhanced above 90%, and the
17
polarized direction can be inverted just by reversing the polarization of the light.
18
Additionally, the valley-polarized conductance is sensitive to the optical and electric
19
field, under proper values, one near perfect K ( K ' ) valley-polarized conductance
20
exceeding 95% is realized. All these findings are well understood from the band
21
structure of silicene and expected to be beneficial for real applications in high
22
performance spintronics and valleytronics.
23
Keywords: Spintronics;Valleytronics; Silicene; Ferromagnetic; Optical
24 25 26 27 28
________ * Corresponding author at: College of Electronics and Information, South-Central University for Nationalities, Wuhan, 430074, China. Tel.:+86 18672323467 E-mail address: [email protected]
1
ACCEPTED MANUSCRIPT 1
I. Introduction
2
Silicene, a close cousin of graphene, has received a lot of attention in recent
3
years due to the distinctive geometrical [1] and electronic structure [2], giving various
4
potential applications ranging from spintronics [3-6], valleytronics [7-9] to silicon
5
based transistor [10] at room temperature. Unlike graphene, silicene has a buckled
6
structure owing to the large atomic radius of silicon, leading to a tuneable bandgap at
7
the Dirac point and consequently triggering various topological quantum states [11].
8
Yokoyama et al have shown that such a band gap is controllable by a
9
perpendicular external electric field and ferromagnetic exchange field, revealing the
10
valley and spin polarization can be achieved in normal/ferromagnetic/normal (NFN)
11
silicene junction [12]. Based on their findings, the ballistic transport in double and
12
multiple ferromagnetic barrier [13,14], magnetic barrier [15] and quantum well [16]
13
have successively been investigated, these studies have found many interesting and
14
novel results such as electric field and exchange field dependent transport gaps and
15
the perfect spin and valley polarizations. Besides, the spin and valley polarized
16
current induced by strain has also been reported, and a highly efficient filtering for all
17
four spin-valley configurations is proposed [17].
18
Although abundant interesting phenomena could be produced from the electric
19
field, ferromagnetic exchange field and strain, to search a convenient control and
20
achieve a high-efficiency spin-valley polarization, is the long-term pursuit of
21
scientific workers. In earlier works, it’s found that the topological phase transition in
22
silicene can be altered by irradiating circular polarized light at fixed electric field, and
23
a photo induced spin-polarized quantum Hall insulator is realized [18]. Very recently,
24
some research groups start paying deserving attention to the light-dependent ballistic
25
transport in silicene, i.e. the ballistic transport through a strip with circularly polarized
26
light and electric field applied in normal silicene is studied by Mohammadi et.al. [19],
27
the photo-induced valley and spin transport together with tunneling magnetoresistance
28
in a ferromagnetic/ferromagnetic/ferromagnetic, ferromagnetic/normal/ferromagnetic
29
[20,21] silicene junction and so on. However, the ballistic electron transport in a NFN
30
silicene junction with the circularly polarized light and electric field applied in
31
ferromagnetic region has not been systematically studied before and is very
32
convenient to realize in experiment, so it is expected that intriguing spin-valley
33
transport can be obtained in this junction.
34
In this paper, we study the charge and spin-valley transports in a NFN silicene 2
ACCEPTED MANUSCRIPT 1
junction. In our proposed scheme, the band structure of ferromagnetic silicene is
2
modified by optical and electric field and a new energy band is formed. We show that
3
the transport gap of charge conductance fully tuned by optical field is broaden
4
compared with electric field, which provides a convenient method to acquire on/off
5
electric switch. The spin polarized conductance is enhanced above 90% and the
6
polarized direction can be inverted by adjusting the optical field together with the
7
ferromagnetic exchange field. In addition, the perfect valley-polarized conductance
8
with 95% can be obtained under the interplay between optical field and electric field
9
in a NFN silicene junction.
10
2. Model and theoretical method
11
We consider a NFN junction based on monolayer silicene shown in Fig. 1. A
12
perpendicular electric field and off-resonant circularly polarized light are placed in the
13
ferromagnetic region to generate a modulation to the band structure of silicene. The
14
circularly polarized light is described by an electromagnetic potential as
15
A(t ) A(sin Ωt ,cos Ωt ) , where Ω is frequency of the light. In our calculation, we
16
focus on the off-resonant regime which is satisfied when ћΩ t0 with t0 1.6eV is
17
the nearest-neighbor transfer energy for silicene. In such regime, the light does not
18
directly excite the electrons instead modifying the electron band structure through
19
virtual photon absorption/emission processes. Ezawa [18] has estimated the lowest
20
frequency in off-resonant regime is 1000 THz. In the limit of eAvF ћΩ 1 (
21
vF 5.5 105 m / s is the Fermi velocity), the off-resonant light can be described as a
22
static effective Hamiltonian [22-24], hence, the effective Hamiltonian in silicene, in
23
the presence of the off-resonant circularly polarized light and perpendicular electric
24
field, is given by [18]
25
H ћvF ( k x x k y y ) (so Δ z Δ Ω ) z h,
26
where the first part in Eq. (1) is the same as the Dirac Hamiltonian for graphene. In
27
this term, i (i x, y , z ) are the Pauli matrixes of the sublattice pseudospin and
28
k ( k x , k y ) is the two dimensional momentum measured from the Dirac points. In the
29
second term, so 3.9meV is the intrinsic SOC, and z is the net electrostatic
30
potential difference between the A and B sublattices, which is induced by the
31
perpendicular electric field along the z axis. Δ Ω ( eAvF )2 ћΩ , and Ω 0 ( Ω 0 )
32
corresponds to right (left) circularly polarized light. In our calculation, a circularly
33
polarized light in the x-ray region with wavelength 100nm ( Ω 3000THz ) and
34
the maximum intensity I ( eAΩ)2 8ћ 3.04 1014 W m 2 are used, where the off3
(1)
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resonant condition and the limit eAvF ћΩ 0.14 1 are still hold. The Δ Ω can be
2
tuned through controlling the intensity of circularly polarized light. In the third term,
3
h is the exchange field induced by magnetic proximity coupling using a magnetic
4
insulator, such as EuO [25]. Throughout the whole Eq. (1), 1 denotes the valley
5
K and K ' and 1 corresponds to the spin-up and spin-down, respectively.
