Electronic States and Transport Phenomena in Quantum Dot Systems

Eto, Mikio

doi:10.1143/jjap.40.1929

Cited by 20 publications

(20 citation statements)

References 37 publications

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“…The steady-state current is consistent with that obtained from the Master equations [30,31]. Especially, in the present case of the same transfer energy and the same density of states for left and right electrodes, the electron occupation and the current become a half and 2πe/ · v 2 D/2, respectively.…”

Section: Model and Methodologysupporting

confidence: 87%

Relaxation Process of Transient Current Through Nanoscale Systems; Density Matrix Calculations

Ishii

Tomita

Shigeno

et al. 2008

e-J. Surf. Sci. Nanotechnol.

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Transient current behavior through a nanoscale system responding to a sudden voltage application was investigated, based on the Liouville equation of density matrix. It was found that the transient current behavior is characterized with the oscillation and relaxation processes. The oscillation originates from the time-dependent electron transitions between the electrode and nanoscale system, and the period depends on the Fermi energy and the bandwidth of electrodes. On the other hand, the relaxation occurs due to the energy dissipation into a number of electronic states in electrodes, thus, the relaxation time depends on the density of states in electrode and the electron transfer energy between the electrode and nanoscale system. Furthermore, we clarified that the strong electron-electron interaction decreases the relaxation time.

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Section: Model and Methodologysupporting

confidence: 87%

Relaxation Process of Transient Current Through Nanoscale Systems; Density Matrix Calculations

Ishii

Tomita

Shigeno

et al. 2008

e-J. Surf. Sci. Nanotechnol.

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“…14(c). It is known that part of such a peak on top of the well-known inelastic tunneling step 72 is due to nonequilibrium occupations 30,[73][74][75] that we also fully take into account. The enhanced conductance at the cotunneling resonance is due to the two-loop renormalization, including the frequency dependence.…”

Section: Cotunneling Resonance: Gap Renormalization and Reduced Brmentioning

confidence: 99%

Fermionic superoperators for zero-temperature nonlinear transport: Real-time perturbation theory and renormalization group for Anderson quantum dots

2012

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We study electron quantum transport through a strongly interacting Anderson quantum dot at finite bias voltage and magnetic field at zero temperature using the real-time renormalization group (RT-RG) in the framework of a kinetic (generalized master) equation for the reduced density operator. To this end, we further develop the general, finite-temperature real-time transport formalism by introducing field superoperators that obey fermionic statistics. This direct second quantization in Liouville Fock space strongly simplifies the construction of operators and superoperators that transform irreducibly under the Anderson-model symmetry transformations. The fermionic field superoperators naturally arise from the univalence (fermion-parity) superselection rule of quantum mechanics for the total system of quantum dot plus reservoirs. Expressed in these field superoperators, the causal structure of the perturbation theory for the effective time-evolution superoperator kernel becomes explicit. Using the constraints of the causal structure, we construct a parametrization of the exact effective time-evolution kernel for which we analytically find the eigenvectors and eigenvalues in terms of a minimal set of only 30 independent coefficients. The causal structure also implies the existence of a fermion-parity protected eigenvector of the exact Liouvillian, explaining a recently reported result on adiabatic driving [Contreras-Pulido et al., Phys. Rev. B 85, 075301 (2012)] and generalizing it to arbitrary order in the tunnel coupling . Furthermore, in the wide-band limit, the causal representation exponentially reduces the number of diagrams for the time-evolution kernel. The remaining diagrams can be identified simply by their topology and are manifestly independent of the energy cutoff term by term. By an exact reformulation of this series, we integrate out all infinite-temperature effects, obtaining an expansion targeting only the nontrivial, finite-temperature corrections, and the exactly conserved transport current follows directly from the time-evolution kernel. From this new series, the previously formulated RT-RG equations are obtained naturally. We perform a complete one-plus-two-loop RG analysis at finite voltage and magnetic field, while systematically accounting for the dependence of all renormalized quantities on both the quantum dot and reservoir frequencies. Using the second quantization in Liouville space and symmetry restrictions, we obtain analytical RT-RG equations, which can be solved numerically in an efficient way, and we extensively study the model parameter space, excluding the Kondo regime where the one-plus-two-loop approach is obviously invalid. The incorporated renormalization effects result in an enhancement of the inelastic cotunneling peak, even at a voltage ∼magnetic field ∼tunnel coupling . Moreover, we find a tunnel-induced nonlinearity of the stability diagrams (Coulomb diamonds) at finite voltage, both in the single-electron tunneling and inelastic cotunneling regime.

