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Quantumness of Electron Transport in Quantum Dots: Nonequilibrium Green's Function Approach

Md. Manirul Ali, Thingujam Yaiphalemba Meitei, Saikumar Krithivasan, Arijit Sen

Published Jan 1, 2024• 0 citations
Publisher
DOI
10.2139/ssrn.4748218

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We investigate the electronic transport through a single-level quantum-dot which is capacitively coupled to a charge-qubit. By employing the method of nonequilibrium Green's functions, we calculate the electric current through quantum dot at finite bias voltages. The Green's functions and self-energies of the system are calculated perturbatively and self-consistently to the second order of interaction between the quantum-dot and the charge-qubit by employing the Majorana fermion representation for isospin operators of the qubit. Our results show that in the particle-hole symmetric situation, the electric current of the QD exhibits a unitary linear conductance at low bias voltage and at the higher bias voltage it has a nonlinear dependence on the bias voltage. Moreover, we find that at some appropriate parameter regimes, the current through the QD as a function of gate voltage, at a fixed bias voltage shows bistability.
This review deals with the state of the art and perspectives of description of nonequilibrium many-body systems using the nonequilibrium Green's function (NGF) method. The basic aim is to describe time evolution of the many-body system from its initial state over its transient dynamics to its long time asymptotic evolution. First, we discuss basic aims of transport theories to motivate the introduction of the NGF techniques. Second, this article summarizes the present view on construction of the electron transport equations formulated within the NGF approach to nonequilibrium. We discuss incorporation of complex initial conditions to the NGF formalism, and the NGF reconstruction theorem, which serves as a tool to derive simplified kinetic equations. Three stages of evolution of the nonequilibrium, the first described by the full NGF description, the second by a non-Markovian generalized master equation and the third by a Markovian master equation will be related to each other.