6 7
According to Eq. (1), the energy dispersions in the ferromagnetic region (region II) are given by
E F ( ћvF k ' )2 (so Δ z Δ Ω )2 h,
8
(2)
9
where k '2 k x' 2 k y 2 and represents the conduction and valance bands,
10
respectively. In the normal region (region I and III), the energy dispersions can be
11
acquired by replacing h 0 , Δ z 0 , Δ Ω 0 and k 2 k x 2 k y 2 in Eq. (2). We
12
assume that the system is translationally invariant along the y direction and the
13
wavefunctions of each region are written as
14
I
15
ћvF ( k x i k y ) ik x ћvF ( k x i k y ) ik x x II a e b e x f f (4)
16
III
17
with E N E F so and f E F so Δ z Δ Ω h , the r , a , b and
18
t are the reflection and transmission coefficients at the first and second interfaces,
19
which can be determined from the continuity of the wave function at x 0 and x L
20 21
. The transmission coefficients through such a silicene junction can be calculated as:
22
23
1 2 EF EN
r ћvF ( k x i k y ) ik x x e EN 2 EF EN
ћvF ( k x i k y ) ik x x e EN (3)
ћvF ( k x i k y ) ik x x e , EN 2 EF EN (5) t
t 4k x k x EN f e ikx L A ,
(6)
A 2( 1 )k x k x EN f ( 1 )[k x 2 f 2 k x' 2 EN 2 k y 2 ( EN f ) 2 ],
(7)
with eikx L .
24
The final transmission probability is evaluated according to the formula
25
T t . Under the zero-temperature regime, the normalized spin and valley
26
resolved conductance in the Landauer–Büttiker formalism [26] are giving by
27 28
2
G
1 2 T cos d . 2 .
(8)
The charge conductance can be introduced as Gc GK GK GK ' GK ' . To 4
ACCEPTED MANUSCRIPT 1
explore the spin and valley polarization through the junction, we define the spin-
2
resolved conductance as G( ) (GK ( ) GK '( ) ) 2
3
conductance as GK ( K ') (GK ( K ') GK ( K ') ) 2 .
and the valley-resolved
4 5
3. Results and discussion
6
We first discuss the charge conductance as functions of circularly polarized light
7
and electric field. From the energy dispersions of Eq. (1), it’s easy to see the energy
8
bands can be modified through circularly polarized light and electric field, so if the
9
light intensity or the electric field is tuned properly, the Fermi level can cross the
10
conductance and valance bands, or drops into the energy gap between conductance
11
and valance bands, which means a good on/off electric switch can be realized. In Fig.
12
2, we have shown the contour plot of charge conductance Gc as functions of Δ Ω and
13
Δ z , we see that the charge conductance is symmetric with respect to Δ z . For
14
Δ Ω 0.0 , the charge conductance monotonically decreases to 0 with Δ z (if Δ z 0.0 )
15
and one transport gap is appearing, these electric modulation results are consistent
16
with Ref 12 and 14. Differently, with Δ z 0.0 , one optical-controlled transport gap is
17
acquired, and it’s wider than electric field modulated transport gap [12,14], which
18
provides a convenient method to acquire an on/off electric switch. On the other hand,
19
it’s worth noted that the transport gap is asymmetric with respect to Δ Ω , since the
20
valley index is coupled with the optical field Δ Ω (see Eq. (1) ), the different
21
response of charge conductance to the right (left) circularly polarized light is
22
observed.
23
Due to the larger spin-valley coupling in silicene, the conductance is expected
24
spin–resolved and give a potential application for spintronics. In the following, we
25
investigate the spin-resolved conductance modulated by optical field. First, the
26
electric field is turned off ( Δ z 0.0 ) in order to explore the full effects of circularly
27
polarized light. In
28
intensity of the circularly polarized light Δ Ω is displayed, generally, G and G reach
29
maxima when the intensity is weak and decrease rapidly as the intensity increases. In
30
particular, when 3.6 Δ Ω so 1.0 and 2.0 Δ Ω so 2.5 , the spin-resolved
31
conductance is spin-up polarized and spin-down polarized respectively, however, the
32
polarized conductance are not enough high, especial for the spin-down polarized
33
conductance. From Eq. (1), we note that spin degeneracy has been broken by the
34
ferromagnetic exchange field, it’s therefore possible to enhance the polarized
35
conductance through exchange field. To understand the influence of exchange field,
Fig. 3 (a), the spin-resolved conductance as a function of the
5
ACCEPTED MANUSCRIPT 1
we first close the optical field, as shown in Fig. 3 (b), the spin-up polarized
2
conductance is greatly enhanced when h so 1.7 . Perhaps more interesting, in
3
Fig. 3 (c), when one left circularly polarized light is applied, spin-up polarization with
4
irrespective of exchange field is observed, and the maximal polarized conductance is
5
estimated to be 90%. In contrast, for a right polarization of the light, it’s found that
6
the spin polarization could be inverted, as shown in Fig. 3 (d), the spin-down
7
polarization with highest conductance is obtained at h so 0.0 , which corresponds
8
to a normal/ normal/ normal silicene junction.
