- Email: [email protected]
Transport through a T-shaped double quantum dot with Fano–Kondo interaction
ARTICLE IN PRESS
Physica E 34 (2006) 464–467 www.elsevier.com/locate/physe
Transport through a T-shaped double quantum dot with Fano–Kondo interaction B.H. Wu, Kang-Hun Ahn Department of Physics, Chungnam National University, Daejeon 305-764, Republic of Korea Available online 17 April 2006
Abstract We present transport properties of a strongly correlated quantum dot attached to two leads with a side coupled non-interacting quantum dot. Transport properties are analyzed using the slave boson mean field theory which is reliable in the zero temperature and low bias regime. It is found that the transport properties are determined by the interplay of two fundamental physical phenomena, i.e. the Kondo effects where the conductance can reach the unitary limit and the Fano interference which leads to an asymmetric shape of the conductance as function of the gate voltage. It is found that the Kondo effects will be suppressed by the Fano interference. The linear conductance will depart from the unitary limit and the zero bias anomaly will be suppressed in the presence of interdot coupling. If the spin degeneracy of the side coupled dot is lifted, for example, by external magnetic field, the linear conductance of electrons with different spin displays dips at different position. This result might be useful for the design of spin filters. r 2006 Elsevier B.V. All rights reserved. PACS: 73.63.Kv; 85.35.Ds; 73.23.Hk; 73.40.Gk Keywords: Kondo effect; Fano interference; Double quantum dot
In the past years, Kondo effect in artificial impurities has attracted much attention. By coupling two quantum dots (QDs), one gets a double quantum dot (DQD) [1]. The interplay of the correlation and quantum interference effects in various DQD arrangement provides us useful model systems for the study of mesoscopic physics. Compared with the usual series and parallel strongly correlated DQD [2–7], study on the T-shaped DQD is relatively insufficient [8,9]. In the T-shaped DQD, only one central QD connects to the two leads, while the other one is side coupled to the central dot. In such configurations, there exist two paths giving rise to Fano interference; one is through the central QD and the other is through the side QD. In this paper, we systematically investigate the nonequilibrium transport properties of a T-shaped DQD where the central dot operates in the Kondo regime. The side dot is assumed to be noninteracting so that the Fano Corresponding author.
E-mail address: [email protected] (K.-H. Ahn). 1386-9477/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2006.03.018
interference can be readily adjusted by changing interdot coupling and the energy level of the side dot. Current and shot noise properties of the DQD are investigated. Both Kondo effect and Fano interference play important roles in determining the transport properties of the T-shaped DQD device. If the spin degeneracy of the side coupled dot is lifted, for example, by external magnetic field, the linear conductance of electrons with different spin displays dips at different positions. A spin filter based on the interplay of Kondo effects and Fano interference is proposed. The schematic diagram of our device is presented in Fig. 1. The central part of our device has two QDs. A single energy level is included on each dot. In our configuration, only one dot QD0 is connected to both leads via tunnelling coupling ta (a ¼ L; R). There is a strong intradot Coulomb interaction U on QD0. Another noninteracting dot QD1 is side coupled to QD0 via interdot tunnelling coupling tc . The energy level of QD0 0s is far below the Fermi energy while the energy level of QD1 1s can be tuned by the external gate voltage. Here, s represents spin. In the following discussion, U is sufficiently large (U ! 1), so
ARTICLE IN PRESS B.H. Wu, K.-H. Ahn / Physica E 34 (2006) 464–467
first write down the constraint and the equation of motion for the slave boson operators. Thus we have two equations with the above two unknowns. Next, the two equations are closed with the nonequilibrium Green’s functions of the central dot by applying the equation of motion and the analytic continuation rules [10] of the lead-dot lesser Green function. These equations in the Fourier space are given by X Z d 1 2 ~ Go (3) b i 00;s ðÞ ¼ , 4p 2 s
U tL
L
QD0
tR
R
tc
QD1
Vg
2
Fig. 1. Schematic plot of the nanodevice. Energy level of QD1 can be adjusted via the gate voltage or a magnetic field.
