Interband magnetoabsorption spectra of Mn-doped ZnO nanowires

Accepted Manuscript Interband magnetoabsorption spectra of Mn-doped ZnO nanowires Qiao-Ying Xu, Wen Xiong

PII:

S0749-6036(15)30286-X

DOI:

10.1016/j.spmi.2015.11.021

Reference:

YSPMI 4074

To appear in:

Superlattices and Microstructures

Received Date: 24 September 2015 Revised Date:

6 November 2015

Accepted Date: 17 November 2015

Please cite this article as: Q.-Y. Xu, W. Xiong, Interband magnetoabsorption spectra of Mn-doped ZnO nanowires, Superlattices and Microstructures (2015), doi: 10.1016/j.spmi.2015.11.021. 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.

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The followings are the lists of the highlights of the manuscript: (1)

The valence subbands of Mn-doped ZnO nanowires with different Mn2+ are calculated; The valence subbands of Mn-doped ZnO nanowires with different temperature are calculated;

(3)

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(2)

The possible optical transitions Mn-doped ZnO nanowires are

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presented;

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(4) The magnetoabsorption spectra of Mn-doped ZnO nanowires are

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presented.

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Interband magnetoabsorption spectra of Mn-doped ZnO nanowires Qiao-Ying Xu

Wen Xiong∗

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Department of Applied Physics, Chongqing University, Chongqing 400044, China

Department of Physics, Chongqing University, Chongqing 400044, China

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Abstract

The electronic structures of Mn-doped ZnO nanowires in the magnetic field are calculated based

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on the six-band k·p effective-mass theory. Through the calculation, it is found that the first two valence subbands with positive spin angular momentum Jh will reverse when the magnetic field is greater than a critical value, while they will not reverse when Jh is negative. Several lowest transitions are shown and the interband magnetoabsorption spectra of Mn-doped ZnO nanowires at the Γ point are also presented in the magnetic field, and it is found that the lowest optical transition is left circular polarized light. Meanwhile, red shifts of the absorption peaks will occur if

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the magnetic field is applied, and the absorption peaks will show blue shifts with the increase of the temperature. In addition, quasi-Fermi level of the valence subbands of Mn-doped ZnO nanowires increase with the increase of the temperature, and more absorption peaks will arise when the carrier

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density and the temperature increase.

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PACS numbers: 78.20.LS, 78.67.Qa, 73.22.-f

∗

[email protected]

1

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I.

INTRODUCTION

Low-dimensional dilute magnetic semiconductors(DMS) have been studied extensively because of their unique optical and magnetic properties[1–4], and many experiments doped

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Co2+ and Mn2+ into III-V and II-VI group low-dimensional semiconductors, such as nanowires[5–8], nanorods[9–11] and quantum dots[12–14]. Mn and Co-doped ZnO nanowires were especially studied due to their easy synthesis and room temperature ferromagnetism[15– 21].

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Co-doped ZnO nanowires were synthesized with a solution phase method, then electron transport and magneto-resistance of Co-doped ZnO nanowires were studied[15]; C. Y. Lin et al. investigated the magnetic and optical properties of Co-doped ZnO nanorods in the mag-

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netic field[11]; L. T. Chang et al. found the ferromagnetism of Mn-doped ZnO nanowires can be controlled by external electric field, and the effect of quantum confinements in nanowires can improve the Curie temperature Tc up to above room temperature[16]; W. S. Yan et al. found the ferromagnetism of Co-doped ZnO quantum dots can be driven by covering a ZnS shell around ZnO core[12]. Though Mn-doped nanostructures have been fabricated

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and studied in many experiments, few papers studied the magnetic and optical properties of Mn-doped nanostructures theoretically. A. Manaselyan et al. have investigated spin interactions in a CdTe quantum dot which contains a single magnetic impurity in theory, and they found that the sp-d spin interaction could bring about level anticrossings between the dark

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and bright exciton states[22]; A. Chazaryan et al. have studied the exciton states in a CdTe quantum ring containing a single magnetic impurity theoretically, and they showed that the bright exciton state can be changed to dark state via the magnetic field[23]; E. Badaeva et

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al. studied the absorption spectra of Mn-doped ZnO quantum dots by using linear-response time-dependent density functional theory, and they found excitonic transition maximum decreases in intensity with increasing Mn2+ concentration. In addition, the lowest transition split in the spin-up and spin-down manifolds due to sp-d magnetic exchange between Mn2+ and carriers[14]. As we know, ZnO is a wide-gap semiconductor with wurtzite structure usually. Therefore, we can neglect the coupling between the conduction band and valence band. Meanwhile, the spin-orbit and the crystal-field splittings can affect the valence band of wurtzite materials, and we can see the valence band structure of bulk wurtzite materials clearly in Refs. [24, 25]. 2

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Because the spin-orbit and crystal-field splittings of ZnO material are △so=-3.52 meV and △cr =39.42 meV, respectively[26, 27], and the valence bands of bulk ZnO material from top to bottom can be labeled as light-hole(LH), heavy-hole(HH), and crystal-field split-off(CH) hole bands according to the analysis of Ref. [25]. In addition, the band gap of ZnO material

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is Eg =3.37 eV, which is far more than spin-orbit and crystal-field splittings, so the sixband k·p effective-mass theory can be used to calculate the valence band structure of ZnO material without regard to the conduction band. Furthermore, W. Xiong et al. have derived six-band k·p Hamiltonian of wurtzite nanowires in the magnetic field based on the effective-

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mass theory[26], then sp-d exchange interaction between magnetic ions and carriers were handled under the mean-field and virtual crystal approximation[27].