9
These scenarios of spin-resolved conductance can be understood from the low
10
energy band structures of the ferromagnetic silicene shown in Fig. 4. From Eq. (2),
11
the K and K ' valleys have the same band structure for Δ z 0.0 and thus are not
12
distinguished in Fig. 4. From Fig. 4 (a-c), the Fermi energy falls within the gap of
13
spin-down band and crosses one spin-up band, where the transmitted wave vector
14
k ' ( EF h) 2 (so Δ z Δ Ω ) 2 ћvF for
15
imaginary in these conditions, and one spatially decaying modes will open, the
16
transport of G is therefore progressively suppressed via evanescent mode, leading to
17
the spin-up polarization in Fig. 3 (a-c). For the spin-down polarization in Fig. 3(d), the
18
same mechanism can be understood according to Fig. 4(d). In addition, the enhanced
19
90% spin-up polarized conductance in Fig. 3(b) and Fig. 3(c) at h / so 1.7 are due
20
to the changing of spin-up band structure ranging from line to parabolat relationship,
21
thus the electron with the same Fermi energy would have larger density of state when
22
it crosses the spin-up conductance band, as shown in Fig. 4(b) and Fig. 4(c).
23
Meanwhile, in Fig. 4(c), a larger spin-down band gap is opened when the left
24
circularly polarized light Δ Ω / so 1.5 is switched on, explaining that the observed
25
spin-up polarization with irrespective of exchange field in Fig. 3 (c).
spin-down
electron
become
26
We further explore the valley-resolved conductance controlled by the optical
27
field and electric field. From the Dirac Hamiltonian of Eq. (1), it reveals the valley
28
degeneracy can be lifted by applying a perpendicular electric field ( Δ z 0.0 ) or an
29
off-resonant circularly polarized light, so the valley-resolved conductance is expected
30
in our model. Fig. 5 (a) shows the dependence of valley resolved conductance on Δ z
31
at Δ Ω 0.0 , as expected, the valley conductance GK and GK ' exhibit slight
32
difference for a nonzero electric field, however, the valley-polarization is invalid,
33
which is necessary for achieving the application of such junction in valleytronics. But,
34
as shown in Fig. 5 (b), when one left circularly polarized light with Δ Ω so 8.0 is 6
ACCEPTED MANUSCRIPT 1
applied, one full K ( K ' ) valley-polarization is achieved for Δ z 3.0 , and more
2
important, the maximal valley-polarized conductance reaches to 95% at Δ z so 8.0
3
and the polarized direction can be switched just through reversing the direction of
4
electric field. The optical field modulated behavior is similar to the electric field
5
modulation, as shown in Fig. 5 (c), with the electric field Δ z so 8.0 applied, the
6
high performance valleytronics can also be acquired by tuning the intensity and
7
polarization of circularly polarized light. To explain these valley-polarized
8
characteristics, we first consider the band structure with Δ Ω 0.0 (see Fig. 6 (a) and
9
6 (b)), the Fermi level crosses the bands near both the K and K ' points, where the
10
transmitted wave vector k ' for K and K ' electron are both real, thus, the
11
conductance stemming from K and K ' are nonzero (see Fig. 5 (a)). The applied left
12
circularly polarized light
13
and locates the Fermi energy inside, moreover, the band gap near the K ' point is
14
reduced so much so that the electron density of state is increased significantly for
15
EF so 9.0 (see Fig. 6 (c) and 6 (d)), which lead to the high K ' valley-polarized
16
conductance. In contrast, one right circularly polarized light ΔΩ so 8.0 produces
17
opposite effects on the band gaps near K and K ' points
18
and gives rise to the K valley-polarization.
Δ Ω so 8.0 enlarges the band gap near the K point
(see Fig. 6 (e) and 6 (f))
19 20
4. Conclusion
21
In summary, we have systematically studied the effects of off-resonant circularly
22
polarized light and electric field on the ballistic transport in a NFN silicene junction.
23
It’s found that one transport gap of charge conductance can be opened by an optical
24
field and electric field, compared with the influences of electric field, the optical field
25
have broadened the transport gap. Owing to the spin-valley coupling in silicene, the
26
spin polarization is obtained by adjusting the intensity of optical field, coupling with
27
the ferromagnetic exchange field, the polarized conductance is further enhanced
28
above 90%, and the polarization is irrespective of exchange field for 0 h so 3.0
29
under radiation of a left circularly polarized light. Additionally, the spin polarization
30
could be inverted by reversing the polarization of the light. In particular, one near
31
perfect K ( K ' ) valley-polarized conductance with 95% conductance is realized in our
32
model by tuning the intensity and direction of electric field and optical field. It’s
33
believed that our results are helpful to clearly comprehend the optical and electric
34
control of spin and valley transport in ferromagnetic silicene junction and benefit 7
ACCEPTED MANUSCRIPT 1
applications in high-efficiency nano-electronics.
2 3
Acknowledgement
4
This work was supported by the National Natural Science Foundation of China
5
(Grant Nos. 11404411, 11204383, 11404412, and U1404112), and the Basic and
6
Advanced Technology Research Program of Henan Province (Grant No.
7
142102310274).
