In this article, we study the effect of electron-electron interaction in a doped nano
cluster sandwich between two electrodes. The Hamiltonian of the cluster is written in
the tight-binding model and electrodes are described in the wide-band approximation.
The GW approximation has been used for the calculation of the exchange-correlation
term in the cluster region. Our results showed that in the presence of the electronelectron
interaction the transmittance gap increases and current decreases. Also, in a
doped nano structure the transmission decreases and many body effect becomes more
important. By considering the exchange-correlation in a doped nano cluster in the GW
approximation the transmission and current decrease drastically.
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/2056

Mirhabibi, M.

Modarresi, M.

Roknabadi, M.R.

Shahtahmasbi, N.

Electronic Sumy State University Institutional Repository

24                   Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I             MANY BODY EFFECTS ON THE TRANSPORT PROPER-TIES OF A DOPED NANO DEVICE M. Modarresi1*, M. R. Roknabadi1, N. Shahtahmasbi1, M. Mirhabibi2  1 Department of Physics, FerdowsiUniversityof Mashhad, Mashhad Iran. 2 Payame Noor University ofKerman  ABSTRACT In this article, we study the effect of electron-electron interaction in a doped nano cluster sandwich between two electrodes. The Hamiltonian of the cluster is written in the tight-binding model and electrodes are described in the wide-band approximation. The GW approximation has been used for the calculation of the exchange-correlation term in the cluster region. Our results showed that in the presence of the electron-electron interaction the transmittance gap increases and current decreases. Also, in a doped nano structure the transmission decreases and many body effect becomes more important. By considering the exchange-correlation in a doped nano cluster in the GW approximation the transmission and current decrease drastically.  Keywords:  nanocluster; doping; many body theory; transport properties.  INTRODUCTION Transportation through a nano device is an interesting topic for theoretical and experimental physicist [1-4]. In realistic systems the impurity effects are Inevitable. The presence of an impurity in a nano system changes the electronic and transport properties of the device. In the one particle approach and in a tight binding approximation the Hamiltonian of cluster is written according to the on-site and hopping term between nearest neighbors in the cluster. In this approach  the  the  impurity  effects  are  limited  in  the  change  of  tight  binding  parameters. But due to the electron-electron and electron-phonon interactions in the nano device, we face a complex many-body problem. The effect of elec-tron-phonon interaction has been studied in previous works[5-8]; in this article, the effect of electron-electron interaction in a doped nano device is studied. The electron-electron interaction plays an important role in solids and responsible for the coulomb blockade and the Kondo effects [9]. Based on the Born-Openheimer approximation, the electronic and the ionic degrees of freedom are decoupled. The Hartree and Hartree-Fock (HF) methods try to deals the elec-tron-electron interactions as a one-particle term in the total Hamiltonian. The Hartree method simply adds the classical repulsion to the one particle Hamilto-nian.  