Abstract

We analyze the universal transport properties of a strongly interacting quantum dot in the Kondo regime when the quantum dot is placed in an external magnetic field. The quantum dot is described by the asymmetric Anderson model with the spin degeneracy removed by the magnetic field resulting in Zeeman splitting. Using an analytical expression for the tunneling density of states found from a Keldysh effective field theory, we obtain in the whole energy range the universal differential conductance and analytically demonstrate its Fermi-liquid and logarithmic behavior at low and high energies, respectively, as a function of the magnetic field. We also show results on the zero-temperature differential conductance as a function of the bias voltage at different magnetic fields as well as results on finite-temperature effects out of equilibrium and at a finite magnetic field. The modern nonequilibrium experimental issues of the critical magnetic field, at which the zero bias maximum of the differential conductance starts to split into two maxima, as well as the distance between these maxima as a function of the magnetic field, are also addressed.

Highlights

  • We analyze the universal transport properties of a strongly interacting quantum dot in the Kondo regime when the quantum dot is placed in an external magnetic field

  • Important nonequilibrium issues that have been addressed in experiments [17, 18] on the Kondo effect in an external magnetic field are: (i) Kondo universality; (ii) the critical magnetic field at which the zero bias maximum of the differential conductance starts to split into two maxima; (iii) the distance between these maxima as a function of the magnetic field; and (iv) the high-field limit of this distance

  • We address the behavior of the Kondo state in an external magnetic field both in equilibrium and nonequilibrium

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Summary

Theoretical model

To describe the strongly interacting QD, we employ the single-impurity Anderson model [34]. Within the SIAM, this means that the Kondo resonance takes place when the QD has one electron This is achieved when the electron–electron interaction U exceeds the energy (see below) resulting from the QD-contacts coupling. The total Hamiltonian of this, in general nonequilibrium, problem is the sum of H QD, H C and H T given by equations (7), (3) and (8), respectively This Hamiltonian together with the constraint in equation (6) represents the theoretical model able to describe the essential behavior of the zero-bias anomaly arising due to the Kondo effect in the presence of an external magnetic field

Keldysh field integral solution and its asymptotics
Full Hilbert space
Universal results in the whole energy range
Conclusion
Full Text
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