that double occupancy of QD0 is forbidden. The infinite U slave boson language was adopted to describe the strongly correlated QD. The Hamiltonian of our model reads: X X X H¼ ka;s cyka;s cka;s þ 0s f ys f s þ 1s d ys d s s
ka;s
s
1 X þ pffiffiffiffiffi ta ðcyka;s by f s þ HCÞ N ka;s tc X y y ðd s b f s þ HCÞ þ pffiffiffiffiffi N s ! X y y þl b bþ f sf s 1 ,
ð1Þ
where cyka;s ðcka;s Þ is the creation (annihilation) operator for an electron with spin s and quantum number k in the a lead. In the slave boson representation, the creation (annihilation) operator for an electron in the N ¼ 2 fold degenerate QD0 with spin s is replaced by f ys b ðf s by Þ where f s (f ys ) is the pseudofermion operator that annihilates (creates) a singly occupied state in QD0 and b (by ) is the slave boson operator which annihilates (creates) an empty state in QD0. We solved this Hamiltonian by using the mean field approximation, where the boson operator is approximated by its expectation value. A real parameter b~ is introduced to replace pffiffiffiffiffi the boson operators in the Hamiltonian, namely, ~ This approximation is exact for describing bðtÞ= N ¼ b. the spin fluctuation (Kondo regime) in the limit N ! 1 and T ¼ 0. By defining the renormalization parameters ~ t~c ¼ tc b~ and ~0s ¼ 0s þ l, the Hamiltonian is t~a ¼ ta b, formally reduced to the free electron model: X X X ~0s f ys f s þ H~ ¼ ka;s cyka;s cka;s þ 1s d ys d s þ
X
s
s
t~a ðcyka;s f s þ HCÞ
ka;s
þ t~c
lb~ ¼ i
X Z d ð ~ 0;s ÞGo 00;s ðÞ, 4p s
X 2 ðd ys f s þ HCÞ þ lðN b~ 1Þ.
ð2Þ
s
Now, the task is to determine the set of parameters: b~ and l in a self-consistent way. Following Ref. [4], one can
(4)
y where G o 00;s ðÞ ¼ ihf s f s i. The retarded and the lesser Green function of QD0 can be obtained by the equation of motion approach. We 2 ~ ¼ b~2 G ¼ G~ L þ G~ R as the renormadefine G~ a ¼ b~ Ga and G lized linewidth P functions. The linewidth function is defined as Ga ðÞ ¼ p ka;s t2a dð ka;s Þ. In the wide band limit, Ga can be reduced to an energy-independent constant for jjoD (D is the band width). After obtaining these parameters self-consistently, the transmission probability T s ð; V LR Þ can be found from
~ L Gr G ~ T s ð; V LR Þ ¼ G a00;s G 00;s R ,
s
ka;s
465
(5)
where V LR is the small DC voltage applied across QD0 and the advanced Green function G a can be calculated from the Hermitian conjugate of G r . Compared with the noninteracting cases, the transmission probability is a function of V LR due to the self-consistent renormalized parameters. We studied the current and shot noise properties of the T-shaped DQD device. At T ¼ 0, only the shot noise is nonzero while the thermal noise is fully suppressed. Expressions for the current and zero frequency shot noise spectrum are given in Refs. [7,11] as Z e X eV LR I¼ dT s ð; V LR Þ (6) h s 0 and S¼
2e2 X h s
Z
eV LR
dT s ð; V LR Þð1 T s ð; V LR ÞÞ,
(7)
0
where e and h are the charge unit and Planck constant. These results are obtained at zero temperature where the Fermi distribution function becomes a unit step function. The shot noise Fano factor g ¼ S=2eI is introduced to characterize the deviation of the shot noise from the Poisson value of shot noise 2eI. Now, we discuss the transport properties of the T-shaped DQD at zero temperature. In the following, G is taken as the energy unit and E F at equilibrium is set to be zero as energy reference. The energy level of the central dot is fixed at 3:5 and the conduction band has a constant DOS with the band width D ¼ 60. At equilibrium and without interdot coupling, the Kondo temperature T 0K of QD0 is then approximate to be 103 . The energy level of QD1 1
ARTICLE IN PRESS B.H. Wu, K.-H. Ahn / Physica E 34 (2006) 464–467
2.0 tc = 0.00 tc = 0.03 tc = 0.04 tc = 0.05
dI/dV (e2/h)
1.5
1.0
0.5
0.0 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
VLR (T0K) Fig. 2. Differential conductance with different interdot coupling parameters as a function of the bias.