In  the  GW approximation  the  self-energy is  approximated  with  the  first                                                 * e-mail: mo_mo226@stu-mail.um.ac.ir,tel:  +98-9133452131 Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I                   25  term in the expansion. Many body effects beyond the GW approximation could be important in the calculation of different properties of solids [10-12] but the GW approximation is reliable in different calculations [1, 3, 13-15]. The HF approximation contains the classical electrostatic and exchange potentials but the GW approximation includes the correlation between electrons in solids [16]. In this work we investigate the many body effect in a doped nano cluster. MODEL AND RESULTS We consider a typical nano cluster with 6 atoms and attach the left and right electrodes to the cluster, as shown in Figure 1.  At first the transport in a pure and doped cluster in a one-particle approach has been investigated. The total Hamiltonian of the above system contains the Hamiltonian of isolated cluster, electrodes and the interaction between them.     Fig. 1– A pure and doped nano cluster with 6 point between two electrodes  The non-interacting part of the Hamiltonian is written in the nearest neighbor tight-binding approximation as follows,   0 , , 1, , , 1,,( )C i i i i i i i iiH C C t C C C CV V V V V VVH      ¦  (1) The index i runs over the cluster sites. The operatorCi,ı+(Ci,ı) cre-ates/annihilates a ʌ electron with spin ı at the i-th site of cluster. İi is the onsite energy of the i-th sites and ti denotes the hopping integral between two neigh-boring sites. The effect of electrodes on the Hamiltonian is fully described by specifying the self-energy of the left and right electrodes. By using the Keldysh Green’s function technique, the current running between two electrodes, through the cluster, is calculated by Meir-Wingreen relation [2, 17]. Neglecting the interaction in the central region, the Mier-Wingreen relation is simplified to the well-known Landauer-Büttiker formula [18, 19],   B(V ) ( ) [ ( ) ( )]L ReI d T f fhZ Z Z Zff ³  (2)  26                   Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I             WhereƒL/R = [exp [E ( Z – PL/R)] + 1]-1is the Fermi distribution function in the left/right electrode with chemical potentialPL/R   Hƒ r (eVb/2) and Fermi energy Hƒ. T(Z) is the transmission coefficient as a function of energy for elec-trons and can be written as follows,   0 0( ) [ ( ) ( )]r aL RT Tr G GZ Z Z * * , (3) where 0 ( )rG Z  is the retarded Green's function of the non-interacting sys-tem and is defined as,  10 0( ) [ I ]rC L RG HZ Z   6 6  (4) ȽL/Rrepresents the coupling between the cluster and left/right electrode. In this article, the spin-flip process has been neglected and the self-energy of elec-trodes has been simply described within the wide-band approximation. In this approximation, the real part of self-energy is neglected and the imaginary part of the self-energy operator is written in an energy-independent form as [5, 20], ¦L/R=(-i / 2) ȽL/R. In the pure cluster we set Hi=0,  ti=3.0eQ,and in the doped cluster for the dopant site we use Hd = -1, td = 2eQ, and electrodes described with the following parameters, ȽL =  ȽR = 0.066 t0. Figure 2 shows the current voltage characteristic and transmission as functions of energy for the above clusters. In both cases the transmission peaks are correspondent to the eigen-value of the non-interacting system.   