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The rest of the paper is presented as follows. In Sec. II, the electron and hole states of Mn-doped ZnO nanowires in the magnetic field are calculated; In Sec. III, the numerical results are given, and several lowest interband magnetoabsorption spectra of Mn-doped ZnO nanowires at the Γ point with different concentration of manganese ions and magnetic field are discussed; In Sec. IV, the findings of the current paper are summarized.

ELECTRON STATES AND HOLE STATES OF WURTZITE NANOWIRES

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II.

DOPED WITH MANGANESE IONS IN THE MAGNETIC FIELD

~ = (0, 0, B) is applied, the valence band Hamiltonian of wurtzite If the magnetic field B

i) ↑,

√1 (|Xi − i|Y 2

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√1 (|Xi + i|Y 2

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structure is represented in the following form for the six Bloch states uih (i = 1, 2, ..., 6):

HhB = −

i) ↑, |Zi ↑ and 

B HhU

1  2m0 0

√1 (|Xi + i|Y 2

0 B HhL



i) ↓,

√1 (|Xi − i|Y 2

h  + Hso + Hzeeman

i) ↓, |Zi ↓[26] (1)

B B where m0 is the free electron mass, HhU = HhL , Hso is the valence band spin-orbit couh ~ is the Zeeman term of the hole. The pling(SOC) Hamiltonian[26], Hzeeman = 21 µB gh~sh · B

B block diagonal matrix HhU can be written as[26]   B B B H H H  11 12 13   B B B B  HhU =  H21 H22  H23   B B B H31 H32 H33

3

(2)

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where i Lp + M h 1 e2 p+ p− + eB~(Lh − ) − B 2 ρ2h + Np2z 2 2 4
L − M + R i e2 p p B H12 = p2− + eBρh e−iθh p− − B 2 ρ2h e−2iθh 4 2 4
i 1 B H13 = √ Qpz p− + eBρh e−iθh 2 2
i e2 Lp − M + Rp 2 B p+ − eBρh eiθh p+ − B 2 ρ2h e2iθh H21 = 4 2 4 h i 2 L + M 1 e p B H22 = p+ p− + eB~(Lh + ) − B 2 ρ2h + Np2z 2 2 4
i Qp z B H23 = √ p+ − eBρh eiθh 2 2
Qpz i B H31 = √ p+ − eBρh eiθh 2 2
i Qpz B H32 = √ p− + eBρh e−iθh 2 2 2
e B H33 = S p− p+ + eBLh ~ − B 2 ρ2h + Tp p2z + 2m0 ∆cr 4

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B H11 =

(3) (4) (5) (6) (7) (8) (9) (10) (11)

Lp , M, N, Rp , S, Tp , Q, ∆cr are the parameters to determine the valence band structure of the

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wurtzite semiconductor.

Except the above Hamiltonian HhB , p-d exchange interaction Hamiltonian between manganese ions and the hole can be expressed as[28] X i

~ i )~sh · S ~i Jv (~rh − R

(12)

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Hex = −

~ i is the coordination of manganese ions, ~sh is where ~rh is the coordination of the hole, R

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~i is the spin of manganese ions which locate at the site R ~ i . By the spin of the hole, S using the mean-field approximation and the virtual crystal approximation, the Hamiltonian of the exchange interaction can be calculated as Hhex = −βN0 xσzh hSz i[28], where N0 is the number of primitive cells per unit volume, x is the concentration of manganese ions, β = hX|Jv (~rh )|Xi is the p-d exchange integral[28], hSz i is the thermal average of the spin of manganese ions which can be expressed as[28] hSz i = SM n B5/2

hg

M n SM n u B B

kB (T + T0 )

i

(13)

where SM n is the spin the manganese ions, gM n is the g factor of manganese ions, T0 is the reduced single-ion contribution due to the antiferromagnetic Mn-Mn coupling[28, 31, 32], 4

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Bs (y) is the Brillouin function which can be expressed as  2S + 1   1  2S + 1 1 Bs (y) = coth y − coth y 2S 2S 2S 2S

(14)

Finally, the hole Hamiltonian of Mn-doped ZnO nanowires in the magnetic field can be

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expressed as Hh = HhB + Hhex

(15)

The hole can be assumed to confined in the infinitely high potential barrier, then the

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envelope wave function ψ(~rh ) of the hole states can be expanded as follows[26]   bLh −1,k,nh,↑ ALh −1,nh jLh −1 (knLhh −1 ρh )ei(Lh −1)θh   c Lh +1 i(Lh +1)θh  A j (k ρ )e L +1,k,n ,,↑ L +1,n L +1 h  h  nh h h h h     L iL θ h h h X dLh ,k,nh,↑ ALh ,nh jLh (knh ρh )e  ikzh ψh (ρh , θh , zh ) =  e Lh iLh θh   bLh ,k,nh,↓ ALh ,nh jLh (knh ρh )e nh      cL +2,k,n ,,↓ AL +2,n jL +2 (k Lh +2 ρh )ei(Lh +2)θh  n h h h h h  h  Lh +1 i(Lh +1)θh dLh+1,k,nh,↓ ALh +1,nh jLh +1 (knh ρh )e