1.00 tc = 0.00 tc = 0.03 tc = 0.04 tc = 0.05
0.75 Fano Factor γ
and the interdot coupling strength tc are assumed to be readily adjustable. In Fig. 2, we plot the nonlinear differential conductance dI=dV as a function of the applied voltage for various interdot couplings. The energy level of QD1 is fixed at T 0K in the numerical calculation. The differential conductance is obtained by numerically differentiating the current expression with respect to the bias voltage. For tc ¼ 0, only one dot (QD0) is active. The unitary limit of the conductance at zero bias is reached due to the Kondo resonance. The differential conductance shows a zero bias anomaly which is the main feature of the differential conductance in the Kondo regime. When tc is nonzero, the differential conductance line shape is modified. The zero bias conductance departs from the unitary limit and the zero bias anomaly peak is suppressed with increasing interdot coupling due to the interplay of the Fano interference and the Kondo effect. When tc is strong enough, the zero bias anomaly eventually vanishes. In Fig. 3, the bias dependent Fano factor is displayed for different interdot couplings. The energy level of QD1 is fixed at T 0K . We are interested in the zero bias limit Fano factor which is given by gjV LR !0 ¼ 1 TðE F ; 0Þ. For tc ¼ 0, QD0 acts as a perfect transparent scatterer dominated by the Kondo resonance. One can see from Fig. 3 that the Kondo unitary limit leads to a complete suppression of the zero bias Fano factor. When the Fano interference plays its role, the Kondo resonance peak of DOS changes from a Breit–Wigner line shape to a composition of a Breit–Wigner and a Fano line shape. At the same time, the zero bias conductance will depart from the unitary limit and the zero bias limit shot noise Fano factor will take on a nonzero value. This enhancement of the shot noise Fano factor can be interpreted as a result of the weakening of the DOS peak at Fermi energy by the Fano interference between the two pathways through the DQD device. When tc becomes much stronger, the Kondo
0.50
0.25
0.00 0.0
0.2
0.4
0.6
0.8 VLR/Tk
1.0
1.2
1.4
1.6
Fig. 3. Bias dependence of the shot noise Fano factor g with different interdot coupling parameters.
1.0
σ= σ=
0.8
0.6 T (EF)
466
0.4
0.2
0.0
-1
0
1
Vg/T0K Fig. 4. When a small energy level splitting of QD1 is included, the transmission probabilities of electrons with different spin display great contrasts at certain energy.
resonance at Fermi energy is destroyed by the Fano interference. The transmission probability at E F becomes very low. As a consequence, g increases very quickly and the shot noise tends to the Poisson value. When the transmission dip caused by the Fano interference is spin dependent, a spin filter device can be realized. In the presence of an external magnetic field, the spin up and spin down energies are different. The transmission dips for different spin are not the same. As a consequence, we may realize a spin filter based on the interplay of Kondo effect and the Fano interference in the presence of external magnetic field. In Fig. 4, we present the spin-related transmission probabilities at a spin splitting of 0:5 T 0K on QD1. This spin splitting may be achieved by applying magnetic field only to QD1 by putting a superconductor plate on top of the QD0. By
ARTICLE IN PRESS B.H. Wu, K.-H. Ahn / Physica E 34 (2006) 464–467
tuning the gate voltage, the device can works as an effective spin filter. One can see there is a dip of the spin down conductance at the resonance energy for the spin up electrons and vice versa. In conclusion, we presented the transport properties of a T-shaped DQD device where the central dot is in the Kondo regime. The Fano interference can act to weaken the Kondo resonance at the Fermi energy. As a consequence, the linear conductance will depart from the unitary limit and the zero bias anomaly will be suppressed in the presence of interdot coupling. The zero bias anomaly will eventually vanish at large interdot coupling strength or the side dot energy is tuned near the Kondo resonance peak. The zero bias shot noise Fano factor increases with the interdot coupling and tends to the Poisson value. In the presence of spin level splitting, a perfect spin filter can be realized based on the interplay of Kondo and Fano effects.
