^{1}, Mahn-Soo Choi

^{2}, I. V. Krive

^{3}and J. M. Kinaret

^{4}

### Abstract

We study theoretically the current-voltage characteristics, shot noise, and full counting statistics of a quantum wire double-barrier structure. We model each wire segment by a spinless Luttinger liquid. Within the sequential tunneling approach, we describe the system’s dynamics using a master equation. We show that at finite bias the nonequilibrium distribution of plasmons in the central wire segment leads to increased average current, enhanced shot noise, and full counting statistics corresponding to a super-Poissonian process. These effects are particularly pronounced in the strong interaction regime, while in the noninteracting case we recover results obtained earlier using detailed-balance arguments.

This work has been supported by the Swedish Foundation for Strategic Research through the CARAMEL consortium, STINT, the SKORE-A program, the eSSC at Postech, and the SK-Fund. J. U. Kim acknowledges partial financial support from Stiftelsen Fru Mary von Sydows, född Wijk, donationsfond. I. V. Krive gratefully acknowledges the hospitality of the Department of Applied Physics at Chalmers University of Technology.

I. INTRODUCTION

II. FORMALISM

A. Model and Hamiltonian

B. Electron transition rates

C. Plasmon relaxation process in the quantum dot

D. Matrix formulation

III. STEADY-STATE PROBABILITY DISTRIBUTION OF NONEQUILIBRIUM PLASMONS

IV. AVERAGE CURRENT

V. CURRENT NOISE

A. Qualitative discussions

B. Two-state model

C. Three-state model

Interaction strength dependence

Interaction strength dependence

D. Numerical results

E. Interplay between several charge states and plasmon excitations near

VI. FULL COUNTING STATISTICS

A. Two-state process;

B. Four-state process;

C. Numerical results

Interaction strength dependence

Interaction strength dependence

VII. CONCLUSIONS

### Key Topics

- Plasmons
- 124.0
- Tunneling
- 41.0
- Quantum dots
- 26.0
- Strong interactions
- 20.0
- Poisson's equation
- 17.0

## Figures

Model system. Two long wires are adiabatically connected to reservoirs, and a short wire is weakly coupled to the two leads. Tunneling resistances at junction points and are , and the junction capacitances are considered equal . The quantum dot is capacitively coupled to the gate electrode.

Model system. Two long wires are adiabatically connected to reservoirs, and a short wire is weakly coupled to the two leads. Tunneling resistances at junction points and are , and the junction capacitances are considered equal . The quantum dot is capacitively coupled to the gate electrode.

The occupation probability as a function of the mode energy . The energy is an abbreviation for , the bias , the asymmetry parameter , and . Two analytic approximations, Eq. (26) (solid curve) and Eq. (B13) (dotted curve), are fitted to the probability distribution of the charge mode (circlets). The interaction parameter is (a) and 0.5 (b). In the inset the case of symmetric junctions is plotted with the same conditions.

The occupation probability as a function of the mode energy . The energy is an abbreviation for , the bias , the asymmetry parameter , and . Two analytic approximations, Eq. (26) (solid curve) and Eq. (B13) (dotted curve), are fitted to the probability distribution of the charge mode (circlets). The interaction parameter is (a) and 0.5 (b). In the inset the case of symmetric junctions is plotted with the same conditions.

Average current as a function of the bias voltage and LL interaction parameter for (highly asymmetric junctions) with no plasmon relaxation (, solid lines) or with fast plasmon relaxation (, dashed lines). The bias voltage is normalized by the charging energy and the current is normalized by the current at with no plasmon relaxation for each . Other parameters are , .

Average current as a function of the bias voltage and LL interaction parameter for (highly asymmetric junctions) with no plasmon relaxation (, solid lines) or with fast plasmon relaxation (, dashed lines). The bias voltage is normalized by the charging energy and the current is normalized by the current at with no plasmon relaxation for each . Other parameters are , .

Fano factor as a function of the gate charge and LL interaction parameter for (highly asymmetric junctions) at .

Fano factor as a function of the gate charge and LL interaction parameter for (highly asymmetric junctions) at .

Fano factor as a function of the gate charge for symmetric junctions at voltage with no plasmon relaxation. Numerical results (solid lines) versus analytic results with three states, Eq. (41) (dashed lines) for , 0.5, and 1.0.

Fano factor as a function of the gate charge for symmetric junctions at voltage with no plasmon relaxation. Numerical results (solid lines) versus analytic results with three states, Eq. (41) (dashed lines) for , 0.5, and 1.0.

Fano factor as a function of the gate charge and LL interaction parameter for (highly asymmetric junctions) at , with no plasmon relaxation (a) and with fast plasmon relaxation (b).

Fano factor as a function of the gate charge and LL interaction parameter for (highly asymmetric junctions) at , with no plasmon relaxation (a) and with fast plasmon relaxation (b).

Fano factor as a function of the bias and LL interaction parameter for (highly asymmetric junctions) at : with no plasmon relaxation (a) and with fast plasmon relaxation (b).

Fano factor as a function of the bias and LL interaction parameter for (highly asymmetric junctions) at : with no plasmon relaxation (a) and with fast plasmon relaxation (b).

Contour of Eq. (55). The arguments of are along the branch cuts , , , and , respectively.

Contour of Eq. (55). The arguments of are along the branch cuts , , , and , respectively.

Probability with no plasmon relaxation during the time , where is the particle current at with no plasmon relaxation : for symmetric junctions (a) and for highly asymmetric junctions (b). Here , , and . The insets show a cross-sectional image of (solid line) as a function of and the reference distribution function in Eq. (63) (dashed line) (a) and the Poisson distribution in Eq. (65) (dashed line) (b), at (I), (II), and (III).

Probability with no plasmon relaxation during the time , where is the particle current at with no plasmon relaxation : for symmetric junctions (a) and for highly asymmetric junctions (b). Here , , and . The insets show a cross-sectional image of (solid line) as a function of and the reference distribution function in Eq. (63) (dashed line) (a) and the Poisson distribution in Eq. (65) (dashed line) (b), at (I), (II), and (III).

The probability that electrons have passed through the right junction during the time , where is the particle current with no plasmon relaxation ; with no plasmon relaxation (a) and with fast plasmon relaxation (b). Here , , , and .

The probability that electrons have passed through the right junction during the time , where is the particle current with no plasmon relaxation ; with no plasmon relaxation (a) and with fast plasmon relaxation (b). Here , , , and .

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