(16)

be expressed as[26]

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As discussed like the hole, the Hamiltonian HeB of the electron in the magnetic filed can

HeB =

eB e2 B 2 2 p2e e + L + ρ + Eg + Hzeeman e 2m∗e 2m∗e 8m∗e e

(17)

e ~ is the Zeeman term of the electron. In addition to the Hamilwhere Hzeeman = 21 µB ge~se · B

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tonian HeB , s-d exchange interaction Hamiltonian between manganese ions and the electron

can be expressed as Heex = −αN0 xσze hSz i in the mean-field approximation and virtual crys-

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tal approximation[28], where α = hS|Jc (~re )|Si is the s-d exchange integral[29]. The total Hamiltonian of the electron can be expressed as He = HeB + Heex

(18)

the electron can also be assumed to be confined in the infinitely high potential barrier and the envelope wave function of the electron can be expressed as[26] ψe (~re ) = ALe ,ne jLe (knLee ρe )eiLe θe eikzh ALe ,ne is the normalization constant of Le order Bessel function jLe (knLee re ), knLee = is the ne th zero point of jLe (knLee re ). 5

(19) e αL ne , R

αnLee

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The optical absorption coefficient of Mn-doped ZnO nanowires can be calculated as follows[33] XZ ~e2 α(E) = |Mnc ,nv (k)|2 [fnc (k) + fnv (k) − 1]δ[Enc (k) − Env (k) − E]dk ε0 Ancm20 E n ,n BZ v

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c

(20)

where ε0 is the vacuum permittivity, n is the index of refraction, A is the cross-section area of the nanowires, c is the speed of the light, m0 is the free electron mass, E is the photon

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energy, Enc (k) and Env (k) are the conduction and valence subband state energies at the wave vector k, respectively. Mnc ,nv (k) is the optical transition matrix element of Mn-doped ZnO nanowires at the wave vector k[26, 27], fnc (k) and fnv (k) are the Fermi-Dirac distribution fnc (k) can be expressed as follows[33] fnc (k) =

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function of the electrons and the holes at the wave vector k, respectively. For example,

1

[Enc (k)−Efc ]/(kB T )

1+e

(21)

where Efc is the quasi-Fermi level of conduction band, and Efc can be obtained as the solution

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of the equation Ne =

XZ nc

BZ

1 fn [Enc (k)]dk 2πA c

(22)

Ne is the density of the electron. Using the similar method, the quasi-Fermi level of valence

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band Efv can also be obtained. In addition, if there are interaction with phonon, as a example, δ[Enc (k) − Env (k) − E] can be replaced by the Lorentzian of width Γ[33]

III.

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δ[Ec (k) − Ev (k) − E] =

Γ/2 π[(Ec (k) − Ev (k) − E)2 + Γ2 /4]

(23)

NUMERIAL RESULTS AND DISCUSSION

The parameters are adopted during the calculation: Eg =3.37 eV, Lp =5.6222, M=0.2813, N=0.4350, Rp =5.3432, S=0.4162, Tp =6.2242, Q=3.2202, ∆cr =39.42 meV, ∆so =-3.52 meV, λ=∆so /3, ge =2, gh =2, SM n =5/2, gM n =2, αN0 =-0.25 eV, βN0 =2.7 eV, T0 =1.4 K, m∗e =0.24 m0 [27], and m0 is the mass of the free electron. Figure 1 shows the valence band structure with |Jh |=1/2, x=0.01, R=3 nm, T =10 K and B=2 T, the solid line and dash line are for Jh =1/2 and Jh =-1/2, respectively. The hole 6

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states are double degenerate without the magnetic field because of the cylindrical symmetry of nanowires, and the degeneracy is broken when the magnetic field is applied. In figure 1(a), h h h h the degenerate ground holes are 1P1/2 u1h + 1P1/2 u2h with Jh =1/2 and 1P1/2 u4h + 1P1/2 u5h with

Jh =-1/2 without the magnetic field, respectively. Considering the spin-orbit coupling(SOC),

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the hole states are the mixed states which can be denoted as Ref. 22. S, P , D, ... for the states with the angular momentum projections on the nanowires are 0, 1, 2, ... without regard to the spin, uih (i=1, 2, ..., 6) are the above six Bloch basis. If the angular momentum is negative, the absolute value is used, and the subscript is the quantum number |Jh =

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Lh + 1/2|, in which Jh is the total angular momentum considering the spin of the hole. During the calculation, we find the hole states with Jh =1/2 will reverse when the magnetic

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h field is applied. For example, the ground hole state with Jh =1/2 will become to 1S1/2 u4h + h h 1D1/2 u5h + 2S1/2 u4h when B=2 T. We find the critical magnetic field is B=1.5 T, namely, the

first two hole states are reversed when B≥1.5 T in figure 1(a). It has been reported that the first two valence subbands of semiconductor nanowires can be reversed if the radius of nanowires varies[34], which is similar to our condition. But the hole states with Jh =-1/2 will not reverse whether B=0 T or 2 T. Figure 1(b) is the same as figure 1(a) but for |Jh |=3/2.

