J Low Temp Phys (2014) 174:311–321DOI 10.1007/s10909-013-1007-2

Photon-Assisted Heat Generation in a Quantum DotDevice with the Charging Effect

Qiao Chen · Li-Li Zhao · Zhi-YongWang ·Zhong-Xiang Xie

Received: 12 November 2013 / Accepted: 5 December 2013 / Published online: 18 December 2013© Springer Science+Business Media New York 2013

Abstract Electrical current induced heat generation through an ultrasmall quantumdot–leads coupled system under AC fields is investigated by employing the nonequilib-rium Green’s function technique. The external AC fields, charging energy and junctioncapacitances influence the heat generation sensitively. We find negative differentialheat generation in our system. The reason for this is the Coulomb interaction, and thenegative differential heat generation becomes larger as the frequency of AC fields ω

increases. In addition, the peak caused by charging energy in Q/ω0 curve increaseswith ω rapidly. A region in which the value Q/I is low emerges due to the charg-ing effect. It is an ideal region for device operation. This region will enlarge as theparameter R and the charging energy Ec increase.

Q. Chen (B)Department of Maths and Physics, Hunan Institute of Engineering, Xiangtan 411104, Chinae-mail: cqhy1127@aliyun.com

Q. ChenDepartment of Applied Physics, Hunan University and Key Lab for Micro-Nano Physicsand Technology of Hunan Province, Changsha 410082, China

L.-L. ZhaoDepartment of Fundamental Courses, Academy of Armored Force Engineering,Beijing 100072, China

Z.-Y. Wang (B)School of Optoelectronic Information, Chongqing University of Technology,Chongqing 400054, Chinae-mail: wzyong@cqut.edu.cn

Z.-X. XieDepartment of Mathematics and Physics, Hunan Institute of Technology,Hengyang 421002, China

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312 J Low Temp Phys (2014) 174:311–321

Keywords Heat generation · AC field · Photon-assisted tunneling · NonequilibriumGreen’s function

1 Introduction

In the past two decades, an increasing amount of attention has been paid inactive theoretical and experimental studies to the transport properties of quan-tum dot (QD) devices. Recently, there is additionally a great interest in thecharge transport accompanied by heat generation [1–14]. In the fundamentalpoint view, inelastic electron collision is the main cause of heat generation, andthe origin of heat generation is basically the same as that in ordinary macro-scopic metals. However, the heat generation in nanodevices emerges from a dif-ferent behavior due to quantum effect such as level quantization and Coulombblockade effect. An electron enters a nanodevice and leaves with diminishedenergy with lost energy transferred to the phonon system via the electron–phonon interaction (EPI). Experimentally, Huang et al. [1,2] observed the current-induced local heating in single molecules by measuring the force required tobreak the molecular-electrode bonds, and they found the local heating weakenswith increasing device dimension. Oron-Carl and Krupke [3] successfully deter-mined the hot phonon generation from a current bias by using the ratio of anti-Stokes to Stokes lines. Theoretically, Lazzeri et al. [6] studied the heat genera-tion in nanotube via the first-principle calculations. Sun and Xie [7] gave a gen-eral formula for heat generation in lead–quantum dot–lead system by nonequi-librium Green’s functions (NGF) method, and some interesting phenomena werefound. All these results demonstrate that the heat generation in nanodevices isimportant.

The heat generation induced by electrical current in Coulomb blockade regime havebeen discussed in previous studies [8,9]. Due to the Coulomb interaction there are twonovel properties of heat generation emerge (i)the heat generation could be very largein the Coulomb blockade regime in which the current is very small; (ii) a negativedifferential heat generation arises. Perturbations induced by microwave fields can giverise to very interesting features, such as photon-assisted tunneling(PAT) [15,16] andphoton-electron pumping effect [17,18]. Photon-electron quantum pumps have beeninvestigated intensively in recent years by applying alternating voltages to produce anonzero direct current. Microwave fields can realize the control of the nano-electronicdevices. Therefore, the study of heat generation in nanodevices under the influence ofmicrowave field is necessary and meaningful.

