Alternative equation of motion approach applied to transport through a quantum dot

Górski, Grzegorz; Mizia, Jerzy; Kucab, Krzysztof

doi:10.1016/j.physe.2015.05.021

Cited by 9 publications

(12 citation statements)

References 34 publications

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“…Using the AEOM method, we obtain the full Green's function

\hat{G} true(ω true)

for which we define the spin‐dependent spectral functions of the quantum dot

ρ_{↑} true(ω true) = - \frac{1}{π} Im 〈 〈 d_{↑}; d_{↑}^{normal†} 〉 〉_{normalω} = - \frac{1}{π} Im {true \overset{italicG}{true}}_{11} true(ω true)

and

ρ_{↓} true(ω true) = - \frac{1}{π} Im 〈 〈 d_{↓}; d_{↓}^{normal†} 〉 〉_{normalω} = - \frac{1}{π} Im {true \overset{italicG}{true}}_{33} true(ω true)

…”

Section: Numerical Resultsmentioning

confidence: 99%

“…For the correlated quantum dot the maxima are located near

ω \approx \pm 2 t_{m ↑} z_{↑}

, where the re‐normalized factor

z_{↑}

is given by

z_{↑}^{- 1} = 1 - {\frac{\partial Σ_{11} (ω)}{\partial ω} |}_{ω \to 0}

, where

Σ_{11}

is the Coulomb correlation self‐energy for the electrons with ↑ spins. The Coulomb correlation self‐energy can be calculated with the use of the AEOM method . As Liu and Baranger stated, the spectral function with three peaks is “showing clearly the presence of the Majorana zero mode.”…”

Section: Numerical Resultsmentioning

confidence: 99%

“…For the correlated system ( U > 0) the full Green's function has to contain the correlated self‐energy, which describes the electron–electron interaction on the dot. To obtain the full quantum dot Green's function,

\hat{G} true(ω true)

, which characterizes our correlated system, we employ the alternative equation of motion method (AEOM) and modified perturbation theory …”

Section: Theoretical Descriptionmentioning

confidence: 99%

See 2 more Smart Citations

The Spin‐Dependent Coupling in the Hybrid Quantum Dot–Majorana Wire System

Górski

Kucab

2018

Physica Status Solidi (b)

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The transport properties of a quantum dot coupled to two metallic contacts and side‐coupled to a topological superconductor wire hosting Majorana zero energy modes (Majorana wire) have been studied. The spin‐dependent tunneling amplitude between quantum dot and Majorana wire has been assumed. The polarization of tunneling amplitudes causes the polarization of spin‐dependent zero‐bias conductance, but the total conductance of a quantum dot depends very weakly on the polarization of tunneling amplitudes. The complex behavior of the zero‐bias anomaly of conductance in the presence of an external magnetic field is shown. The zero‐bias conductance peaks at high external magnetic field can be the fingerprint of the presence of Majorana fermions.

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“…Using the AEOM method, we obtain the full Green's function

\hat{G} true(ω true)

for which we define the spin‐dependent spectral functions of the quantum dot

ρ_{↑} true(ω true) = - \frac{1}{π} Im 〈 〈 d_{↑}; d_{↑}^{normal†} 〉 〉_{normalω} = - \frac{1}{π} Im {true \overset{italicG}{true}}_{11} true(ω true)

and

ρ_{↓} true(ω true) = - \frac{1}{π} Im 〈 〈 d_{↓}; d_{↓}^{normal†} 〉 〉_{normalω} = - \frac{1}{π} Im {true \overset{italicG}{true}}_{33} true(ω true)

…”

Section: Numerical Resultsmentioning

confidence: 99%

“…For the correlated quantum dot the maxima are located near

ω \approx \pm 2 t_{m ↑} z_{↑}

, where the re‐normalized factor

z_{↑}

is given by

z_{↑}^{- 1} = 1 - {\frac{\partial Σ_{11} (ω)}{\partial ω} |}_{ω \to 0}

, where

Σ_{11}

Section: Numerical Resultsmentioning

confidence: 99%

\hat{G} true(ω true)

, which characterizes our correlated system, we employ the alternative equation of motion method (AEOM) and modified perturbation theory …”

Section: Theoretical Descriptionmentioning

confidence: 99%

See 1 more Smart Citation

The Spin‐Dependent Coupling in the Hybrid Quantum Dot–Majorana Wire System

Górski

Kucab

2018

Physica Status Solidi (b)

Self Cite

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“…For 1 d n = in this approach the Abrikosov-Suhl peak disappear. Less frequently used method in solving the EOM is differentiating the double-time Green's function over the second time ( ' t ).In the energy representation this leads to the following equation [7]:…”

Section: The Modelmentioning

confidence: 99%

“…The weak point of standard equation of motion (EOM) approach is that it does not describe the Kondo state in the particle-hole symmetric case. We use modified (EOM) approach [7] in which we differentiate Green functions over both time variables. This differs from the standard EOM method where the time derivative was taken only over primary time variable.…”

Section: Introductionmentioning

confidence: 99%

Irreducible Green Functions Method Applied to Nanoscopic Systems

Górski

2016

Acta Phys. Pol. A

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The equation of motion method for the Green functions is one of the tools used in the analysis of quantum dot system coupled with the metallic and superconducting leads. We investigate modified equation of motion, based on differentiation of double-time temperature dependent Green functions both over the primary time t and secondary time t . Our equation of motion approach allows us to obtain the Abrikosov-Suhl resonance in the particle-hole symmetric case and also in the asymmetric cases. We will apply the irreducible Green functions technique to analyses of the equation of motion applied to the dot system. This method gives a workable decoupling scheme breaking the infinite set of the Green function equations. We apply this technique to calculate the density of the states and the differential conductance of single-level quantum dot with the Coulomb repulsion attached to one metallic and one superconducting leads (N-QD-SC). Our results are compared with the previous calculations.

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