Fig. 2– Current volt-voltage characteristic and transmission as a function of energy  for the case of (a) pure and (b) doped nano cluster  The  symmetry  around the  Fermi  energy in  the  pure  cluster  is  due  to  the  symmetry of the Hamiltonian in the pure cluster. In the doped structure the symmetry around the Fermi energy vanishes. By increasing the applied voltage the energy window opens and the current increases. When a transmission peak enters in the energy window, current increases more rapidly which leads to a step-like form in the current-voltage curve. In the next step, we consider the interacting cluster and study the effect of electron-electron interaction on the Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I                   27  transport properties of a pure and doped 2D cluster in the Hartree and G0W0. The quasi-particle equation for interacting electrons can be written as [21, 22],   ' ' '0[ ] ( ) ( , , ) ( ) ( )C H i i i i iH V r r r r dr rH H <  6 <  <³  (5) Where VH is the electrostatic or Hartree potential of the electronic system and Ȉ is the self-energy which is a non-local, energy-dependent and non-hermitian operator containing all exchange and correlation effects beyond the Hartree approximation. In the GW method, the time-ordered self-energy opera-tor is approximated as [1, 23, 24],  '' ' ' ' ' '( , , ) ( , , ) ( , , )2iGWir r d W r r G r r e Z GZ Z Z Z ZSff6 ³  (6) Where G is the one-particle Green’s function, W is the dynamically screened coulomb interaction and į is a positive infinitesimal. The GW method can be considered as a generalization of the HF approximation, in which the bare coulomb interaction  X(r, rc)= 1/ _r - rc_is replaced with the dynamically screened interaction W. In this article, the Green’s function is approximated with the non-interacting Green’s function [16, 22, 25]. The screened interaction can be calculated in terms of the inverse dielectric function H-1by means of,  ' ' 1 '' ''( , , ) ( , , ) ( , )W r r dr r r r rZ H Z X ³  (7) In the direct space, the dielectric function can be written asH   1 – XP. In its simplest form, the polarization operator P can be written in the independent particle approximation as [25],  * ' '',( ) ( ) ( ) ( )( , , ) ( )( )i j j ii ji j j ir r r rP r r f fiZ Z H H K< < < <    ¦  (8) Where; fi is the occupation of the i-th state and iKis a small imaginary part which leads to an imaginary part of P. The above equation for polarization is the form of the random-phase approximation (RPA) first used by Lindhard for the homogeneous electron gas [26, 27]. The imaginary part has peaks inG( Hj – HI –  E)  which  shows  the  conservation  of  energy  in  case  of  excitation  of  an  electron from state i to state j. The retarded Green’s function can be written as,   10( ) [ ( ( )]r r r rC C H L R GWG I H VZ Z Z    6 6  6  (9) Where rGW6 is the retarded self-energy operator due to the electron-electron interaction. A. Ferretti and et al. proposed a Landauer-like expression for current in the presence of many-body interactions as follows[2],  28                   Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I              ',B(V ) [ ( ) ( )][ ( ) ( )]r r r aL C R C L ReI d Tr G G f fhV V Z Z Z Z Zff * * / ³  (10) We set 1/  and restrict the changes in the definition of the retarded Green’s function which is correspondent to the strong coupling with electrodes. Figure 3 shows the transmission as a function of energy in the Hartree and GW approximations.  Fig. 3– Current volt-voltage characteristic and transmission as a function of energy in the Hartree and GW approximation for the case of (a) pure and (b) doped nano cluster  In the Hartree approximation, the 0H in the equation 4 is replaced with 0 0 HH H Vo  . In the Hartree model the transmission spectrum in the pure cluster does not change. But the transmission for the doped cluster decreases and transmission gap increases with respect to the non-interacting case. A com-parison between the Hartree and GW appears the many body effects in the cluster region. In the GW approximation the real part of