Equation of motion solutions to Hubbard model retaining Kondo effect

Mizia

Physica Status Solidi (b)

2016

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We consider the extended Hubbard model with included nearest neighbors off‐diagonal correlated hopping interaction. This model is analyzed using the modified equation of motion (EOM) approach with double‐time Green's functions. In modified EOM method we calculate the retarded Green's function of the impurity by differentiating Green's functions over both time variables. The proposed model is used to investigate possibility of ferromagnetism in the itinerant system. We calculate the Curie temperature for different carrier concentrations, state densities with different asymmetry, different values of the Coulomb interaction and correlated hopping interaction. Results of our relatively simple method are compared and agree with the results of previous Quantum Monte Carlo and Modified Perturbation Theory calculations. This legitimates further use of this model in different physical applications, e.g., quantum dots.

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“…As we have shown in our previous articles , for large

U

values the self‐energy given by Eq. is not convergent.…”

Section: The Modelsupporting

confidence: 73%

Section: Introductionmentioning

confidence: 99%

Modified equation of motion approach for metallic ferromagnetic systems with the correlated hopping interaction

Mizia

Physica Status Solidi (b)

2016

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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%

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

Physica Status Solidi (b)

2018

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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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Effect of assisted hopping on spin-dependent thermoelectric transport through correlated quantum dot

Physica B: Condensed Matter

2018