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h h h In the figure, the degenerate ground holes are 1S3/2 u1h + 1D3/2 u2h + 2S3/2 u1h with Jh =3/2 and h h h u5h with Jh =-3/2 without the magnetic field, respectively. The u5h + 2S3/2 u4h + 1S3/2 1D3/2

ground hole state is also reversed with Jh =3/2 when B=2 T, and the ground state is not reversed with Jh =-3/2 when the magnetic field is applied. Figure 1(c) and 1(d) are the

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same as figure 1(b) but each for |Jh |=5/2 and |Jh |=7/2. The valence subbands are also presented when T =100 K. In the figure, the hole states are the same as figure 1. Through

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the calculation, we find that the hole states are not reversed when the magnetic field is applied, which is not like the condition in figure 1. For example, the ground hole state h h u2h in figure 2(a) and the ground hole state with Jh =3/2 is with Jh =1/2 is 1P1/2 u1h + 1P1/2 h h h u1h in figure 2(b) regardless of B=0 T or B=2 T. u2h + 2S3/2 u1h + 1D3/2 1S3/2

As shown in figure 3(a), the several lowest interband magnetoabsorption spectra of Mndoped ZnO nanowires have been presented at the Γ point with x=0.005, B=2 T, T =10 K and the carrier density Ne =15×1024 m−3 . According to the transition rules in nanowires[26, 27], e the first peak represents the optical transition which is from the electron state 1S1/2 u2e to h h h the hole state 1D3/2 u4h + 1S3/2 u5h + 2S3/2 u5h with σ − at the energy E=3.4955 eV, where σ −

represents the left circularly polarized light. Through the calculation, the polarization of the 7

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lowest optical transition is σ − whether B=0 T or 2 T. Because the total angular momentum h h h Jh of the hole state 1D3/2 u4h +1S3/2 u5h +2S3/2 u5h is negative, and this hole state is not reversed

even though the magnetic field is applied. The second peak represents the optical transition e h h h which is from the electron state 1S1/2 u2e to the hole state 1S1/2 u4h + 1D1/2 u5h + 2S1/2 u4h with

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σ + at the energy E=3.4961 eV, where σ + represents the right circularly polarized light. In figure 3(b), the condition is the same as figure 3(a) but for T =100 K. There are four close peaks in figure 3(b), and the optical transitions corresponding to the first two peaks are the same as figure 3(a). The third peak represents the optical transition which is from

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e h h h u1h + 1S1/2 u2h + 2S1/2 u2h with σ − at the energy E=3.5013 eV, and the fourth 1S1/2 u1e to 1D1/2 e h h h peak represents the optical transition which is from 1S1/2 u1e to 1S3/2 u1h + 1D3/2 u2h + 2S3/2 u1h

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with σ + at the energy E=3.5022 eV. In figure 3(a), the quasi-Fermi level of the valence h h h band is Efv =-0.0232 eV, and the energies of hole states 1D3/2 u4h + 1S3/2 u5h + 2S3/2 u5h and h h h 1S1/2 u4h + 1D1/2 u5h + 2S1/2 u4h are -0.02393 eV and -0.02454 eV, respectively, so the occupy h h h u4h + 1S3/2 probability fnv (k) of the hole state 1D3/2 u5h + 2S3/2 u5h is larger than that of the h h h hole state 1S1/2 u4h + 1D1/2 u5h + 2S1/2 u4h . Meanwhile, the absorption coefficient of each peak

is proportion to the expression fnc (k) + fnv (k) − 1, so the absorption coefficient of the first

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peak is almost two times greater than that of the second peak in figure 3(a). Figure 3(b) is the same as figure 3(a) but for T =100 K. As seen in figure 3(b), two additional peaks arise, and the absorption coefficients of these four optical transitions are slightly different. Figure 4(a) shows the several lowest interband magnetoabsorption spectra of Mn-doped

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ZnO nanowires at the Γ point with x=0.01, B=2 T, T =10 K and Ne =15×1024 m−3 . Through the analysis, optical transitions in figure 4(a) are the same as that in figure 3(a). But in figure

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4(a), the absorption coefficient of the first peak is almost equal to that of the second peak. Because the quasi-Fermi level of the valence band is Efv =-0.0205 eV, and the energies of hole h h h h h h u4h are -0.01944 eV and -0.02 u5h +2S1/2 u4h +1D1/2 u5h and 1S1/2 u5h +2S3/2 u4h +1S3/2 states 1D3/2

eV, respectively, so the energies of these two hole states are all close to Efv . In addition, from the expression (20), the absorption coefficient is not only proportion to fnc (k) + fnv (k) − 1, but also proportion to the optical transition matrix |Mnc ,nv (k)|2 . |Mnc ,nv (k)|2 of these two

optical transitions are almost the same in figure 4(a). Figure 4(b) is the same as figure 4(a) but for T =100 K. Because |Mnc ,nv (k)|2 and fnc (k) + fnv (k) − 1 of these four optical transitions are slightly different, so does the absorption coefficients. As seen in figure 5(a), the several lowest interband magnetoabsorption spectra of Mn8