8
8
ACCEPTED MANUSCRIPT Reference [1] C. C. Liu, W. X. Feng, and Y. G. Yao, Phys. Rev. Lett. 107 (2011) 076802. [2] N. D. Drummond, V. Zólyomi, and V. I. Fal’ko, Phys. Rev. B 85 (2012), 075423. [3] I. Zutic, J. Fabian, and S. Das Sarma, Rev. Mod. Phys. 76 (2004), 323. [4] Y. Wang, R. Quhe, D. Yu, J. Li, and J. Lu, Chin. Phys. B 24 (2015) 087201. [5] S. Rachel and M. Ezawa, Phys. Rev. B 89 (2014) 195303. [6] Y. Wang, J. Zheng, Z. Ni, R. Fei, Q. Liu, R. Quhe, C. Xu, J. Zhou, Z. Gao, and J. Lu, Nano. 7 (2012) 1250037. [7] H. Pan, Z. Li, C. C. Liu, G. Zhu, Z. Qiao, and Y. Yao, Phys. Rev. Lett. 112 (2014) 106802. [8] A. Kundu, H. Fertig, and B. Seradjeh, Phys. Rev. Lett. 116 (2016) 016802. [9] R. Saxena, A. Saha, and S. Rao, Phys. Rev. B 92 (2015) 245412. [10] L. Tao, E. Cinquanta, D. Chiappe, C. Grazianetti, M. Fan-ciulli, M. Dubey, A. Molle, and D. Akinwande, Nat. Nanotechnol. 10 (2015) 227. [11] W. F. Tsai, C. Y. Huang, T. R. Chang, H. Lin, H. T. Jeng, and A. Bansil, Nature Commun. 4 (2013) 1500. [12] T. Yokoyama, Phys. Rev. B 87 (2013) 241409(R). [13] V. Vargiamidis and P. Vasilopoulos, Appl. Phys. Lett. 105 (2014) 223105. [14] N. Missault, P. Vasilopoulos, V. Vargiamidis, F. M. Peeters, and B. Van Duppen, Phys. Rev. B 92 (2015) 195423. [15] X. Q.Wu and H. Meng, J. Appl. Phys. 117 (2015) 203903. [16] Yu Wang, Appl. Phys. Lett. 104 (2014) 032105. [17] C. Yesilyurt, S. G. Tan, L. Gengchiau, and M. B. A. Jalil, Appl. Phys. Express. 8 (2015) 105201. [18] M. Ezawa, Phys. Rev. Lett. 110 (2013) 026603. [19] Y. Mohammadi and B. A. Nia, Superlattices Microstruct. 96 (2016) 259. [20] Z. P. Niu and S. Dong, Eur. Lett. 111 (2015) 37007. [21] L. B. Ho and T. N. Lan, J. Phys. D: Appl. Phys. 49 (2016) 375106. [22] T. Kitagawa, T. Oka, A. Brataas, L. Fu, and E. Demler, Phys. Rev. B 84 (2011) 235108. [23] T. Kitagawa, M. S. Rudner, E. Berg, and E. Demler, Phys. Rev. A 82 (2010) 0033429. [24] T. Kitagawa, E. Berg, M. Rudner, and E. Demler, Phys. Rev. B 82 (2010) 235114. [25] H. Haugen, D. H. Hernando, and A, Brataas, Phys. Rev. B 77 (2008) 115406. [26] M. Büttiker, Phys. Rev. Lett. 57 (1986) 1761.
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ACCEPTED MANUSCRIPT Figure captions Fig. 1. (Color online) Schematic of setup of a NFN junction with off-resonant circularly polarized light and perpendicular electric field in the ferromagnetic region. L is the length of the ferromagnetic region, and the transport direction is along the x-axis. Fig. 2. (Color online) Contour plot of charge conductance Gc as functions of Δ Ω and
Δ z . The other parameters are L 2ћvF so , E F so 2.0 , and h so 0.6 . Fig. 3. (Color online) (a) The spin-resolved conductance as a function of the intensity
Δ Ω with h so 0.6 . (b-d) The spin-resolved conductance as a function of the ferromagnetic exchange field h at Δ Ω 0.0 (b) and Δ Ω so 1.5 (c) and
Δ Ω so 1.5 (d). The red solid curve and the blue dashed curve indicate the
G
and G , respectively. The other parameters are
L 2ћvF so ,
E F so 2.0 , and Δ z 0.0 . Fig. 4. (Color online) Low energy band structures of the ferromagnetic silicene around Dirac points K and K ' as a function of ћvF k so at Δ z 0.0 . (a)
Δ Ω / so 1.0 , h / so 0.6 , (b) Δ Ω 0.0 , h / so 1.7 , (c) Δ Ω / so 1.5 , h / so 1.7 , (d) . Δ Ω / so 1.5 ,
h / so 0.0 . The red solid lines indicate the
spin-up bands and the blue dotted lines indicate the spin-down bands. Black horizontal dashed dotted line denotes the Fermi energy E F so 2.0 . Other parameters are the same as in Fig. 3. Fig. 5. (Color online) (a) and (b) Dependences of valley resolved conductance on Δ z with Δ Ω 0.0 (a) and Δ Ω so 8.0 (b). (c) The optical intensity dependent valley resolved conductance with Δ z so 8.0 . The red solid curve and the blue dashed curve indicate the GK and GK ' , respectively. The other parameters are L 2ћvF so , E F so 9.0 , and h so 0.6 . Fig. 6. (Color online) Low energy band structures of the ferromagnetic silicene around Dirac points K (right) and K ' (left) as a function of ћvF k so at
Δ z / so 8.0 . (a, b) Δ Ω 0.0 , (c, d) Δ Ω / so 8.0 , (e, f) Δ Ω / so 8.0 . The red solid lines indicate the spin-up bands and the blue dotted lines indicate the spin-down bands. Black horizontal dashed dotted line denotes the Fermi energy E F so 9.0 . Other parameters are the same as in Fig. 5
10
ACCEPTED MANUSCRIPT Fig. 1.
11
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12
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13
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14
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15
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16
ACCEPTED MANUSCRIPT Highlights •The charge and spin-valley transport in a normal/ferromagnetic/normal silicene junction is investigated. •One wider transport gap of charge conductance can be produced by the optical field than the electric field. •The spin-polarized conductance is enhanced above 90% under a proper optical field and ferromagnetic exchange field. •One near perfect K ( K ' ) valley-polarized conductance exceeding 95% conductance is realized.