In this letter, we investigate the photon-assisted heat generation of an ultra-small QDsystem in the Coulomb blockade regime, where the effect of an oscillating potentialand the charging energy dominate the transport process. We will reveal the behaviourof compounding Coulomb blockade effects, as well as PAT heat generation originatingfrom the charging and external AC fields. We derive the formula of heat generationusing the NGF technique, and thus the photon-assisted heat generation under theinfluence of the Coulomb blockade effect is obtained. All the charging effects arecontained in the Green’s function of center QD. This paper is organized as follows.

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J Low Temp Phys (2014) 174:311–321 313

Our model and theoretical procedure are presented in Sect. 2, where the formula of theheat generation is obtained by using the NGFs. Numerical results for the the ultra smallQD system are given in Sect. 3. The final section is devoted to the brief concludingremarks of our achievement in this letter.

2 Model and Formalism

The system is composed of three parts: the ultra-small QD [19,20] being coupledto two normal metal leads by tunneling junctions with capacitances CL and CR . Weshow graphically the structure of our system in Fig. 1. A DC voltage V applied tothe two leads. The difference of chemical potentials μL and μR is related to thevoltage by eV = μL − μR . External MWFs with the same frequency are applied tothe two leads and the gate. The energy spectra of the two leads are modified by theexternal fields to form the ac potential εγ,kσ = ε

(0)γ,kσ + �γ cos ωt, where ε

(0)γ,kσ are

the isolated energy of the leads. The gate potential is described by the time-dependentone as eVg(t) = μg + �g cos ωt , where μg is the chemical potential of gate in theabsence of external field. The ultra-small QD with EPI is described by the Coulombblockade mode originated from the charging-discharging effect. λq is the couplingstrength of EPI, so the heat is generated when the current flows through the device.The Hamiltonian of our system is given by

H(t) =∑

γ kσ

εγ,kσ (t)c†γ,kσ cγ,kσ + E0

c

∑

�σ

n�σ [n�σ + 2n0(t)]

+∑

�σ

[E�σ + λq(a†q + aq)]n�σ +

∑

γ k�σ

[Rγ c†γ,kσ d�σ + H.c] + ωqa†

qaq ,

(1)

Here, the operators c†kγ,σ (ckγ,σ ) and d†

σ (dσ ) are the creation(annihilation) opera-

tors of electron in the two leads and center QD, respectively. Analogously, a†q(aq)

is the phonon creation (annihilation) operator and ωq is the vibrational frequencyof the phonon. Rγ is the coupling strength between the two leads and the center

Fig. 1 Schematic diagram of a QD coupled to two leads with tunneling strength α and the electron in theQD is also coupled to a single-phonon mode. The AC fields are applied to the QD and the leads

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314 J Low Temp Phys (2014) 174:311–321

QD. E0c = e2/2C is the charging energy with C = ∑

i=L ,R,g Ci , and en0(t) =CL VL(t)+ CR VR(t)+ CgVg(t) is related to the polarization charges produced by thetime-dependent voltages of the left and right terminals, eVγ (t) = μγ +�γ cos ωt , andthe time-dependent gate voltage eVg(t). In order to handle the problem conveniently,we make the gauge transformation �(t) = U (t)�(t) over the Schrödinger equation,where the unitary operator is defined by

U (t) = exp{

− i

hω

[ ∑

γ kσ

�γ c†γ,kσ cγ,kσ +

∑

�σ

�d†�σ d�σ

]sin ωt

}.

In the unitary operator, we have defined the relation � = ∑i=L ,R,g Ci�i/C for

writing the formula more concisely. The Hamiltonian of the system is transformed tothe new form after the gauge transformation

H ′ =∑

γ kσ

ε(0)γ,kσ c†

γ,kσ cγ,kσ + E0c

∑

�σ

n�σ

⎡

⎣n�σ + 2

e2

∑

i=L ,R,g

Ciμi

⎤

⎦

+∑

�σ

[E�σ + λq(a†q + aq)]n�σ +

∑

γ k�σ

[Rγ (t)c†γ,kσ d�σ + H.c] + ωqa†

qaq .