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doped ZnO nanowires at the Γ point with x=0.005, B=2 T, T =10 K and Ne =30×1024 m−3 has been shown. There are six optical transitions in the figure, and the first two optical transitions are the same as that in figure 3(a). The optical transition of the third h h h peak is from 1P3/2 u2e to 1P1/2 u4h + 1P1/2 u5h with σ + at the energy E=3.63967 eV, and there

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other optical transitions are presented in Table I. Through the calculation, it is found that the quasi-Fermi level of valence band is Efv =-0.0281 eV, and the energy of the hole state h h h 1D3/2 u4h + 1S3/2 u5h + 2S3/2 u5h is -0.02393 eV. Obviously, the energy difference between Efv and h h h u5h is much larger than thermal excitation energy kB T , which is u5h + 2S3/2 1D3/2 u4h + 1S3/2

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h h u5h + about 0.8618 meV when the temperature T =10 K. Thus, the hole state 1D3/2 u4h + 1S3/2 h h h h u4h , u5h + 2S1/2 u4h + 1D1/2 2S3/2 u5h is almost totally occupied. Similarly, the hole states 1S1/2

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e e e e 1P1/2 u4e + 1P1/2 u5e and 1P1/2 u1e + 1P1/2 u2e are almost totally occupied. So the absorption

coefficients of six peaks are proportion to |Mnc ,nv (k)|2 , and the absorption coefficients of the last four peaks are nearly three times greater than that of the first two peaks. When the temperature T rises to 100 K, two additional peaks arise in figure 5(b), and all optical transitions are shown in Table II. Compared with figure 5(a), two additional peaks are h h h e u2h and the u2h + 2S1/2 u1h + 1S1/2 u1e to 1D1/2 the third optical transition which is from 1S1/2

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e h h h fourth optical transition which is from 1S1/2 u1e to 1S3/2 u1h + 1D3/2 u2h + 2S3/2 u1h . Through

the calculation, the quasi-Fermi level of the valence band is Efv =-0.0261 eV, and the hole energies of the first four peaks are close to Efv , so the absorption coefficients of the first four peaks are mainly proportion to |Mnc ,nv (k)|2 . But the hole energies of the last four peaks

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are much greater than Efv , so the occupy probabilities fnv (k) of the hole states of the last four peaks are larger than that of the first four peaks. Figure 6(a) is the same as figure 5(a)

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but for x=0.01, and each optical transitoin is presented in Table III. Obviously, the optical transitions in figure 6(a) are the same as figure 5(a). Compared with figure 5(a). We find that the absorption coefficients of the last two peaks in figure 6(a) are smaller than that in e e u2e is close to Efv =-0.0265 u1e + 1P1/2 figure 5(a), because the energy of the hole state 1P1/2

eV. When the temperature rises to T =100 K, two additional peaks also arise in figure 6(b), and all optical transitions are shown in Table IV. Compared with Figure 5(b), the last two optical transitions exchange. Through the calculation, the quasi-Fermi level Efv =-0.0261 eV, and we find that the absorption coefficients of the last four optical transitions are much greater than that of the first four optical transitions, it is because that |Mnc ,nv (k)|2 of the last four optical transitions are almost three times greater than that of the first four optical 9

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transitions.

IV.

SUMMARY

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In summary, the electron states and hole states of Mn-doped ZnO nanowires in the magnetic field are calculated based on the six-band k·p effective-mass theory and 10 lowest valence subbands with different Jh are presented in the paper. It is found that the hole states with positive Jh will reverse, while they will not reverse with negative Jh when the

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magnetic field is applied. The several lowest interband magnetoabsorption spectra of Mndoped ZnO nanowires at the Γ point are also shown in the paper, and the absorption peaks will show red shifts when the magnetic field is applied and blue shifts with the increase of the

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temperature, respectively. Through the analysis, the number of the absorption peaks will increase with the increase of the carrier density and the temperature. It is found that the quasi-Fermi level of the conduction band is almost not changed by the doped concentration of manganese ions, but the quasi-Fermi level of the valence band increase with the increase

V.

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of the concentration of manganese ions.

ACKNOWLEDGMENTS

This research was supported by the National Natural Science Foundation of China(No.

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JXY).

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61404015) and the Fundamental Research Funds for the Central Universities (No. 2015CD-

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[1] X. Wang, Q. W. Li, Z. B. Liu, J. Zhang, Z. F. Liu, and R. M. Wang, Appl. Phys. Lett. 84, 4941 (2004).

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[2] S. W. Lee, M. C. Jeong, and J. M. Myoung, Appl. Phys. Lett. 90, 133115 (2007).

[3] M. Gao, W. L. Li, Q. Li, Q. Chen, and L. M. Peng, Appl. Phys. Lett. 92, 113112 (2008). [4] Y. Z. Wang, B. L. Wang, Q. F. Zhang, D. N. Shi, S. J. Yunoki, F. J. Kong, and N. Xu, J. Appl. Phys. 113, 034301 (2013).

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[5] W. P. Jr., S. Kumar, C. Borschel, P. Wu, C. M. Canali, C. Ronning, L. Samuelson, and H. Pettersson, Nano Lett. 12, 4838 (2012).