Xuejun Qiu, Zhenzhou Cao, Jiemei Lei, Jian Shen, Chaochao Qin PII:
S0749-6036(17)30713-9
DOI:
10.1016/j.spmi.2017.05.059
Reference:
YSPMI 5040
To appear in:
Superlattices and Microstructures
Received Date:
22 March 2017
Revised Date:
08 May 2017
Accepted Date:
09 May 2017
Please cite this article as: Xuejun Qiu, Zhenzhou Cao, Jiemei Lei, Jian Shen, Chaochao Qin, Optical and electric control of charge and spin-valley transport in ferromagnetic silicene junction, Superlattices and Microstructures (2017), doi: 10.1016/j.spmi.2017.05.059
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
1
Optical and electric control of charge and spin-valley
2
transport in ferromagnetic silicene junction
3 4 5 6 7
Xuejun Qiua,*, Zhenzhou Caoa, Jiemei Leia, Jian Shena, Chaochao Qinb aCollege
of Electronics and Information, Hubei Key Laboratory of Intelligent Wireless
Communications, South-Central University for Nationalities, Wuhan 430074, China bCollege
of Physics and Electronic Engineering, Henan Normal University, Xinxiang, 453007,
8
China
9 10
Abstract: We theoretically investigate the charge and spin-valley transport in a
11
normal/ferromagnetic/normal silicene junction, where the ferromagnetic region is
12
exposed to an off-resonant circularly polarized light and perpendicular electric field.
13
We show that one wider transport gap can be produced by the optical field than the
14
electric field, which provides a simple way to fabricate an optical controlled on/off
15
switch. On the other hand, in the presence of a proper optical field and ferromagnetic
16
exchange field, the spin-polarized conductance is enhanced above 90%, and the
17
polarized direction can be inverted just by reversing the polarization of the light.
18
Additionally, the valley-polarized conductance is sensitive to the optical and electric
19
field, under proper values, one near perfect K ( K ' ) valley-polarized conductance
20
exceeding 95% is realized. All these findings are well understood from the band
21
structure of silicene and expected to be beneficial for real applications in high
22
performance spintronics and valleytronics.
23
Keywords: Spintronics;Valleytronics; Silicene; Ferromagnetic; Optical
24 25 26 27 28
________ * Corresponding author at: College of Electronics and Information, South-Central University for Nationalities, Wuhan, 430074, China. Tel.:+86 18672323467 E-mail address: [email protected]
1
ACCEPTED MANUSCRIPT 1
I. Introduction
2
Silicene, a close cousin of graphene, has received a lot of attention in recent
3
years due to the distinctive geometrical [1] and electronic structure [2], giving various
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potential applications ranging from spintronics [3-6], valleytronics [7-9] to silicon
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based transistor [10] at room temperature. Unlike graphene, silicene has a buckled
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structure owing to the large atomic radius of silicon, leading to a tuneable bandgap at
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the Dirac point and consequently triggering various topological quantum states [11].
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Yokoyama et al have shown that such a band gap is controllable by a
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perpendicular external electric field and ferromagnetic exchange field, revealing the
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valley and spin polarization can be achieved in normal/ferromagnetic/normal (NFN)
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silicene junction [12]. Based on their findings, the ballistic transport in double and
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multiple ferromagnetic barrier [13,14], magnetic barrier [15] and quantum well [16]
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have successively been investigated, these studies have found many interesting and
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novel results such as electric field and exchange field dependent transport gaps and
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the perfect spin and valley polarizations. Besides, the spin and valley polarized
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current induced by strain has also been reported, and a highly efficient filtering for all
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four spin-valley configurations is proposed [17].
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Although abundant interesting phenomena could be produced from the electric
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field, ferromagnetic exchange field and strain, to search a convenient control and
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achieve a high-efficiency spin-valley polarization, is the long-term pursuit of
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scientific workers. In earlier works, it’s found that the topological phase transition in
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silicene can be altered by irradiating circular polarized light at fixed electric field, and
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a photo induced spin-polarized quantum Hall insulator is realized [18]. Very recently,
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some research groups start paying deserving attention to the light-dependent ballistic
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transport in silicene, i.e. the ballistic transport through a strip with circularly polarized
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light and electric field applied in normal silicene is studied by Mohammadi et.al. [19],
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the photo-induced valley and spin transport together with tunneling magnetoresistance
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in a ferromagnetic/ferromagnetic/ferromagnetic, ferromagnetic/normal/ferromagnetic
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[20,21] silicene junction and so on. However, the ballistic electron transport in a NFN
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silicene junction with the circularly polarized light and electric field applied in
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ferromagnetic region has not been systematically studied before and is very
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convenient to realize in experiment, so it is expected that intriguing spin-valley
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transport can be obtained in this junction.
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In this paper, we study the charge and spin-valley transports in a NFN silicene 2
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junction. In our proposed scheme, the band structure of ferromagnetic silicene is
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modified by optical and electric field and a new energy band is formed. We show that
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the transport gap of charge conductance fully tuned by optical field is broaden
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compared with electric field, which provides a convenient method to acquire on/off
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electric switch. The spin polarized conductance is enhanced above 90% and the
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polarized direction can be inverted by adjusting the optical field together with the
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ferromagnetic exchange field. In addition, the perfect valley-polarized conductance
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with 95% can be obtained under the interplay between optical field and electric field
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in a NFN silicene junction.