(2)

Through the transformation, the time-dependent energies in the subsystems becometime-independent ones, while the interaction strength Rγ is transformed to the time-dependent one

Rγ (t) = Rγ exp(i�γ sin ωt),

where �γ = (�γ − �)/ω. The physics of the system is unchanged under the gaugetransformation. Take the same procedure as in our pervious study [21], the formula ofheat generation of our system can be obtained

Q = Re∑

ll ′,σσ ′ωqλ2

q

∑

mnp

∑

γ γ ′

∫dε

2π{Jm(�γ )Jn(�γ )Jp(�γ ′)Jq(�γ ′)γ γ ′

× Gr�σ,�′σ ′(ε)Ga

�σ,�′σ ′(εnm)Gr�σ,�′σ ′(εnm − ω0)G

a�σ,�′σ ′(ε − ω0) fγ (ε − nω)

×[1 − fγ ′(ε − ω0 − qω)] − 2Nph J 2n (�)γ × [Gr

�σ,�′σ ′(ω)|Gr�σ,�′σ ′(ε − ω0)|2

× fγ (ε − ω0 − nω) + |Gr�σ,�′σ ′(ω)|2Ga

�σ,�′σ ′(ε − ω0) fγ (ω − nω)]}, (3)

where εnm = ε − nω + mω and q = n − m + p. In order to solve for the Green’sfunctions, we first make a canonical transformation with the unitary operator U =exp{(λq/ωq)(a†

q−aq)nlσ }. After this transformation, the Hamiltonian (Eq. 2) becomes

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J Low Temp Phys (2014) 174:311–321 315

H =∑

γ kσ

ε(0)γ,kσ c†

γ,kσ cγ,kσ + Ec

∑

�σ

n�σ

⎡

⎣n�σ + 2

e2

∑

i=L ,R,g

Ciμi

⎤

⎦

+∑

�σ

E�σ n�σ +∑

γ k�σ

[Rγ (t)c†γ,kσ d�σ X + H.c] + ωqa†

qaq , (4)

where Ec = E0c − 2λ2

q/ωq , E�σ = E�σ −λ2q/ωq and X = exp{−(λq/ωq)(a†

q − aq)}.Because the e-p interaction has been decoupled in this canonical transform, the single-electron Green’s functions can be obtained by the equation of motion (EOM) techniqueas follows [22]

Gr(a)

�σ,�′σ ′(ε) = (ε − ξ�σ − 2Ec(1 − 〈n�σ 〉))δ��′δσσ ′

(ε − ξ�σ )(ε − ξ�σ − 2Ec) ± i2 (ε − ξ�σ − 2Ec(1 − 〈n�σ 〉)) , (5)

where ξ�σ = E�σ + ∑i=L ,R,g Ciμi/C . The linewidth function = L + R ,and

γ = 2π |Rγ |2〈X〉2 ∑k δ(ε − ε

(0)γ,kσ ). We make an approximation to replace the

operator X by its mean value 〈X〉 = exp{−(λq/ωq)2(Nq + 1/2)} [26], whereNq = 1/[exp(ωq/kB T ) − 1] refers to the phonon number. Finally, the occu-pation number 〈nlσ 〉 must be determined selfconsistently by solving the inte-ger equation 〈nlσ 〉 = i

∫(dε/2π)G<

lσ,lσ (ε). The Fourier transformed KeldyshGreen’s functions are described by the pseudo-equilibrium formula G<

�σ,�′σ ′(ε, ε′) =∑γ σ1

Gr�σ,�′σ1

(ε)�<γσ1

(ε, ε′)Galσ1,�′σ ′(ε′). The selfenergy is given by �<

γσ (ε, ε′) =−i

∑mn γ fγ (ε − mω)δ(ε − ε′ + nω − mω).

Equation (3) is one of the main results of this paper. The formula describing theheat generation contains the information concerning the AC field and the Coulombblockade effect. As the magnitude of AC filed approaches zero, our formula revertsto the one obtained by Sun et al. [7,8]. The time-averaged current of the γ th leadis determined by the Landauer–Büttiker-like formula derived by the NGF approach[23–25]

Iγ = 2e

h

∑

lσ

∑

kmnβ

∫dεLk J 2

m(�)J 2n (�)γ β |Gr

lσ,lσ (ε − kω0)|2

×[ fγ (ε − nω) − fβ(ε − mω)], (6)

where Lk = e−g(2Nph+1) Ik(2g√

Nph(Nph + 1))enω0β/2, Ik is the kth Bessel functionof the complex argument.

3 Numerical Results and Discussion

Now we discuss the numerical results of the heat generation in the Coulomb blockaderegime perturbed by AC fields at limited temperature. We take μR as the reference ofenergy measurement by setting μR = 0. In the numerical calculation, we only considerone-single level QD E0σ = 0, which presents main behaviors of quantum transport.