self-energy shifts the transmission peaks and increases the conductance gap. The imaginary part of self-energy leads to decreasing transmission and broadening in the transmission peaks. Figure 3 shows the current-voltage characteristic of the cluster in Har-tree and GW approximation. The exchange-correlation term described in the GW approximation decreases the transmission and current which is correspond with an additional resistance in the cluster. In the doped nano cluster the elec-trons are accumulate in the dopant site. As a result the many body effect be-comes more important in a doped cluster, thus the transmission reduces drasti-cally in the GW approximation. CONCLUSIONS Briefly speaking, we have considered a typical nano structure and have studied the effect of electron-electron interaction on the transport properties in Hartree and GW approximations. Our results showed that in the presence of e-e interaction, conductance gap increases and current decreases. The reduction of transmission and current is increases in a doped cluster.  Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I                   29  Acknowledgements We would like to express our gratitude to Dr. Andrea Ferretti, Dr. Kris-tianSommerThygesen, and Dr. Mikkel Strange for their useful consultations.  REFERENCES [1] P. Darancet, A. Ferretti, D. Mayou, and V. Olevano, Phys. Rev., B 75 (2007) 075102. [2] Ferretti, A. Calzolari, R. Di Felice, and F. Manghi, Phys. Rev., B 72 (2005) 125114. [3] K. S. Thygesen, Phys. Rev. lett.,100 (2008) 166804. [4] Q. Yu, L. A. Jauregui, W. Wu, R. Colby, J. Tian, Z. Su, H. Cao, Z. Liu, D. Pandey, D. Wei, T. F. Chung, P. Peng, N. P. Guisinger, E. A. Stach, J. Bao, S.-S. Pei, and Y. P. Chen, Nat. Mater.Advan.online public.,2011. [5] M. Modarresi, M. R. Roknabadi, N. Shahtahmasbi, D. VahediFakhrabad, and H. Arabshahi, Phys. B,Conden. Matt., 406 (2011) 478. [6] M. Pourfath and et al., J. of Phys., Conference Series, 109 (2008) 012029. [7] K. Walczak, Chem. Phys., 333 (2007) 63. [8] Z.-Z. Chen, Rong, and B.-f. Zhu, Phys. Rev., B 71, (2005) 165324. [9] J. Park, A. N. Pasupathy, J. I. Goldsmith, C. Chang, Y. Yaish, J. R. Petta, M. Rinkoski, J. P. Sethna, H. D. Abruna, P. L. McEuen, and D. C. Ralph, Nature, 417 (2002) 722. [10] P. Sun and G. Kotliar, Phys.Rev.Lett., 92 (2004) 196402. [11] M. G. Vergniory, J. M. Pitarke, and P. M. Echenique, Phys. Rev., B 76 (2007) 245416. [12] P. Romaniello, S. Guyot, and L. Reining, J. of Chem.Phys., 131 (2009) 154111. [13] G. Pal, Y. Pavlyukh, H. C. Schneider, and W. Huebner, European Phys.J. B-Condensed Matter and Complex Systems, 70 (2009) 483. [14] X. Wang, C. D. Spataru, M. S. Hybertsen, and A. J. Millis, Phys. Rev. B, 77 (2008) 045119. [15] K. S. Thygesen and A. Rubio, Phys. Rev., B 77 (2008) 115333. [16] J. C. Inkson, Cavendish Lab., Univ. of Cambridge, Cambridge, 1984. [17] Z. Z. Chen, R. Lü, and B. Zhu, Phys.Revi., B 71 (2005) 165324. [18] H. D. Cornean, A. Jensen, and V. Moldoveanu, J. of Math.Phys., 46 (2005) 042106. [19] D. S. Fisher and P. A. Lee, Phys. Rev., B 23 (1981) 6851. [20] P. Cui, X.-Q. Li, J. Shao, and Y. Yan, Phys.Lett., A 357 (2006) 449. [21] V. I. Anisimov, F. Aryasetiawan, and A. Lichtenstein, J. of Phys, Condensed Matter, 9 (1997) 767. [22] P. Garcia-Gonzalez and R. Godby, Comp.Phys. Commun., 137 (2001) 108. [23] N. Hamada, M. Hwang, and A. Freeman, Phys. Rev., B 41 (1990) 3620. [24] T. A. Niehaus, M. Rohlfing, F. Della Sala, A. Di Carlo, and T. Frauenheim, Phys. Rev., A 71 (2005) 022508. [25] G. Onida, L. Reining, and A. Rubio, Rev. of Mod. Phys., 74 (2002) 601. [26] K. D. V. S. M. F. M. J. Lindhard, 8 (1954),   [27] N. D. Mermin, Phys. Rev., B 1 (1970) 2362. 