467
This work was supported by Korea Research Foundation, Grant no. (KRF-2003-070-C00020). References [1] W.G. van der Wiel, S. De Franceschi, J.M. Elzerman, T. Fujisawa, S. Tarucha, L.P. Kouwenhoven, Rev. Mod. Phys. 75 (2003) 1. [2] A. Georges, Y. Meir, Phys. Rev. Lett. 82 (1999) 3508. [3] H. Jeong, A.M. Chang, M.R. Melloch, Science 293 (2001) 2221. [4] R. Aguado, D.C. Langreth, Phys. Rev. Lett. 85 (2000) 1946. [5] T. Aono, M. Eto, Phys. Rev. B 63 (2001) 125327. [6] D. Boese, W. Hofstetter, H. Schoeller, Phys. Rev. B 66 (2002) 125315. [7] R. Lo´pez, R. Aguado, G. Platero, Phys. Rev. B 69 (2004) 235305. [8] T.S. Kim, S. Hershfield, Phys. Rev. B 63 (2001) 245326. [9] P.S. Cornaglia, D.R. Grempel, Phys. Rev. B 71 (2005) 075305. [10] H. Haug, A.-P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors, Springer, Berlin, 1998. [11] Y. Meir, N.S. Wingreen, Phys. Rev. Lett. 68 (1992) 2512.
Physica E 34 (2006) 464–467 www.elsevier.com/locate/physe
Transport through a T-shaped double quantum dot with Fano–Kondo interaction B.H. Wu, Kang-Hun Ahn Department of Physics, Chungnam National University, Daejeon 305-764, Republic of Korea Available online 17 April 2006
Abstract We present transport properties of a strongly correlated quantum dot attached to two leads with a side coupled non-interacting quantum dot. Transport properties are analyzed using the slave boson mean field theory which is reliable in the zero temperature and low bias regime. It is found that the transport properties are determined by the interplay of two fundamental physical phenomena, i.e. the Kondo effects where the conductance can reach the unitary limit and the Fano interference which leads to an asymmetric shape of the conductance as function of the gate voltage. It is found that the Kondo effects will be suppressed by the Fano interference. The linear conductance will depart from the unitary limit and the zero bias anomaly will be suppressed in the presence of interdot coupling. If the spin degeneracy of the side coupled dot is lifted, for example, by external magnetic field, the linear conductance of electrons with different spin displays dips at different position. This result might be useful for the design of spin filters. r 2006 Elsevier B.V. All rights reserved. PACS: 73.63.Kv; 85.35.Ds; 73.23.Hk; 73.40.Gk Keywords: Kondo effect; Fano interference; Double quantum dot
In the past years, Kondo effect in artificial impurities has attracted much attention. By coupling two quantum dots (QDs), one gets a double quantum dot (DQD) [1]. The interplay of the correlation and quantum interference effects in various DQD arrangement provides us useful model systems for the study of mesoscopic physics. Compared with the usual series and parallel strongly correlated DQD [2–7], study on the T-shaped DQD is relatively insufficient [8,9]. In the T-shaped DQD, only one central QD connects to the two leads, while the other one is side coupled to the central dot. In such configurations, there exist two paths giving rise to Fano interference; one is through the central QD and the other is through the side QD. In this paper, we systematically investigate the nonequilibrium transport properties of a T-shaped DQD where the central dot operates in the Kondo regime. The side dot is assumed to be noninteracting so that the Fano Corresponding author.