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2. Model and theoretical method
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We consider a NFN junction based on monolayer silicene shown in Fig. 1. A
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perpendicular electric field and off-resonant circularly polarized light are placed in the
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ferromagnetic region to generate a modulation to the band structure of silicene. The
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circularly polarized light is described by an electromagnetic potential as
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A(t ) A(sin Ωt ,cos Ωt ) , where Ω is frequency of the light. In our calculation, we
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focus on the off-resonant regime which is satisfied when ћΩ t0 with t0 1.6eV is
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the nearest-neighbor transfer energy for silicene. In such regime, the light does not
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directly excite the electrons instead modifying the electron band structure through
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virtual photon absorption/emission processes. Ezawa [18] has estimated the lowest
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frequency in off-resonant regime is 1000 THz. In the limit of eAvF ћΩ 1 (
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vF 5.5 105 m / s is the Fermi velocity), the off-resonant light can be described as a
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static effective Hamiltonian [22-24], hence, the effective Hamiltonian in silicene, in
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the presence of the off-resonant circularly polarized light and perpendicular electric
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field, is given by [18]
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H ћvF ( k x x k y y ) (so Δ z Δ Ω ) z h,
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where the first part in Eq. (1) is the same as the Dirac Hamiltonian for graphene. In
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this term, i (i x, y , z ) are the Pauli matrixes of the sublattice pseudospin and
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k ( k x , k y ) is the two dimensional momentum measured from the Dirac points. In the
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second term, so 3.9meV is the intrinsic SOC, and z is the net electrostatic
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potential difference between the A and B sublattices, which is induced by the
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perpendicular electric field along the z axis. Δ Ω ( eAvF )2 ћΩ , and Ω 0 ( Ω 0 )
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corresponds to right (left) circularly polarized light. In our calculation, a circularly
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polarized light in the x-ray region with wavelength 100nm ( Ω 3000THz ) and
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the maximum intensity I ( eAΩ)2 8ћ 3.04 1014 W m 2 are used, where the off3
(1)
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resonant condition and the limit eAvF ћΩ 0.14 1 are still hold. The Δ Ω can be
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tuned through controlling the intensity of circularly polarized light. In the third term,
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h is the exchange field induced by magnetic proximity coupling using a magnetic
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insulator, such as EuO [25]. Throughout the whole Eq. (1), 1 denotes the valley
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K and K ' and 1 corresponds to the spin-up and spin-down, respectively.
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According to Eq. (1), the energy dispersions in the ferromagnetic region (region II) are given by
E F ( ћvF k ' )2 (so Δ z Δ Ω )2 h,
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(2)
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where k '2 k x' 2 k y 2 and represents the conduction and valance bands,
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respectively. In the normal region (region I and III), the energy dispersions can be
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acquired by replacing h 0 , Δ z 0 , Δ Ω 0 and k 2 k x 2 k y 2 in Eq. (2). We
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assume that the system is translationally invariant along the y direction and the
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wavefunctions of each region are written as
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I
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ћvF ( k x i k y ) ik x ћvF ( k x i k y ) ik x x II a e b e x f f (4)
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III
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with E N E F so and f E F so Δ z Δ Ω h , the r , a , b and
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t are the reflection and transmission coefficients at the first and second interfaces,
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which can be determined from the continuity of the wave function at x 0 and x L
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. The transmission coefficients through such a silicene junction can be calculated as:
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1 2 EF EN
r ћvF ( k x i k y ) ik x x e EN 2 EF EN
ћvF ( k x i k y ) ik x x e EN (3)
ћvF ( k x i k y ) ik x x e , EN 2 EF EN (5) t
t 4k x k x EN f e ikx L A ,
(6)
A 2( 1 )k x k x EN f ( 1 )[k x 2 f 2 k x' 2 EN 2 k y 2 ( EN f ) 2 ],
(7)
with eikx L .
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The final transmission probability is evaluated according to the formula
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T t . Under the zero-temperature regime, the normalized spin and valley
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resolved conductance in the Landauer–Büttiker formalism [26] are giving by
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2
G
1 2 T cos d . 2 .
(8)
The charge conductance can be introduced as Gc GK GK GK ' GK ' . To 4
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explore the spin and valley polarization through the junction, we define the spin-
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resolved conductance as G( ) (GK ( ) GK '( ) ) 2
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conductance as GK ( K ') (GK ( K ') GK ( K ') ) 2 .
and the valley-resolved
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3. Results and discussion
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We first discuss the charge conductance as functions of circularly polarized light
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and electric field. From the energy dispersions of Eq. (1), it’s easy to see the energy
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bands can be modified through circularly polarized light and electric field, so if the
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light intensity or the electric field is tuned properly, the Fermi level can cross the
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conductance and valance bands, or drops into the energy gap between conductance
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and valance bands, which means a good on/off electric switch can be realized. In Fig.
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2, we have shown the contour plot of charge conductance Gc as functions of Δ Ω and
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Δ z , we see that the charge conductance is symmetric with respect to Δ z . For
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Δ Ω 0.0 , the charge conductance monotonically decreases to 0 with Δ z (if Δ z 0.0 )
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and one transport gap is appearing, these electric modulation results are consistent
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with Ref 12 and 14. Differently, with Δ z 0.0 , one optical-controlled transport gap is
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acquired, and it’s wider than electric field modulated transport gap [12,14], which
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provides a convenient method to acquire an on/off electric switch. On the other hand,
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it’s worth noted that the transport gap is asymmetric with respect to Δ Ω , since the
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valley index is coupled with the optical field Δ Ω (see Eq. (1) ), the different
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response of charge conductance to the right (left) circularly polarized light is
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observed.
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Due to the larger spin-valley coupling in silicene, the conductance is expected
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spin–resolved and give a potential application for spintronics. In the following, we
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investigate the spin-resolved conductance modulated by optical field. First, the
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electric field is turned off ( Δ z 0.0 ) in order to explore the full effects of circularly
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polarized light. In
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intensity of the circularly polarized light Δ Ω is displayed, generally, G and G reach
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maxima when the intensity is weak and decrease rapidly as the intensity increases. In
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particular, when 3.6 Δ Ω so 1.0 and 2.0 Δ Ω so 2.5 , the spin-resolved
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conductance is spin-up polarized and spin-down polarized respectively, however, the
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polarized conductance are not enough high, especial for the spin-down polarized
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conductance. From Eq. (1), we note that spin degeneracy has been broken by the
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ferromagnetic exchange field, it’s therefore possible to enhance the polarized
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conductance through exchange field. To understand the influence of exchange field,
Fig. 3 (a), the spin-resolved conductance as a function of the
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we first close the optical field, as shown in Fig. 3 (b), the spin-up polarized
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conductance is greatly enhanced when h so 1.7 . Perhaps more interesting, in
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Fig. 3 (c), when one left circularly polarized light is applied, spin-up polarization with
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irrespective of exchange field is observed, and the maximal polarized conductance is
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estimated to be 90%. In contrast, for a right polarization of the light, it’s found that
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the spin polarization could be inverted, as shown in Fig. 3 (d), the spin-down
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polarization with highest conductance is obtained at h so 0.0 , which corresponds
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to a normal/ normal/ normal silicene junction.