Many body effects on the transport properties of a doped nano device

SocioEconomic Challenges Journal (Sumy State University)

24                   Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I            
 
MANY BODY EFFECTS ON THE TRANSPORT PROPER-
TIES OF A DOPED NANO DEVICE 
M. Modarresi1*, M. R. Roknabadi1, N. Shahtahmasbi1, M. Mirhabibi2 
 
1 Department of Physics, FerdowsiUniversityof Mashhad, Mashhad Iran. 
2 Payame Noor University ofKerman 
 
ABSTRACT 
In this article, we study the effect of electron-electron interaction in a doped nano 
cluster sandwich between two electrodes. The Hamiltonian of the cluster is written in 
the tight-binding model and electrodes are described in the wide-band approximation. 
The GW approximation has been used for the calculation of the exchange-correlation 
term in the cluster region. Our results showed that in the presence of the electron-
electron interaction the transmittance gap increases and current decreases. Also, in a 
doped nano structure the transmission decreases and many body effect becomes more 
important. By considering the exchange-correlation in a doped nano cluster in the GW 
approximation the transmission and current decrease drastically. 
 
Keywords:  nanocluster; doping; many body theory; transport properties. 
 
INTRODUCTION 
Transportation through a nano device is an interesting topic for theoretical 
and experimental physicist [1-4]. In realistic systems the impurity effects are 
Inevitable. The presence of an impurity in a nano system changes the electronic 
and transport properties of the device. In the one particle approach and in a 
tight binding approximation the Hamiltonian of cluster is written according to 
the on-site and hopping term between nearest neighbors in the cluster. In this 
approach  the  the  impurity  effects  are  limited  in  the  change  of  tight  binding  
parameters. But due to the electron-electron and electron-phonon interactions in 
the nano device, we face a complex many-body problem. The effect of elec-
tron-phonon interaction has been studied in previous works[5-8]; in this article, 
the effect of electron-electron interaction in a doped nano device is studied. The 
electron-electron interaction plays an important role in solids and responsible 
for the coulomb blockade and the Kondo effects [9]. Based on the Born-
Openheimer approximation, the electronic and the ionic degrees of freedom are 
decoupled. The Hartree and Hartree-Fock (HF) methods try to deals the elec-
tron-electron interactions as a one-particle term in the total Hamiltonian. The 
Hartree method simply adds the classical repulsion to the one particle Hamilto-
nian.  In  the  GW approximation  the  self-energy is  approximated  with  the  first  
                                               
* e-mail: mo_mo226@stu-mail.um.ac.ir,tel:  +98-9133452131 
Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I                   25 
 
term in the expansion. Many body effects beyond the GW approximation could 
be important in the calculation of different properties of solids [10-12] but the 
GW approximation is reliable in different calculations [1, 3, 13-15]. The HF 
approximation contains the classical electrostatic and exchange potentials but 
the GW approximation includes the correlation between electrons in solids 
[16]. In this work we investigate the many body effect in a doped nano cluster. 
MODEL AND RESULTS 
We consider a typical nano cluster with 6 atoms and attach the left and 
right electrodes to the cluster, as shown in Figure 1.  At first the transport in a 
pure and doped cluster in a one-particle approach has been investigated. The 
total Hamiltonian of the above system contains the Hamiltonian of isolated 
cluster, electrodes and the interaction between them.  
 
 
 
Fig. 1– A pure and doped nano cluster with 6 point between two electrodes 
 
The non-interacting part of the Hamiltonian is written in the nearest 
neighbor tight-binding approximation as follows, 
 
 0 , , 1, , , 1,
,
( )C i i i i i i i i
i
H C C t C C C CV V V V V V
V
H      ¦  (1) 
The index i runs over the cluster sites. The operatorCi,ı+(Ci,ı) cre-
ates/annihilates a ʌ electron with spin ı at the i-th site of cluster. İi is the onsite 
energy of the i-th sites and ti denotes the hopping integral between two neigh-
boring sites. The effect of electrodes on the Hamiltonian is fully described by 
specifying the self-energy of the left and right electrodes. By using the Keldysh 
Green’s function technique, the current running between two electrodes, 
through the cluster, is calculated by Meir-Wingreen relation [2, 17]. Neglecting 
the interaction in the central region, the Mier-Wingreen relation is simplified to 
the well-known Landauer-Büttiker formula [18, 19], 
 
 B(V ) ( ) [ ( ) ( )]L R
eI d T f f
h
Z Z Z Z
f
f
 ³  (2) 
 
26                   Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I            
 
WhereƒL/R = [exp [E ( Z – PL/R)] + 1]-1is the Fermi distribution function in 
the left/right electrode with chemical potentialPL/R   Hƒ r (eVb/2) and Fermi 
energy Hƒ. T(Z) is the transmission coefficient as a function of energy for elec-
trons and can be written as follows, 
 
 0 0( ) [ ( ) ( )]
r a
L RT Tr G GZ Z Z * * , (3) 
where 0 ( )
rG Z  is the retarded Green's function of the non-interacting sys-
tem and is defined as, 
 10 0( ) [ I ]
r
C L RG HZ Z   6 6  (4) 
ȽL/Rrepresents the coupling between the cluster and left/right electrode. In 
this article, the spin-flip process has been neglected and the self-energy of elec-
trodes has been simply described within the wide-band approximation. In this 
approximation, the real part of self-energy is neglected and the imaginary part 
of the self-energy operator is written in an energy-independent form as [5, 20], 
¦L/R=(-i / 2) ȽL/R. In the pure cluster we set Hi=0,  ti=3.0eQ,and in the doped 
cluster for the dopant site we use Hd = -1, td = 2eQ, and electrodes described 
with the following parameters, ȽL =  ȽR = 0.066 t0. Figure 2 shows the current 
voltage characteristic and transmission as functions of energy for the above 
clusters. In both cases the transmission peaks are correspondent to the eigen-
value of the non-interacting system.  
 