E-mail address: [email protected] (K.-H. Ahn). 1386-9477/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2006.03.018
interference can be readily adjusted by changing interdot coupling and the energy level of the side dot. Current and shot noise properties of the DQD are investigated. Both Kondo effect and Fano interference play important roles in determining the transport properties of the T-shaped DQD device. If the spin degeneracy of the side coupled dot is lifted, for example, by external magnetic field, the linear conductance of electrons with different spin displays dips at different positions. A spin filter based on the interplay of Kondo effects and Fano interference is proposed. The schematic diagram of our device is presented in Fig. 1. The central part of our device has two QDs. A single energy level is included on each dot. In our configuration, only one dot QD0 is connected to both leads via tunnelling coupling ta (a ¼ L; R). There is a strong intradot Coulomb interaction U on QD0. Another noninteracting dot QD1 is side coupled to QD0 via interdot tunnelling coupling tc . The energy level of QD0 0s is far below the Fermi energy while the energy level of QD1 1s can be tuned by the external gate voltage. Here, s represents spin. In the following discussion, U is sufficiently large (U ! 1), so
ARTICLE IN PRESS B.H. Wu, K.-H. Ahn / Physica E 34 (2006) 464–467
first write down the constraint and the equation of motion for the slave boson operators. Thus we have two equations with the above two unknowns. Next, the two equations are closed with the nonequilibrium Green’s functions of the central dot by applying the equation of motion and the analytic continuation rules [10] of the lead-dot lesser Green function. These equations in the Fourier space are given by X Z d 1 2 ~ Go (3) b i 00;s ðÞ ¼ , 4p 2 s
U tL
L
QD0
tR
R
tc
QD1
Vg
2
Fig. 1. Schematic plot of the nanodevice. Energy level of QD1 can be adjusted via the gate voltage or a magnetic field.
that double occupancy of QD0 is forbidden. The infinite U slave boson language was adopted to describe the strongly correlated QD. The Hamiltonian of our model reads: X X X H¼ ka;s cyka;s cka;s þ 0s f ys f s þ 1s d ys d s s
ka;s
s
1 X þ pffiffiffiffiffi ta ðcyka;s by f s þ HCÞ N ka;s tc X y y ðd s b f s þ HCÞ þ pffiffiffiffiffi N s ! X y y þl b bþ f sf s 1 ,
ð1Þ
where cyka;s ðcka;s Þ is the creation (annihilation) operator for an electron with spin s and quantum number k in the a lead. In the slave boson representation, the creation (annihilation) operator for an electron in the N ¼ 2 fold degenerate QD0 with spin s is replaced by f ys b ðf s by Þ where f s (f ys ) is the pseudofermion operator that annihilates (creates) a singly occupied state in QD0 and b (by ) is the slave boson operator which annihilates (creates) an empty state in QD0. We solved this Hamiltonian by using the mean field approximation, where the boson operator is approximated by its expectation value. A real parameter b~ is introduced to replace pffiffiffiffiffi the boson operators in the Hamiltonian, namely, ~ This approximation is exact for describing bðtÞ= N ¼ b. the spin fluctuation (Kondo regime) in the limit N ! 1 and T ¼ 0. By defining the renormalization parameters ~ t~c ¼ tc b~ and ~0s ¼ 0s þ l, the Hamiltonian is t~a ¼ ta b, formally reduced to the free electron model: X X X ~0s f ys f s þ H~ ¼ ka;s cyka;s cka;s þ 1s d ys d s þ
X
s
s
t~a ðcyka;s f s þ HCÞ
ka;s
þ t~c
lb~ ¼ i
X Z d ð ~ 0;s ÞGo 00;s ðÞ, 4p s
X 2 ðd ys f s þ HCÞ þ lðN b~ 1Þ.