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[6] C. C. Chen, Y. J. Hsu, Y. F. Lin, and S. Y. Lu, J. Phys. Chem. C 112, 17964 (2008). [7] J. S. Ruiz, G. M. Criado, M. H. Chu, S. Geburt, and C. Ronning, Nano Lett. 11, 5322 (2011). [8] M. H. Chu, G. M. Criado, J. S. Ruiz, S. Geburt, and C. Ronning, Appl. Phys. Lett. 103, 141911 (2013).

[9] B. Panigrahy, M. Aslam, and D. Bahadur, J. Phys. Chem. C 114, 11758 (2010).

8832 (2008).

TE D

[10] Y. Guo, X. B. Gao, X. M. Lan, C. Zhao, X. D. Xue, and Y. Y. Song, J. Phys. Chem. C 112,

[11] C. Y. Lin, W. H. Wang, C. S. Lee, K. W. Sun, and Y. W. Suen, Appl. Phys. Lett. 94, 151909 (2009).

EP

[12] W. S. Yan, Q. H. Liu, C. Wang, X. Y. Yang, T. Yao, J. F. He, Z. H. Sun, Z. Y. Pan, F. C. Hu, Z. Y. Wu, Z. Xie, and S. Q. Wei, J. Am. Chem. Soc. 136, 1150 (2014). [13] C. R. Lecuna, R. M. Rodr´iguez, J. A. Gonz´ alez, F. Rodr´iguez, G. Almonacid, A. Segura, V.

AC C

M. Sanjos´ e, D. R. Gamelin, and R. Valiente, 26, 1100 (2014). [14] E. Badaeva, J. W. May, J. Ma, D. R. Gamelin, and X. S. Li, J. Phys. Chem. C 115, 20986 (2011).

[15] W. J. Liang, B. D. Yuhas, and P. Yang, Nano Lett. 9, 892 (2009). [16] L. T. Chang, C. Y. Wang, J. S. Tang, T. X. Nie, W. J. Jiang, C. P. Chu, S. Arafin, L. He, M. Afsal, L. J. Chen, and K. L. Wang, Nano Lett. 14, 1823 (2014). [17] R. Deng, H. Zhou, Y. F. Li, T. Wu, B. Yao, J. M. Qin, Y. C. Wan, D. Y. Jiang, Q. C. Liang, and L. Liu, J. Appl. Phys. 114, 033910 (2013). [18] T. L. Phan, and S. C. Yu, J. Phys. Chem. C 117, 6443 (2013).

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[19] S. Han, D. Zhang, and C. W. Zhou, Appl. Phys. Lett. 88, 133109 (2006). [20] Y. J. Kang, D. S. Kim, S. H. Lee, and J. Park, J. Phys. Chem. C 111, 14956 (2007). [21] X. M. Zhang, Y. Zhang, Z. L. Wang, W. J. Mai, Y. D. Gu, W. S. Chu, and Z. Y. Wu, Appl. Phys. Lett. 92, 162102 (2008).

RI PT

[22] A. Manaselyan, and T. Chakraborty, Nanotechnology 21, 355401 (2010).

[23] A. Ghazaryan, A. Manaselyan, and T. Chakraborty, Physica E 66, 157 (2015). [24] I. Vurgaftman, and J. R. Meyer, J. Appl. Phys. 94, 3675 (2003).

[26] W. Xiong, J. Appl. Phys. 111, 044305 (2012). [27] W. Xiong, J. Appl. Phys. 112, 044310 (2012).

M AN U

[28] J. K. Furdyna, J. Appl. Phys. 64, R29 (1988).

SC

[25] S. L. Chuang, and C. S. Chang, Phys. Rev. B 54, 2491 (1996).

[29] A. K. Bhattacharjee, and J. P´ erez-Conde, Phys. Rev. B 68, 045303 (2003). [30] P. I. Archer, S. A. Santangelo, and D. R. Gamelin, Nano Lett. 7, 1037 (2007). [31] T. Dietl, H. Ohno, and F. Matsukura, Phys. Rev. B 63, 195205 (2001). [32] Y. Shapira, S. Foner, P. Becla, and D. N. Domingues, M. J. Naughton, and J. S. Brooks, Phys. Rev. B 33, 356 (1986).

TE D

[33] M. Tadi´ c, and F. M. Peeters, Phys. Rev. B 71, 125342 (2005).

AC C

EP

[34] M. P. Persson, and A. D. Carlo, J. Appl. Phys. 104, 073718 (2008).

12

ACCEPTED MANUSCRIPT

TABLE I: The possible transitions at the Γ point with x=0.005, T =10 K and B=2 T. The Transition Polarized Electron states

Hole states

e 1S1/2 u2e

light

h h h 1D3/2 u4h + 1S3/2 u5h + 2S3/2 u5h

3.49553

σ−

e 1S1/2 u2e

h h h 1S1/2 u4h + 1D1/2 u5h + 2S1/2 u4h

3.49614

σ+

e 1P3/2 u2e

h h 1P1/2 u4h + 1P1/2 u5h

3.63967

σ+

e 1P1/2 u2e

h h 1P1/2 u4h + 1P1/2 u5h

3.64057

σ−

e 1P3/2 u1e

h h 1P1/2 u1h + 1P1/2 u2h

3.64985

σ−

e 1P1/2 u1e

h h 1P1/2 u1h + 1P1/2 u2h

SC

RI PT

energies (eV)

