Nonequilibrium Kondo effect in a graphene-coupled quantum dot in the presence of a magnetic field

Abstract

Quantum dots connected to larger systems containing a continuum of states like charge reservoirs allow the theoretical study of many-body effects such as the Coulomb blockade and the Kondo effect. Here, we analyze the nonequilibrium Kondo effect and transport phenomena in a quantum dot coupled to pure monolayer graphene electrodes under external magnetic fields for finite on-site Coulomb interaction. The system is described by the pseudogap Anderson Hamiltonian. We use the equation of motion technique to determine the retarded Green's function of the quantum dot. An analytical formula for the Kondo temperature is derived for electron and hole doping of the graphene leads. The Kondo temperature vanishes in the vicinity of the particle-hole symmetry point and at the Dirac point. In the case of particle-hole asymmetry, the Kondo temperature has a finite value even at the Dirac point. The influence of the on-site Coulomb interaction and the magnetic field on the transport properties of the system shows a tendency similar to the previous results obtained for quantum dots connected to metallic electrodes. Most remarkably, we find that the Kondo resonance does not show up in the density of states and in the differential conductance for zero chemical potential due to the linear energy dispersion of graphene. An analytical method to calculate self-energies is also developed which can be useful in the study of graphene-based systems. Our graphene-based quantum dot system provides a platform for potential applications of nanoelectronics. Furthermore, we also propose an experimental setup for performing measurements in order to verify our model.

Phonon-Assisted Tunneling through Quantum Dot Systems Connected to Majorana Bound States

“…The dressed lesser (greater) Green’s function is calculated by employing the Keldysh equation with the use of corresponding lesser (greater) self-energy . Thus, the current given in relation ( 7 ), at finite temperature, reads [ 60 ] The dressed retarded Green’s functions of the QD, and , in Equation ( 11 ) are calculated by employing the equation of motion technique [ 60 , 72 ]: with . Note that if , the retarded Green’s functions given by Equation ( 12 ) reduce to the results of [ 56 ].…”

Quantum transport through a quantum dot side-coupled to a Majorana bound state pair in the presence of electron-phonon interaction

“…In this section, we calculate the dot retarded Green's functions for arbitrary values of ε M , λ 1 and λ 2 by using the EOM technique. In order to do this, we define the retarded Green's function for fermionic operators A and B as A(t)|B(0) r t = −iθ(t) {A(t), B(0)} where θ(t) is the Heaviside function [141][142][143]. The Fourier transform for A(t)|B(0) r t is given by A|B r ε .…”

“…The Fourier transform for A(t)|B(0) r t is given by A|B r ε . We write down the EOM for the retarded Green's function in energy space as ε + A|B r ε + [ Hel , A]|B r ε = {A, B} where ε + = ε + iδ with δ, a positive infinitesimal [141][142][143]. We introduce the electron-electron and electron-hole retarded Green's functions for the dot as Gr The EOM for Gr d11 (ε) is expressed as…”