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“…3͑c͒. The elastic cotunneling rate ⌫ B± through the B state for positive ͑ϩ͒ and negative ͑Ϫ͒ current contributes to the linear conductance:14 …”

mentioning

confidence: 99%

Pauli spin blockade in cotunneling transport through a double quantum dot

et al. 2005

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We study spin correlation in a double quantum dot containing a few electrons in each dot ͑around 10͒. Clear current rectification with negative differential conductance is observed in the cotunneling regime, which is well explained by a Pauli spin blockade. The current feature is discussed in connection with exchange singlet-triplet splitting based on two simple models, one of which takes coherent interdot coupling and the other incoherent interdot coupling into account.The two-electron system in a double quantum dot ͑DQD͒ is attractive for studying fundamental spin correlations. The exchange Coulomb interaction between the electrons induces a singlet-triplet ͑ST͒ splitting, which has been discussed as a way to demonstrate spin logic gates ͑NOT, SWAP, etc.͒ and entangled states. 1-3 Spin correlation also leads to a Pauli spin blockade, at which the transport is blocked when the two electrons have a spin triplet correlation. 4 This kind of spindependent tunneling has possible application to a spin-qubit readout. 5 More recently, a Pauli spin blockade with nearly degenerated ST splitting has been employed for studying hyperfine coupling between electron and nuclear spins. 6,7 Besides appearing in the two-electron system, these spin effects may appear generally in a DQD with more than two electrons. In this paper, we investigate the Pauli spin blockade and ST splitting in an effective two-electron DQD containing about 10 electrons in each dot. Pauli spin blockade transport is clearly identified by the current rectification with negative differential conductance ͑NDC͒ in the cotunneling regime, where the ST splitting can be detected with improved resolution. 8 We discuss the cotunneling transport between the effective two-electron states by considering the coherent and incoherent coupling between the dots, which will be helpful for studying voltage-controlled exchange splitting in a DQD.The left ͑L͒ and right ͑R͒ dots in our sample are electrostatically defined in an AlGaAs/ GaAs heterostructure ͑inset of Fig. 1͒. 9 We control the tunneling rate ␥ L ͑␥ R ͒ of the left ͑right͒ barrier separating the left ͑right͒ dot and the source ͑drain͒ electrode and the interdot coupling t c of the central barrier by voltages applied to gates G L͑R͒ and G C , respectively. All experiments were performed using dc current measurement at zero magnetic field ͑unless noted otherwise͒ at an electron temperature of T e ϳ 25 mK ͑similar to the lattice temperature at ϳ25 mK͒. Figure 1 shows a color plot of current I flowing through the double dot as a function of gate voltages V GL and V GR , which change the equilibrium electron numbers ͑n , m͒ in the left and right dots, respectively. Each dot might have accommodated a few electrons ͑around 10͒, but the labeled effective electron numbers n and m in the range from 0 to 2 explain our experiments well. Sequential tunneling current flowing through the dots appears at the corners of the hexagons, where three charge states are energetically degenerated. 10 Current is also visible along some sid...

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Electronic States and Transport Phenomena in Quantum Dot Systems

Cited by 20 publications

References 37 publications

Relaxation Process of Transient Current Through Nanoscale Systems; Density Matrix Calculations

Relaxation Process of Transient Current Through Nanoscale Systems; Density Matrix Calculations

Fermionic superoperators for zero-temperature nonlinear transport: Real-time perturbation theory and renormalization group for Anderson quantum dots

Pauli spin blockade in cotunneling transport through a double quantum dot

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