M AN U

3.65085

σ+

TABLE II: The possible transitions at the Γ point x=0.005, T =100 K and B=2 T. The Transition Polarized

Electron states

Hole states

e 1S1/2 u2e

light

h h h 1D3/2 u4h + 1S3/2 u5h + 2S3/2 u5h

3.49980

σ−

e 1S1/2 u2e

h h h 1S1/2 u4h + 1D1/2 u5h + 2S1/2 u4h

3.50040

σ+

e 1S1/2 u1e

h h h 1D1/2 u1h + 1S1/2 u2h + 2S1/2 u2h

3.50130

σ−

h h h 1S3/2 u1h + 1D3/2 u2h + 2S3/2 u1h

3.50219

σ+

h h 1P1/2 u4h + 1P1/2 u5h

3.64394

σ+

h h 1P1/2 u4h + 1P1/2 u5h

3.64494

σ−

e 1S1/2 u1e e 1P3/2 u2e

EP

e 1P1/2 u2e

TE D

energies (eV)

h h 1P1/2 u1h + 1P1/2 u2h

3.64559

σ−

e 1P1/2 u1e

h h 1P1/2 u1h + 1P1/2 u2h

3.64649

σ+

AC C

e 1P3/2 u1e

13

ACCEPTED MANUSCRIPT

TABLE III: The possible transitions at the Γ point with x=0.01, T =10 K and B=2 T. The Transition Polarized Electron states

Hole states

e 1S1/2 u2e

light

h h h 1D3/2 u4h + 1S3/2 u5h + 2S3/2 u5h

3.49054

σ−

e 1S1/2 u2e

h h h 1S1/2 u4h + 1D1/2 u5h + 2S1/2 u4h

3.49115

σ+

e 1P3/2 u2e

h h 1P1/2 u4h + 1P1/2 u5h

3.63482

σ+

e 1P1/2 u2e

h h 1P1/2 u4h + 1P1/2 u5h

3.63571

σ−

e 1P3/2 u1e

h h 1P1/2 u1h + 1P1/2 u2h

3.65484

σ−

e 1P1/2 u1e

h h 1P1/2 u1h + 1P1/2 u2h

SC

RI PT

energies (eV)

3.65574

σ+

M AN U

TABLE IV: The possible transitions at the Γ point with x=0.01, T =100 K and B=2 T. The Transition Polarized

Electron states

Hole states

e 1S1/2 u2e

light

h h h 1D3/2 u4h + 1S3/2 u5h + 2S3/2 u5h

3.49928

σ−

e 1S1/2 u2e

h h h 1S1/2 u4h + 1D1/2 u5h + 2S1/2 u4h

3.49988

σ+

e 1S1/2 u1e

h h h 1D1/2 u1h + 1S1/2 u2h + 2S1/2 u2h

3.50182

σ−

h h h 1S3/2 u1h + 1D3/2 u2h + 2S3/2 u1h

3.50271

σ+

h h 1P1/2 u4h + 1P1/2 u5h

3.64342

σ+

h h 1P1/2 u4h + 1P1/2 u5h

3.64442

σ−

h h 1P1/2 u1h + 1P1/2 u2h

3.64711

σ+

h h 1P1/2 u1h + 1P1/2 u2h

3.65404

σ−

e 1S1/2 u1e e 1P3/2 u2e e 1P1/2 u2e

EP

e 1P1/2 u1e

TE D

energies (eV)

AC C

e 1P3/2 u1e

14

ACCEPTED MANUSCRIPT

0.00

0.00

(a)

(b)

RI PT

-0.05

-0.05

-0.10 -0.10 -0.15 -0.15

E (eV)

-0.20

-0.20

-0.30

-0.25

-0.35

Hole states Solid line: J

-0.35

dash line:

h

J

=1/2

h

-0.40

0.05

Solid line: J dash line:

=-1/2

h

J

-0.45

x=0.01, T=10 K, B=2 T -0.40 0.00

Hole states

0.10

=3/2

h

M AN U

-0.30

SC

h

-0.25

0.15

=-3/2

x=0.01, T=10 K, B=2 T

-0.50 0.20 0.00

0.05

0.10

0.15

0.20

0.00

0.00

(c)

(d)

-0.05

-0.05

-0.10

-0.10

-0.15

TE D

h

E (eV)

-0.15

-0.20

-0.25

-0.30

-0.35

Hole states

Solid line: J dash line:

-0.45

h

J

AC C 0.05

-0.30

-0.35

-0.40

=5/2

h

0.10

Å

k(

Hole states Solid line: J

-0.50

=-5/2

dash line: -0.55

x=0.01, T=10 K, B=2 T -0.50 0.00

-0.25

-0.45

EP

-0.40

-0.20

0.15

-0.60 0.00 0.20

-1

h

J

=7/2

h

=-7/2

x=0.01, T=10 K, B=2 T 0.05

0.10

Å

k(

)

-1

0.15

0.20

)

FIG. 1: (a)The valence band structure of Mn-doped ZnO nanowires with |Jh |=1/2, x=0.01, T =10 K and B=2 T. The solid line is for Jh =1/2, and the dash line is for Jh =-1/2. (b) is the same as (a) but for |Jh |=3/2. (c) and (d) are the same as (b) but each for |Jh |=5/2 and |Jh |=7/2.