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These scenarios of spin-resolved conductance can be understood from the low
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energy band structures of the ferromagnetic silicene shown in Fig. 4. From Eq. (2),
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the K and K ' valleys have the same band structure for Δ z 0.0 and thus are not
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distinguished in Fig. 4. From Fig. 4 (a-c), the Fermi energy falls within the gap of
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spin-down band and crosses one spin-up band, where the transmitted wave vector
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k ' ( EF h) 2 (so Δ z Δ Ω ) 2 ћvF for
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imaginary in these conditions, and one spatially decaying modes will open, the
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transport of G is therefore progressively suppressed via evanescent mode, leading to
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the spin-up polarization in Fig. 3 (a-c). For the spin-down polarization in Fig. 3(d), the
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same mechanism can be understood according to Fig. 4(d). In addition, the enhanced
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90% spin-up polarized conductance in Fig. 3(b) and Fig. 3(c) at h / so 1.7 are due
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to the changing of spin-up band structure ranging from line to parabolat relationship,
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thus the electron with the same Fermi energy would have larger density of state when
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it crosses the spin-up conductance band, as shown in Fig. 4(b) and Fig. 4(c).
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Meanwhile, in Fig. 4(c), a larger spin-down band gap is opened when the left
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circularly polarized light Δ Ω / so 1.5 is switched on, explaining that the observed
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spin-up polarization with irrespective of exchange field in Fig. 3 (c).
spin-down
electron
become
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We further explore the valley-resolved conductance controlled by the optical
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field and electric field. From the Dirac Hamiltonian of Eq. (1), it reveals the valley
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degeneracy can be lifted by applying a perpendicular electric field ( Δ z 0.0 ) or an
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off-resonant circularly polarized light, so the valley-resolved conductance is expected
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in our model. Fig. 5 (a) shows the dependence of valley resolved conductance on Δ z
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at Δ Ω 0.0 , as expected, the valley conductance GK and GK ' exhibit slight
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difference for a nonzero electric field, however, the valley-polarization is invalid,
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which is necessary for achieving the application of such junction in valleytronics. But,
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as shown in Fig. 5 (b), when one left circularly polarized light with Δ Ω so 8.0 is 6
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applied, one full K ( K ' ) valley-polarization is achieved for Δ z 3.0 , and more
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important, the maximal valley-polarized conductance reaches to 95% at Δ z so 8.0
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and the polarized direction can be switched just through reversing the direction of
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electric field. The optical field modulated behavior is similar to the electric field
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modulation, as shown in Fig. 5 (c), with the electric field Δ z so 8.0 applied, the
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high performance valleytronics can also be acquired by tuning the intensity and
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polarization of circularly polarized light. To explain these valley-polarized
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characteristics, we first consider the band structure with Δ Ω 0.0 (see Fig. 6 (a) and
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6 (b)), the Fermi level crosses the bands near both the K and K ' points, where the
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transmitted wave vector k ' for K and K ' electron are both real, thus, the
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conductance stemming from K and K ' are nonzero (see Fig. 5 (a)). The applied left
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circularly polarized light
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and locates the Fermi energy inside, moreover, the band gap near the K ' point is
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reduced so much so that the electron density of state is increased significantly for
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EF so 9.0 (see Fig. 6 (c) and 6 (d)), which lead to the high K ' valley-polarized
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conductance. In contrast, one right circularly polarized light ΔΩ so 8.0 produces
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opposite effects on the band gaps near K and K ' points
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and gives rise to the K valley-polarization.
Δ Ω so 8.0 enlarges the band gap near the K point
(see Fig. 6 (e) and 6 (f))
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4. Conclusion
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In summary, we have systematically studied the effects of off-resonant circularly
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polarized light and electric field on the ballistic transport in a NFN silicene junction.
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It’s found that one transport gap of charge conductance can be opened by an optical
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field and electric field, compared with the influences of electric field, the optical field
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have broadened the transport gap. Owing to the spin-valley coupling in silicene, the
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spin polarization is obtained by adjusting the intensity of optical field, coupling with
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the ferromagnetic exchange field, the polarized conductance is further enhanced
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above 90%, and the polarization is irrespective of exchange field for 0 h so 3.0
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under radiation of a left circularly polarized light. Additionally, the spin polarization
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could be inverted by reversing the polarization of the light. In particular, one near
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perfect K ( K ' ) valley-polarized conductance with 95% conductance is realized in our
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model by tuning the intensity and direction of electric field and optical field. It’s
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believed that our results are helpful to clearly comprehend the optical and electric
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control of spin and valley transport in ferromagnetic silicene junction and benefit 7
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applications in high-efficiency nano-electronics.
2 3
Acknowledgement
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This work was supported by the National Natural Science Foundation of China
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(Grant Nos. 11404411, 11204383, 11404412, and U1404112), and the Basic and
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Advanced Technology Research Program of Henan Province (Grant No.
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142102310274).
