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

## TL;DR

This paper investigates the nonequilibrium Kondo effect in a graphene-coupled quantum dot under magnetic fields, revealing unique behaviors due to graphene's linear dispersion and providing analytical tools and experimental proposals for future studies.

## Contribution

It introduces an analytical approach to study the Kondo effect in graphene-coupled quantum dots, highlighting the impact of Dirac points and magnetic fields on Kondo phenomena.

## Key findings

- Kondo temperature vanishes near particle-hole symmetry and Dirac point
- Kondo resonance is absent at zero chemical potential due to graphene's dispersion
- Analytical formulas for self-energies and Kondo temperature are developed

## 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.