Theoretical Investigations Of Strong Correlation Effects And Novel Quantum Phenomena In Triangular Lattice Systems

Strongly correlated system is one of the main research contents in the field of con-densed matter physics.In addition to the interactions between electrons,the spin-orbital coupling and electron-phonon coupling also have a great impact on the properties of solid state materials.In real materials,these interactions may exist at the same time and compete or cooperate with each other to produce novel quantum phenomena.For example,the spin-orbital Mott insulator originate from the interplay between electron interaction and the spin-orbital coupling;the coexistence of charge density wave with the Mott insulator resulted from the interplay between electron correlation and electron-phonon coupling.Of particular concern is the spin-orbital Mott insulator,which has been shown to be a promising approach to explore exotic quantum spin states such as quantum spin liquid.On the other hand,doping is one of the important means to change the physical properties of materials,and doping Mott insulators will produce very rich physical phenomena.In this dissertation,we first study the Heisenberg-Kitaev-? model defined on the triangular lattice where the direction-dependent exchanges may originate from the spin-orbital coupling;and secondly,we carry out theoretical study of the novel phenomena observed in 1T-TaS₂ upon surface alkali doping.1.We carry out a comprehensive study of the Heisenberg-Kitaev-? model on the triangular lattice covering the whole parameter region,using the combination of the exact diagonalization,classical Monte Carlo and analytic methods,with an emphasis on the effects of the?term.We find nine magnetically ordered phases and a phase ascribed to be a QSL.The nine ordered magnetic phases consist of three stripe phases(dubbed Stripe-A,Stripe-B and Stripe-C),three FM phases(dubbed FM-A,FM-B and FM-C),one 120?Néel phase,one Dual Néel phase and one modulated stripe phase.The difference between the three stripe phases and the three FM phases is that they have different magnetic moment directions.For the 120?Néel,Dual Néel and Stripe-A phases that already exist in the Heisenberg-Kitaev model,we find they are robust against the introduction of the?interaction.Interestingly,the FM-A and Stripe-B only exist in the ?=0 limit and an infinitesimal?interaction will induce phase transitions.Depending on the sign of the?interaction,the FM-A phase transits into the FM-B(?>0) and FM-C(?<0) with different spin orientations.Similarly,the Stripe-B phase transits into Stripe-C(?>0) and Stripe-A(?<0) phases.Our study of the global phase diagram on a generic spin model paves the way for future studies of a large group of triangular transition-metal materials with an appreciable spin-orbital coupling and electronic correlations.2.In this study,the electron doping is achieved by depositing K atoms onto the surface of 1T-TaS₂.Upon electron doping,additional excitations appear inside the Mott gap.Interestingly,the in-gap excitation is near the top of the lower Hubbard band,in contrast to a conventional electron-doped Mott insulator where it is beneath the upper Hubbard band.To account for this novel phenomenon,we carry out theoretical study on 1T-TaS₂ with surface alkali doping.With the presence of the long-range CDW order in mind,we expect that every Star-of-David has only one half-filled active orbit.At the meantime,the electron concentration for the Star-of-David's with K⁺ ions is larger than those without K⁺ ions due the Coulomb attraction of the positive charge of K⁺ ions,which is equivalent to the decrease of the effective on-site Hubbard-U.Based on these considerations,we construct a single-band site-dependent Hubbard model.We calculate the electron local density of states by using the cluster perturbation theory.The theoretical results are qualitatively consistent with the experimental observation.This study paves the way toward the understanding of the correlation between a CDW and Mott insulators in transition metal dichalcogenides.