Numerical RG Investigation of Kondo Effect in Ferromagnetic Graphene

Author:Li Gao Yang

Supervisor:luo hong gang fang tie feng


Degree Year:2019





Quantum impurity model is the coupling between a system with large degrees of freedom,called bath,and a system with small degrees of freedom,called impurity.Both systems are governed by the quantum mechanics.The coupling between different ener-gy scales in these systems usually causes the so-called infrared divergence,making the traditional perturbative methods fail to grasp the important physical interactions.Non-perturbative methods must be developed to address these systems,which brings huge challenge to theoretical researches.Investigating on the quantum impurity problems is one of the basis aspects in studying condensed matter physics.Various quantum im-purity systems are prepared in the last 30 years by experimentalists thanks to the rapid growth of micro-nano technology.These systems include the magnetic atom absorbed on the surface of metal or graphene,single molecule connected to metal lead,quantum dot(QD)etc.Thermodynamic and transport properties in these systems usually behave abnormally due to strong many-body correlation effects.These properties make quan-tum impurity model a perfect playground to inspect many-body theories and many-body problems.Furthermore,investigation on quantum impurity models helps understand-ing the fundamental of many-body physics,which in turn promotes the application of micro-nano technologies.Kondo effect is one of the most important many-body effects in condensed mat-ter physics.It describes an effect that the local moments provided by impurity being screened by conduction electrons under specific conditions.When the impurity local moments are screened by conduction electrons,a many-body ground state is developed in system,the conduction electrons on Fermi surface are strongly scattered by impuri-ty via a resonace state formed by impurity and electrons.This resonance changes the thermodynamic and transport properties of the system dramatically.We consider here one specific quantum impurity system,the magnetic impurity absorbed on ferromagnetic graphene,and study the Kondo effect in this system.The nontrivial band dispersion of ferromagnetic graphene gives rise to interesting Kondo physics different from that in conventional ferromagnetic materials.The adatom ab-sorbed on the surface of graphene provides local moments,conduction electrons are provided by graphene.A metal gate could be placed on graphene to tune the Fermi surface of the conduction electrons.Moreover,ferromagnetism in graphene could be induced by a magnetic insulator layer.We study the cooperative of competitive relation-ship between ferromagnetism and Kondo correlation in this system.We can also place the whole setup in a magnetic field to investigate the compensation effects of magnetic fieldSome interesting results are achieved by using the full density matrix numerical renormalization group method.Kondo resonance is induced when ferromagnetism is introduced in neutral graphene,in which there is no Kondo resonance.The resonance in impurity spectral function is different from that of the spin-splitted Kondo peaks in QD connected to ferromagnetic metal leads,on the contrary,it’s a shoulder-like struc-ture.The shoulder-like Kondo split could be enhanced to a full resonance state with a sharp Kondo peak at Fermi surface or suppressed to a state totally without Kondo res-onance by a compensation field.The calculation of Kondo temperate dependence on ferromagnetism h implies that ferromagnetism is in favor of Kondo singlet,which is contradictory to conventional understanding of the relationship between ferromag-netism and Kondo resonanceWe further find a special regime where ferromagnetism is introduced in n/p doped graphene.In this regime the spectral function of impurity behave abnormally,with Kondo shoulder on one spin exponent but absent on the other.Since it is similar to the behavior in half-metal where only one spin species contributes to the transport in system,we call the regime Kondo half-metal regime.Similarly,the half-metal behavior can be compensated by an external magnetic field.When the critcal compensation field Bc is reached,the Kondo shoulder on one spin is again compensated to a full Kondo resonance state with a sharp Kondo peak on Fermi surface,while the other spin spectral function is totally trivial near Fermi surface.This anormal behavior is important for applications of spinelectronics