ð2Þ
s
Now, the task is to determine the set of parameters: b~ and l in a self-consistent way. Following Ref. [4], one can
(4)
y where G o 00;s ðÞ ¼ ihf s f s i. The retarded and the lesser Green function of QD0 can be obtained by the equation of motion approach. We 2 ~ ¼ b~2 G ¼ G~ L þ G~ R as the renormadefine G~ a ¼ b~ Ga and G lized linewidth P functions. The linewidth function is defined as Ga ðÞ ¼ p ka;s t2a dð ka;s Þ. In the wide band limit, Ga can be reduced to an energy-independent constant for jjoD (D is the band width). After obtaining these parameters self-consistently, the transmission probability T s ð; V LR Þ can be found from
~ L Gr G ~ T s ð; V LR Þ ¼ G a00;s G 00;s R ,
s
ka;s
465
(5)
where V LR is the small DC voltage applied across QD0 and the advanced Green function G a can be calculated from the Hermitian conjugate of G r . Compared with the noninteracting cases, the transmission probability is a function of V LR due to the self-consistent renormalized parameters. We studied the current and shot noise properties of the T-shaped DQD device. At T ¼ 0, only the shot noise is nonzero while the thermal noise is fully suppressed. Expressions for the current and zero frequency shot noise spectrum are given in Refs. [7,11] as Z e X eV LR I¼ dT s ð; V LR Þ (6) h s 0 and S¼
2e2 X h s
Z
eV LR
dT s ð; V LR Þð1 T s ð; V LR ÞÞ,
(7)
0
where e and h are the charge unit and Planck constant. These results are obtained at zero temperature where the Fermi distribution function becomes a unit step function. The shot noise Fano factor g ¼ S=2eI is introduced to characterize the deviation of the shot noise from the Poisson value of shot noise 2eI. Now, we discuss the transport properties of the T-shaped DQD at zero temperature. In the following, G is taken as the energy unit and E F at equilibrium is set to be zero as energy reference. The energy level of the central dot is fixed at 3:5 and the conduction band has a constant DOS with the band width D ¼ 60. At equilibrium and without interdot coupling, the Kondo temperature T 0K of QD0 is then approximate to be 103 . The energy level of QD1 1
ARTICLE IN PRESS B.H. Wu, K.-H. Ahn / Physica E 34 (2006) 464–467
2.0 tc = 0.00 tc = 0.03 tc = 0.04 tc = 0.05
dI/dV (e2/h)
1.5
1.0
0.5
0.0 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
VLR (T0K) Fig. 2. Differential conductance with different interdot coupling parameters as a function of the bias.
1.00 tc = 0.00 tc = 0.03 tc = 0.04 tc = 0.05
0.75 Fano Factor γ
and the interdot coupling strength tc are assumed to be readily adjustable. In Fig. 2, we plot the nonlinear differential conductance dI=dV as a function of the applied voltage for various interdot couplings. The energy level of QD1 is fixed at T 0K in the numerical calculation. The differential conductance is obtained by numerically differentiating the current expression with respect to the bias voltage. For tc ¼ 0, only one dot (QD0) is active. The unitary limit of the conductance at zero bias is reached due to the Kondo resonance. The differential conductance shows a zero bias anomaly which is the main feature of the differential conductance in the Kondo regime. When tc is nonzero, the differential conductance line shape is modified. The zero bias conductance departs from the unitary limit and the zero bias anomaly peak is suppressed with increasing interdot coupling due to the interplay of the Fano interference and the Kondo effect. When tc is strong enough, the zero bias anomaly eventually vanishes. In Fig. 3, the bias dependent Fano factor is displayed for different interdot couplings. The energy level of QD1 is fixed at T 0K . We are interested in the zero bias limit Fano factor which is given by gjV LR !0 ¼ 1 TðE F ; 0Þ. For tc ¼ 0, QD0 acts as a perfect transparent scatterer dominated by the Kondo resonance. One can see from Fig. 3 that the Kondo unitary limit leads to a complete suppression of the zero bias Fano factor. When the Fano interference plays its role, the Kondo resonance peak of DOS changes from a Breit–Wigner line shape to a composition of a Breit–Wigner and a Fano line shape. At the same time, the zero bias conductance will depart from the unitary limit and the zero bias limit shot noise Fano factor will take on a nonzero value. This enhancement of the shot noise Fano factor can be interpreted as a result of the weakening of the DOS peak at Fermi energy by the Fano interference between the two pathways through the DQD device. When tc becomes much stronger, the Kondo
0.50
0.25
0.00 0.0
0.2
0.4
0.6
0.8 VLR/Tk
1.0
1.2
1.4
1.6
Fig. 3. Bias dependence of the shot noise Fano factor g with different interdot coupling parameters.