15

ACCEPTED MANUSCRIPT

0.00

0.00

(a)

(b)

RI PT

-0.05

-0.05

-0.10

-0.10

-0.15

E (eV)

-0.15 -0.20

h

-0.20 -0.25

-0.25

SC

-0.30 -0.30 -0.35

Hole states Solid line: J dash line:

h

J

-0.40

=1/2

h

-0.40

=-1/2

Hole states

Solid line: J dash line:

h

J

-0.45

x=0.01, T=100 K, B=2 T -0.45 0.00

0.05

0.10

0.15

=3/2

h

M AN U

-0.35

=-3/2

x=0.01, T=100 K, B=2 T

-0.50 0.20 0.00

0.05

0.10

0.15

0.20

0.00

0.00

(c)

(d)

-0.05

-0.05

-0.10

-0.10

-0.15

TE D

-0.15

E (eV)

-0.20

h

-0.25

-0.30

-0.35

-0.40

EP

Hole states

Solid line: J dash line:

-0.45

h

J

AC C 0.05

-0.30

-0.35

-0.40

dash line:

=-5/2

0.10

Å

k(

-1

Hole states

-0.45

-0.50

x=0.01, T=100 K, B=2 T -0.50 0.00

-0.25

Solid line: J

=5/2

h

-0.20

0.15

h

J

=7/2

h

=-7/2

x=0.01, T=100 K, B=2 T

-0.55 0.00 0.20

0.05

0.10

Å

k(

)

-1

0.15

0.20

)

FIG. 2: (a)The valence band structure of Mn-doped ZnO nanowires with |Jh |=1/2, x=0.01, T =100 K and B=2 T. The solid line is for Jh =1/2, and the dash line is for Jh =-1/2. (b) is the same as (a) but for |Jh |=3/2. (c) and (d) are the same as (b) but each for |Jh |=5/2 and |Jh |=7/2.

16

ACCEPTED MANUSCRIPT

σ− 0.1

0.05

0.05

0 3.49

3.495

3.5

(a)

0 0.1 0.1

0.05

0.05

0 3.495

0 3.45

SC

+

σ−σ − σ σ+

3.5

3.5

3.505

M AN U

Absorption(arb. units)

σ+

RI PT

0.1

3.55

3.6

(b)

3.65

3.7

E (eV)

FIG. 3: (a)The several lowest interband magnetoabsorption spectra of Mn-doped ZnO nanowires

AC C

EP

for T =100 K.

TE D

at the Γ point when x=0.005, B=2 T, T =10 K, and Ne =15×1024 m−3 ; (b) is the same as (a) but

17

ACCEPTED MANUSCRIPT

0.4 0.4

σ− + 0.2

3.49

3.495

RI PT

0 3.485

(a)

0

0.1 0.1

SC

+

σ−σ σ− σ+

0.05

0.05 0 3.495

0 3.45

3.5

3.5

3.505

M AN U

Absorption(arb. units)

σ

0.2

3.55

3.6

(b)

3.65

3.7

E (eV)

FIG. 4: (a)The several lowest interband magnetoabsorption spectra of Mn-doped ZnO nanowires

AC C

EP

for T =100 K.

TE D

at the Γ point when x=0.01, B=2 T, T =10 K, and Ne =15×1024 m−3 ; (b) is the same as (a) but

18

ACCEPTED MANUSCRIPT

1

− σ+σ− σ σ+ 1

0.5

σ−σ+

0.2 0 3.63 0 3.49

3.495

3.64

3.65

3.66

3.5

(a)

0 0.4 0.2

0 3.495

0 3.45

0.2

σσ−+ − σ + 0.1 σ

3.5

0 3.642 3.5

3.644

SC

σ+σ−− σ+ σ

0.4

0.2

RI PT

0.5

3.646

3.648

M AN U

Absorption(arb. units)

0.4

3.505

3.55

3.6

(b)

3.65

3.7

E (eV)

FIG. 5: (a)The several lowest interband magnetoabsorption spectra of Mn-doped ZnO nanowires

AC C

EP

for T =100 K.

TE D

at the Γ point when x=0.005, B=2 T, T =10 K, and Ne =30×1024 m−3 ; (b) is the same as (a) but

19

ACCEPTED MANUSCRIPT

1

σ+σ−

1

+

σ− σ

0.4

0.2

+

σ−σ

0 3.63 0 3.485

3.49

3.64

3.65

3.66

3.495

(a)

0

0.4

+

σ−

0.2 0.2

+ − 0.1

σ−σσ + σ

0 3.45

+

0 3.642 0 3.495

3.5

SC

σ σ−

0.4

0.2

RI PT

0.5

3.5

σ

3.644

3.646

3.648

M AN U

Absorption(arb. units)

0.5

3.505

3.55

3.6

(b)

3.65

3.7

E (eV)

FIG. 6: (a)The several lowest interband magnetoabsorption spectra of Mn-doped ZnO nanowires

AC C

EP

for T =100 K.

TE D

at the Γ point when x=0.01, B=2 T, T =10 K, and Ne =30×1024 m−3 ; (b) is the same as (a) but

20