A Theoretical Study On Kondo Systems

One of the significant areas in condensed matter physics concerns strongly correlated systems.Kondo systems contain heavy-fermion?HF?compounds and the single-impurity Kondo systems.Due to their importance in strongly correlat-ed systems,Kondo systems have been extensively researched.In recent years,the water-intercalated sodium cobaltates Na_xCo₂·y H₂O was found in layered metal oxides Na_xCoO₂through a chemical oxidation process and the families of organic charge-transfer salts?-?ET?₂X and Pd?dmit?₂are two examples to exhibit un-conventional superconductivity.The essential physics of these materials lies on the geometrically frustrated triangular lattice.These phenomena motivated us to investigate the pairing symmetry of the Kondo-Heisenberg model?KHM?on triangular lattice.Among quantum critical heavy-fermion materials YbRh₂Si₂,its magnetic field dependent thermopower,thermal conductivity,resistivity and Hall effect shows three transitions at high fields and the Lifshitz transitions are argued to be their origin.Therefore,the possibility of Lifshitz transition on tri-angular lattice should be investigated firstly.We investigate a modified Anderson model at the large-N limit,where Coulomb interaction is replaced by Sachdev-Ye-Kitaev random interaction,and we call it Sachdev-Ye-Kitaev-Anderson model?SYKAM?.The resistivity of conduction electron?_chas a minimum value around temperature T^?,which is similar to the Kondo system,but the impurity electron's density of state A_d???demonstrates no sharp-peak like Kondo resonance around the Fermi surface.This provides a counterintuitive example where resistivity minimum exists without Kondo resonance.In this thesis,we concentrate on KHM and SYKAM,and we use the fermionic large-N mean-field method and the large-N limit perturbation theory.A brief summary of results is listed below:Among the triangular lattice HF superconductor,it is found that the pair-ing symmetry favours an extended s-wave for small Heisenberg antiferromagnetic coupling and high conduction electron density but a chiral d+id-wave for large Heisenberg antiferromagnetic coupling and low conduction electron density.De-pending on the strength of the interactions,the transition between these two pairing symmetries is found to be first-order.On the triangular lattice HF quantum critical materials,we find that the Heisenberg antiferromagnetic interaction induces twice Fermi surface?FS?topol-ogy change.The effective mass enhancement of the triangular lattice is smooth to lead to the continuous quantum phase transition around the Lifshitz transi-tion points.The Kondo coupling,the Heisenberg antiferromagnetic correlation coupling and the ratio of the tunneling amplitude of f-electron versus conduction electron's influence the shape-line of the differential conductance theoretically.On the SYKAM,it is shown that the system is a Fermi liquid at T<T^?,and becomes a non-Fermi liquid at T>T^?.The renormalization group analysis confirms the crossover from the Fermi liquid to the non-Fermi behavior.The con-duction electrons'resistivity has a minimum at temperature T^?,which is similar to Kondo effect,but the impurity electron's density of the state does not have the sharp Kondo resonance peak around FS.It means that Kondo resonance is the intrinsical characteristic of Kondo effect,where Kondo effect has two char-acteristics,i.e.resistivity minimum and Kondo resonance.Resistivity minimum may not has the relation to Kondo screening,but Kondo resonance means Kondo screening and resistivity minimum.Our results may provide a possible scenario to understand the pairing sym-metry of the HF superconductivity and the FS topology and the quantum critical point in HF compounds,and also provide an alterative example showing resistiv-ity minimum in condensed matter physics,which is helpful to deepen understand the single-impurity Kondo problem.With the development of experimental tech-niques,our results may be achieved in near-future experiments of Kondo systems.