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316 J Low Temp Phys (2014) 174:311–321

0

0.1

0.2

0.3

0.4T

ran

smis

sio

n

0

0.1

0.2

0.3

Tra

nsm

issi

on

0 2 4 6 8 10 12 14 160

0.1

0.2

0.3

ε/Δ

Tra

nsm

issi

on

ω=0ω=1.0ω=1.5

Ec=0

Ec=3.0

Ec=4.0

Ec=5.0

Γ=0.1

Γ=0.3

Γ=0.5

(a)

(b)

(c)

Fig. 2 Transmission coefficient T versus the energy. We set the parameters as: ω0 = 1.0, � = 1.2 fora Ec = 4.0, = 0.1; for b ω = 1.0, = 0.1; for c ω = 1.0, Ec = 4.0

The symmetric system is studied by setting = 2L = 2R and � = �L = �R . Wedefine the parameter R = CL/C = CR/C for convenience. The quantity � = 1meVis taken as the energy scale for the numerical calculations. The heat generation andthe current are scaled by λ2

q and 2e/h, respectively.In order to investigate the heat generation of the system, we give the transmission

coefficient T with different parameters first (Fig. 2). In addition to the energy levelsof QD, the Coulomb blockade effect, PAT and phonon-assisted tunneling can providechannels for electron transport. Herein, the transmission spectrum displays an abun-dant resonance structure. The resonant peaks caused by Coulomb blockade effect arelocated at E0σ + eVg + 2Ec. The peaks caused by PAT are located at E0σ + eVg ± nω

and E0σ +eVg +2Ec ±nω(n = 0, 1, 2, . . .) and the heights of these peaks are propor-tional to the J 2

n (�). The locations of peaks caused by phonon-assisted tunneling areE0σ +eVg +kω0. The function Lk is approximately equal to zero as k < 0 at very lowtemperature. Therefore, the k is positive integers and zero, i.e., k = 0, 1, 2 . . .. Thelinewidth function has a significant effect on the transport properties. The resonantpeaks become wide and blunt as the linewidth function increases. This effect canlead the steps in current and heat generation becomes smaller [27–35].

As the AC fields are applied to the system, the PAT will occur. The frequency of ACfield plays a very important role in PAT. Figure 3 gives the curves of heat generationQ and the corresponding current I versus the bias V with different frequency ω.

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J Low Temp Phys (2014) 174:311–321 317

0

0.1

0.2

0.3

0.4

0.5

Q/λ

q2

0 2 4 6 8 10 12 14 16 180

0.2

0.4

eV/Δ

I/I0

ω =0ω =1.0ω =1.5

(a)

(b)

Fig. 3 The heat generation Q of a single-level QD system versus the source-drain bias eV . We set theparameters as: the coupling strength λq = 1.0, the temperature T = 0.001, the gate voltage eVg = 3.0,the linewidth function = 0.1, the charging energy Ec = 4.0, � = 1.2 and R = 0

In the absence of AC field, the heat generation displays a small dip at the locationeV = 2Ec +eV g. This negative differential heat generation is caused by the Coulombinteraction [8,9]. The linewidth function is small, so there are some steps in thecurves of heat generation and current. These steps will disappear gradually as the

increases [27–35]. As the AC fields turn on,novel steps caused by PAT emerge bothin heat generation and current. The dip at the location eV = E0σ + 2Ec + eV gis broaden by AC field. The reason is the combining effect of EPI, photon assistedtunneling and Coulomb interaction. As the frequency of AC fields increases, negativedifferential heat generation also emerges in the low bias region. Liu et al. [8]. pointedout that the change of heat generation lags the change of the current, and the delayis offset by ωq . In the presence of AC fields, this delay is offset by absorption of aphoton.