Fig. 2– Current volt-voltage characteristic and transmission as a function of energy  
for the case of (a) pure and (b) doped nano cluster 
 
The  symmetry  around the  Fermi  energy in  the  pure  cluster  is  due  to  the  
symmetry of the Hamiltonian in the pure cluster. In the doped structure the 
symmetry around the Fermi energy vanishes. By increasing the applied voltage 
the energy window opens and the current increases. When a transmission peak 
enters in the energy window, current increases more rapidly which leads to a 
step-like form in the current-voltage curve. In the next step, we consider the 
interacting cluster and study the effect of electron-electron interaction on the 
Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I                   27 
 
transport properties of a pure and doped 2D cluster in the Hartree and G0W0. 
The quasi-particle equation for interacting electrons can be written as [21, 22], 
 
 ' ' '0[ ] ( ) ( , , ) ( ) ( )C H i i i i iH V r r r r dr rH H <  6 <  <³  (5) 
Where VH is the electrostatic or Hartree potential of the electronic system 
and Ȉ is the self-energy which is a non-local, energy-dependent and non-
hermitian operator containing all exchange and correlation effects beyond the 
Hartree approximation. In the GW method, the time-ordered self-energy opera-
tor is approximated as [1, 23, 24], 
 
'' ' ' ' ' '( , , ) ( , , ) ( , , )
2
i
GW
ir r d W r r G r r e Z GZ Z Z Z ZS
f

f
6 ³  (6) 
Where G is the one-particle Green’s function, W is the dynamically 
screened coulomb interaction and į is a positive infinitesimal. The GW method 
can be considered as a generalization of the HF approximation, in which the 
bare coulomb interaction  X(r, rc)= 1/ _r - rc_is replaced with the dynamically 
screened interaction W. In this article, the Green’s function is approximated 
with the non-interacting Green’s function [16, 22, 25]. The screened interaction 
can be calculated in terms of the inverse dielectric function H-1by means of, 
 ' ' 1 '' ''( , , ) ( , , ) ( , )W r r dr r r r rZ H Z X ³  (7) 
In the direct space, the dielectric function can be written asH   1 – XP. In 
its simplest form, the polarization operator P can be written in the independent 
particle approximation as [25], 
 
* ' '
'
,
( ) ( ) ( ) ( )
( , , ) ( )
( )
i j j i
i j
i j j i
r r r r
P r r f f
i
Z Z H H K
< < < <    ¦  (8) 
Where; fi is the occupation of the i-th state and iKis a small imaginary part 
which leads to an imaginary part of P. The above equation for polarization is 
the form of the random-phase approximation (RPA) first used by Lindhard for 
the homogeneous electron gas [26, 27]. The imaginary part has peaks inG( Hj –
 HI –  E)  which  shows  the  conservation  of  energy  in  case  of  excitation  of  an  
electron from state i to state j. The retarded Green’s function can be written as, 
 
 10( ) [ ( ( )]
r r r r
C C H L R GWG I H VZ Z Z    6 6  6  (9) 
Where rGW6 is the retarded self-energy operator due to the electron-
electron interaction. A. Ferretti and et al. proposed a Landauer-like expression 
for current in the presence of many-body interactions as follows[2], 
 
28                   Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I            
 
 
',
B(V ) [ ( ) ( )][ ( ) ( )]
r r r a
L C R C L R
eI d Tr G G f f
h
V V Z Z Z Z Z
f
f
 * * / ³  (10) 
We set 1/  and restrict the changes in the definition of the retarded 
Green’s function which is correspondent to the strong coupling with electrodes. 
Figure 3 shows the transmission as a function of energy in the Hartree and GW 
approximations. 
 