1.0
σ= σ=
0.8
0.6 T (EF)
466
0.4
0.2
0.0
-1
0
1
Vg/T0K Fig. 4. When a small energy level splitting of QD1 is included, the transmission probabilities of electrons with different spin display great contrasts at certain energy.
resonance at Fermi energy is destroyed by the Fano interference. The transmission probability at E F becomes very low. As a consequence, g increases very quickly and the shot noise tends to the Poisson value. When the transmission dip caused by the Fano interference is spin dependent, a spin filter device can be realized. In the presence of an external magnetic field, the spin up and spin down energies are different. The transmission dips for different spin are not the same. As a consequence, we may realize a spin filter based on the interplay of Kondo effect and the Fano interference in the presence of external magnetic field. In Fig. 4, we present the spin-related transmission probabilities at a spin splitting of 0:5 T 0K on QD1. This spin splitting may be achieved by applying magnetic field only to QD1 by putting a superconductor plate on top of the QD0. By
ARTICLE IN PRESS B.H. Wu, K.-H. Ahn / Physica E 34 (2006) 464–467
tuning the gate voltage, the device can works as an effective spin filter. One can see there is a dip of the spin down conductance at the resonance energy for the spin up electrons and vice versa. In conclusion, we presented the transport properties of a T-shaped DQD device where the central dot is in the Kondo regime. The Fano interference can act to weaken the Kondo resonance at the Fermi energy. As a consequence, the linear conductance will depart from the unitary limit and the zero bias anomaly will be suppressed in the presence of interdot coupling. The zero bias anomaly will eventually vanish at large interdot coupling strength or the side dot energy is tuned near the Kondo resonance peak. The zero bias shot noise Fano factor increases with the interdot coupling and tends to the Poisson value. In the presence of spin level splitting, a perfect spin filter can be realized based on the interplay of Kondo and Fano effects.
467
This work was supported by Korea Research Foundation, Grant no. (KRF-2003-070-C00020). References [1] W.G. van der Wiel, S. De Franceschi, J.M. Elzerman, T. Fujisawa, S. Tarucha, L.P. Kouwenhoven, Rev. Mod. Phys. 75 (2003) 1. [2] A. Georges, Y. Meir, Phys. Rev. Lett. 82 (1999) 3508. [3] H. Jeong, A.M. Chang, M.R. Melloch, Science 293 (2001) 2221. [4] R. Aguado, D.C. Langreth, Phys. Rev. Lett. 85 (2000) 1946. [5] T. Aono, M. Eto, Phys. Rev. B 63 (2001) 125327. [6] D. Boese, W. Hofstetter, H. Schoeller, Phys. Rev. B 66 (2002) 125315. [7] R. Lo´pez, R. Aguado, G. Platero, Phys. Rev. B 69 (2004) 235305. [8] T.S. Kim, S. Hershfield, Phys. Rev. B 63 (2001) 245326. [9] P.S. Cornaglia, D.R. Grempel, Phys. Rev. B 71 (2005) 075305. [10] H. Haug, A.-P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors, Springer, Berlin, 1998. [11] Y. Meir, N.S. Wingreen, Phys. Rev. Lett. 68 (1992) 2512.