In order to investigate the influence of Coulomb interaction on heat generation, wedisplay the heat generation, the corresponding current and the ratio of heat generationand current. We present the situations where Ec = 0 and the situations where Ec �= 0for comparison. For the system in the absence of Coulomb interaction, one observesthat the heat generation Q is larger than in the system with Coulomb interaction. In thepresence of Coulomb interaction, the charging energy acts as a threshold to resist theelectron tunneling. Herein, a huge platform emerges in both the heat generation and thecurrent in the region eVg < eV < eVg +2Ec. As eV > eVg +2Ec, the heat generationand the current display a rapid jump, then reach the saturate value. The saturate value ofheat generation in the absence of Coulomb interaction is larger than the condition with

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318 J Low Temp Phys (2014) 174:311–321

0

0.2

0.4

0.6

0.8

Q/λ

2

0

0.2

0.4

I/I0

0 5 10 15 200

0.5

1

eV/Δ

Rat

io(Q

/I)

Ec=0

Ec=3.0

Ec=4.0

Ec=5.0

(a)

(b)

(c)

Fig. 4 The heat generation Q of a single-level QD system versus the source-drain bias eV . We set theparameters as: the coupling strength λq = 1.0, the temperature T = 0.001, the gate voltage eVg = 3.0,the linewidth function = 0.1, the frequency of AC fields ω = 1.0, � = 1.2 and R = 0.1.

Coulomb interaction. However, the saturate value of the current is the same for bothconditions. From Fig. 4c, one observes that the ratio of heat generation and current,i.e. Q/I , displays a low platform, and the length of this platform increases with thecharging energy Ec. The reason is that the Coulomb interaction suppresses the heatgeneration in transport (Fig. 4).

The capacitances of junctions play important roles in the electron tunneling process.Figure 5 shows the variation of heat generation, current and the ratio versus the source-drain bias V with different capacitances. The heat generation and the current aresensitive to the capacitances of junctions. The two obvious phenomenon caused bycapacitances are as following: (1) the valley caused by Coulomb interaction movesto the right as the parameter R increases; and (2) the width of the valley increaseswith the parameter R. Therefore, the length of platform increases as the parameter Rincreases. It is an ideal region for device operation.

In order to further study the influence of AC fields on heat generation, we show theheat generation versus the frequency of phonon with different AC fields. When the ω0

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J Low Temp Phys (2014) 174:311–321 319

0

0.2

0.4

Q/λ

2

0

0.2

0.4

I/I0

0 5 10 15 200

0.5

1

eV/Δ

Rat

io(Q

/I)

R=0R=0.1R=0.2R=0.3

(a)

(c)

(b)

Fig. 5 The heat generation Q of a single-level QD system versus the source-drain bias eV . We set theparameters as: the coupling strength λq = 1.0, the temperature T = 0.001, the gate voltage eVg = 3.0,the linewidth function = 0.1, the frequency of AC fields ω = 1.0, � = 1.2 and the charging energyEc = 4.0

approaches to zero, so does the heat generation. As the ω0 increases from zero, theheat generation exhibits two peaks. One of the peak is close to zero, another locates atω0 = 2Ec. In the absence of AC fields, the first peak is higher than the second peak.It is the same with the result in reference [8]. Diagram (a) and (b) exhibit the curve ofQ − ω0 with different frequency ω and magnitude � of AC fields, respectively. Theheat generation Q increases as the frequency ω increases. It is worth noting that thepeak which is caused by charging energy increases rapidly. This peak is higher thanthe first peak as ω increases. The heat generation Q also displays the same behavior asthe magnitude of AC field � increases. It suggests that the heat generation in Coulombregion is affected by AC fields significantly (Fig. 6).

4 Summary

We have presented the calculation of heat generation and the corresponding currentfor a QD system in Coulomb blockade regime when irradiated with AC fields. We

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320 J Low Temp Phys (2014) 174:311–321

0

0.2

0.4

0.6

0.8

Q/λ

2

0 2 4 6 8 10 12 140

0.2

0.4

0.6

ω0/Δ

Q/λ

2

no ac field

Λ=0.5

Λ=1.0

Λ=1.5

no ac field

ω=1.0

ω=2.0

ω=3.0

(a)

(b)