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ACCEPTED MANUSCRIPT Reference [1] C. C. Liu, W. X. Feng, and Y. G. Yao, Phys. Rev. Lett. 107 (2011) 076802. [2] N. D. Drummond, V. Zólyomi, and V. I. Fal’ko, Phys. Rev. B 85 (2012), 075423. [3] I. Zutic, J. Fabian, and S. Das Sarma, Rev. Mod. Phys. 76 (2004), 323. [4] Y. Wang, R. Quhe, D. Yu, J. Li, and J. Lu, Chin. Phys. B 24 (2015) 087201. [5] S. Rachel and M. Ezawa, Phys. Rev. B 89 (2014) 195303. [6] Y. Wang, J. Zheng, Z. Ni, R. Fei, Q. Liu, R. Quhe, C. Xu, J. Zhou, Z. Gao, and J. Lu, Nano. 7 (2012) 1250037. [7] H. Pan, Z. Li, C. C. Liu, G. Zhu, Z. Qiao, and Y. Yao, Phys. Rev. Lett. 112 (2014) 106802. [8] A. Kundu, H. Fertig, and B. Seradjeh, Phys. Rev. Lett. 116 (2016) 016802. [9] R. Saxena, A. Saha, and S. Rao, Phys. Rev. B 92 (2015) 245412. [10] L. Tao, E. Cinquanta, D. Chiappe, C. Grazianetti, M. Fan-ciulli, M. Dubey, A. Molle, and D. Akinwande, Nat. Nanotechnol. 10 (2015) 227. [11] W. F. Tsai, C. Y. Huang, T. R. Chang, H. Lin, H. T. Jeng, and A. Bansil, Nature Commun. 4 (2013) 1500. [12] T. Yokoyama, Phys. Rev. B 87 (2013) 241409(R). [13] V. Vargiamidis and P. Vasilopoulos, Appl. Phys. Lett. 105 (2014) 223105. [14] N. Missault, P. Vasilopoulos, V. Vargiamidis, F. M. Peeters, and B. Van Duppen, Phys. Rev. B 92 (2015) 195423. [15] X. Q.Wu and H. Meng, J. Appl. Phys. 117 (2015) 203903. [16] Yu Wang, Appl. Phys. Lett. 104 (2014) 032105. [17] C. Yesilyurt, S. G. Tan, L. Gengchiau, and M. B. A. Jalil, Appl. Phys. Express. 8 (2015) 105201. [18] M. Ezawa, Phys. Rev. Lett. 110 (2013) 026603. [19] Y. Mohammadi and B. A. Nia, Superlattices Microstruct. 96 (2016) 259. [20] Z. P. Niu and S. Dong, Eur. Lett. 111 (2015) 37007. [21] L. B. Ho and T. N. Lan, J. Phys. D: Appl. Phys. 49 (2016) 375106. [22] T. Kitagawa, T. Oka, A. Brataas, L. Fu, and E. Demler, Phys. Rev. B 84 (2011) 235108. [23] T. Kitagawa, M. S. Rudner, E. Berg, and E. Demler, Phys. Rev. A 82 (2010) 0033429. [24] T. Kitagawa, E. Berg, M. Rudner, and E. Demler, Phys. Rev. B 82 (2010) 235114. [25] H. Haugen, D. H. Hernando, and A, Brataas, Phys. Rev. B 77 (2008) 115406. [26] M. Büttiker, Phys. Rev. Lett. 57 (1986) 1761.
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ACCEPTED MANUSCRIPT Figure captions Fig. 1. (Color online) Schematic of setup of a NFN junction with off-resonant circularly polarized light and perpendicular electric field in the ferromagnetic region. L is the length of the ferromagnetic region, and the transport direction is along the x-axis. Fig. 2. (Color online) Contour plot of charge conductance Gc as functions of Δ Ω and
Δ z . The other parameters are L 2ћvF so , E F so 2.0 , and h so 0.6 . Fig. 3. (Color online) (a) The spin-resolved conductance as a function of the intensity
Δ Ω with h so 0.6 . (b-d) The spin-resolved conductance as a function of the ferromagnetic exchange field h at Δ Ω 0.0 (b) and Δ Ω so 1.5 (c) and
Δ Ω so 1.5 (d). The red solid curve and the blue dashed curve indicate the
G
and G , respectively. The other parameters are
L 2ћvF so ,
E F so 2.0 , and Δ z 0.0 . Fig. 4. (Color online) Low energy band structures of the ferromagnetic silicene around Dirac points K and K ' as a function of ћvF k so at Δ z 0.0 . (a)
Δ Ω / so 1.0 , h / so 0.6 , (b) Δ Ω 0.0 , h / so 1.7 , (c) Δ Ω / so 1.5 , h / so 1.7 , (d) . Δ Ω / so 1.5 ,
h / so 0.0 . The red solid lines indicate the
spin-up bands and the blue dotted lines indicate the spin-down bands. Black horizontal dashed dotted line denotes the Fermi energy E F so 2.0 . Other parameters are the same as in Fig. 3. Fig. 5. (Color online) (a) and (b) Dependences of valley resolved conductance on Δ z with Δ Ω 0.0 (a) and Δ Ω so 8.0 (b). (c) The optical intensity dependent valley resolved conductance with Δ z so 8.0 . The red solid curve and the blue dashed curve indicate the GK and GK ' , respectively. The other parameters are L 2ћvF so , E F so 9.0 , and h so 0.6 . Fig. 6. (Color online) Low energy band structures of the ferromagnetic silicene around Dirac points K (right) and K ' (left) as a function of ћvF k so at
Δ z / so 8.0 . (a, b) Δ Ω 0.0 , (c, d) Δ Ω / so 8.0 , (e, f) Δ Ω / so 8.0 . The red solid lines indicate the spin-up bands and the blue dotted lines indicate the spin-down bands. Black horizontal dashed dotted line denotes the Fermi energy E F so 9.0 . Other parameters are the same as in Fig. 5
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ACCEPTED MANUSCRIPT Highlights •The charge and spin-valley transport in a normal/ferromagnetic/normal silicene junction is investigated. •One wider transport gap of charge conductance can be produced by the optical field than the electric field. •The spin-polarized conductance is enhanced above 90% under a proper optical field and ferromagnetic exchange field. •One near perfect K ( K ' ) valley-polarized conductance exceeding 95% conductance is realized.