Fig. 3– Current volt-voltage characteristic and transmission as a function of energy in 
the Hartree and GW approximation for the case of (a) pure and (b) doped nano cluster 
 
In the Hartree approximation, the 0H in the equation 4 is replaced with 
0 0 HH H Vo  . In the Hartree model the transmission spectrum in the pure 
cluster does not change. But the transmission for the doped cluster decreases 
and transmission gap increases with respect to the non-interacting case. A com-
parison between the Hartree and GW appears the many body effects in the 
cluster region. In the GW approximation the real part of self-energy shifts the 
transmission peaks and increases the conductance gap. The imaginary part of 
self-energy leads to decreasing transmission and broadening in the transmission 
peaks. Figure 3 shows the current-voltage characteristic of the cluster in Har-
tree and GW approximation. The exchange-correlation term described in the 
GW approximation decreases the transmission and current which is correspond 
with an additional resistance in the cluster. In the doped nano cluster the elec-
trons are accumulate in the dopant site. As a result the many body effect be-
comes more important in a doped cluster, thus the transmission reduces drasti-
cally in the GW approximation. 
CONCLUSIONS 
Briefly speaking, we have considered a typical nano structure and have 
studied the effect of electron-electron interaction on the transport properties in 
Hartree and GW approximations. Our results showed that in the presence of e-e 
interaction, conductance gap increases and current decreases. The reduction of 
transmission and current is increases in a doped cluster. 
 
Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I                   29 
 
Acknowledgements 
We would like to express our gratitude to Dr. Andrea Ferretti, Dr. Kris-
tianSommerThygesen, and Dr. Mikkel Strange for their useful consultations. 
 
REFERENCES 
[1] P. Darancet, A. Ferretti, D. Mayou, and V. Olevano, Phys. Rev., B 75 (2007) 
075102. 
[2] Ferretti, A. Calzolari, R. Di Felice, and F. Manghi, Phys. Rev., B 72 (2005) 125114. 
[3] K. S. Thygesen, Phys. Rev. lett.,100 (2008) 166804. 
[4] Q. Yu, L. A. Jauregui, W. Wu, R. Colby, J. Tian, Z. Su, H. Cao, Z. Liu, D. Pandey, 
D. Wei, T. F. Chung, P. Peng, N. P. Guisinger, E. A. Stach, J. Bao, S.-S. Pei, and Y. 
P. Chen, Nat. Mater.Advan.online public.,2011. 
[5] M. Modarresi, M. R. Roknabadi, N. Shahtahmasbi, D. VahediFakhrabad, and 
H. Arabshahi, Phys. B,Conden. Matt., 406 (2011) 478. 
[6] M. Pourfath and et al., J. of Phys., Conference Series, 109 (2008) 012029. 
[7] K. Walczak, Chem. Phys., 333 (2007) 63. 
[8] Z.-Z. Chen, Rong, and B.-f. Zhu, Phys. Rev., B 71, (2005) 165324. 
[9] J. Park, A. N. Pasupathy, J. I. Goldsmith, C. Chang, Y. Yaish, J. R. Petta, 
M. Rinkoski, J. P. Sethna, H. D. Abruna, P. L. McEuen, and D. C. Ralph, Nature, 
417 (2002) 722. 
[10] P. Sun and G. Kotliar, Phys.Rev.Lett., 92 (2004) 196402. 
[11] M. G. Vergniory, J. M. Pitarke, and P. M. Echenique, Phys. Rev., B 76 (2007) 
245416. 
[12] P. Romaniello, S. Guyot, and L. Reining, J. of Chem.Phys., 131 (2009) 154111. 
[13] G. Pal, Y. Pavlyukh, H. C. Schneider, and W. Huebner, European Phys.J. B-
Condensed Matter and Complex Systems, 70 (2009) 483. 
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Many body effects on the transport properties of a doped nano device

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