Fig. 6 The heat generation Q of a single-level QD system versus the frequency of phonon. We set theparameters as: the coupling strength λq = 1.0, the temperature T = 1.0, the gate voltage eVg = 3.0, thelinewidth function = 0.1, the charging energy Ec = 3.0, R = 0.3, and for a � = 1.0, for b ω = 1.0

have derived a formula for the heat generation by employing the NGF technique,and this formula contains all possible effects concerning the Coulomb blockadeand the applied AC fields. In the absence of AC fields, our results are in agreementwith the theoretical results of Liu et al. [8]. The AC fields and the charging effect affectthe heat generation significantly. Negative differential heat generation emerges due tothe Coulomb interaction, and the negative differential heat generation becomes largeras the AC fields are turned on. The peak caused by charging energy increases rapidlywith the magnitude and frequency of AC fields, while the peak near ω0 = 0 only hassmall changes. It suggests that the AC field affect the heat generation significantly inthe Coulomb blockade regime. The threshold of heat generation also decreases dueto the absorption of photons. In the presence of charging effect, a region in which thevalue Q/I is low emerges. It is an ideal region for device operation. This region willenlarge as the parameter R and the charging energy Ec increase.

Acknowledgments This work was supported by the National Natural Science Foundation of China (No.11204074) and by Hunan Provincial Natural Science Foundation of China (No. 11JJ4005).

References

1. Z. Huang et al., Nano Lett. 6, 1240 (2006)2. Z. Huang et al., Nanotechnology 2, 698 (2007)3. M. Oron-Cark, R. Krupke, Phys. Rev. Lett. 100, 27401 (2008)4. Y.C. Chen, M. Zwolak, M.D. Ventra, Nano Lett. 4, 621 (2005)

123

J Low Temp Phys (2014) 174:311–321 321

5. Y.C. Chen, M. Zwolak, M.D. Ventra, Nano Lett. 3, 1691 (2003)6. M. Lazzeri et al., Phys. Rev. Lett. 95, 236802 (2005)7. Q.F. Sun, X.C. Xie, Phys. Rev. B 75, 155306 (2007)8. J. Liu, J.T. Song, Q.F. Sun, X.C. Xie, Phys. Rev. B 79, 161309 (2009)9. L.L. Zhou, Y. Li, Phys. Lett. A 376, 2506 (2012)

10. F. Chi, J. Zheng, Y.S. Liu, Y. Guo, Appl. Phys. Lett. 100, 233106 (2012)11. Q. Wang, H. Xie, H. Jiao, Y.H. Nie, EPL 101, 47008 (2013)12. Q. Chen, Y.M. Zhang, Commun. Theor. Phys. 54, 171 (2010)13. Q. Chen, Y.H. Deng, Commun. Theor. Phys. 56, 517 (2011)14. Q. Chen, M.C. Xu, Z.Y. Wang, Phys. E 48, 106 (2013)15. P.K. Tien, J.P. Gordon, Phys. Rev. 129, 647 (1963)16. L.P. Kouwenhoven et al., Phys. Rev. B 50, 2019 (1994)17. R.H. Blick et al., Appl. Phys. Lett. 67, 3924 (1995)18. P.S.S. Guimarães et al., Phys. Rev. Lett. 70, 3792 (1993)19. C. Bruder, H. Schoeller, Phys. Rev. Lett. 72, 1076 (1994)20. A. Yacoby, M. Heiblum, D. Mahalu, H. Shtrikman, Phys. Rev. Lett. 74, 4047 (1995)21. Q. Chen, L.M. Tang, K.Q. Chen, H.K. Zhao, J. Appl. Phys. 114, 084301 (2013)22. Q. Chen, H.K. Zhao, Eur. Phys. J. B 64, 237 (2008)23. R. Lü, Z.R. Liu, J. Phys. Condens. Matter 17, 5859 (2005)24. H.K. Zhao, Z. Phys. B 102, 415 (1997)25. H.K. Zhao, Phys. Lett. A 226, 105 (1997)26. G.D. Mahan, Many-Partical Physics, 3rd edn. (Plenum Press, New York, 2000)27. S.K. Maiti, Solid State Commun. 149, 973 (2009)28. S.K. Maiti, Solid State Commun. 149, 1623 (2009)29. S.K. Maiti, Solid State Commun. 149, 1684 (2009)30. S.K. Maiti, Solid State Commun. 149, 2146 (2009)31. S.K. Maiti, Phys. Lett. A 366, 114 (2007)32. S.K. Maiti, Phys. Lett. A 373, 4470 (2009)33. S.K. Maiti, Phys. E 36, 199 (2007)34. S.K. Maiti, Phys. E 40, 2730 (2008)35. S.K. Maiti, S.K. Maiti, Org. Electron. 12, 1017 (2011)

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