Theoretical Study Of Quantum Effects In The Ground State And Phase Transition Of Nanostructures Based On Si Surface

In the past decades,nanostructures formed on silicon surface have attracted intensive attention due to their many exotic phenomena and great potential applications in many fileds.Figureing out the role of quantum effects?including quantum tunneling,spin-orbit coupling effect,and quantum spin effect,etc?in determining the geometric and electronic characters as well as phase transition mechanism of those silicon-based nanostructures,is one of the frontier hot topics in condensed matter physics.This subject is not only intriguing and challenging from a fundamental scientific point of view but also very important for the potential applications in nanoelectronics,spinelectronics,quantum devices,as well as modern integrated circuit devices.Therefore,in this thesis,based on density functional theory,takeing several nanostructures formed on the reconstructed silicon surface as prototypical models,we investigated the underlying mechanism of different quantum effects in the ground state and phase transition of those nanostructures.The contents of the thesis can be divided into four parts and are listed as follows:1.It has been a long-standing puzzle why buckled dimers of the Si?001?surface appeared symmetric below ²0 K in scanning tunneling microscopy?STM?experiments.Although such symmetric dimer images were concluded to be due to an artifact induced by STM measurements,its underlying mechanism is still veiled.Here,we demonstrate,based on a first-principles density-functional theory calculation,that the symmetric dimer images are originated from the flip-flop motion of buckled dimers,driven by quantum tunneling?QT?.It is revealed that at low temperature the tunnelinginduced surface charging with holes reduces the energy barrier for the flipping of buckled dimers,thereby giving rise to a sizable QT-driven frequency of the flip-flop motion.However,such a QT phenomenon becomes marginal in the tunnelinginduced surface charging with electrons.Our findings provide an explanation for lowtemperature STM data that exhibits apparent symmetric?buckled?dimer structure in the filled-state?empty-state?images.2.Using first-principles density-functional theory?DFT?calculations with/without including the spin-orbit coupling?SOC?,we systematically investigate the?4/3?-monolayer structure of Pb on the Si?111?or Ge?111?surface within the two competing structural models termed the H₃ and T₄ structures.We find that the SOC influences the relative stability of the two structures in both the Pb/Si?111?and the Pb/Ge?111?systems,i.e.,our DFT calculation without including the SOC predicts that the T₄ structure is energetically favored over the H₃ structure by ?E= 25 me V for Pb/Si?111?and 22 me V for Pb/Ge?111?,but the inclusion of SOC reverses their relative stability as ?E =-12 and-7 me V,respectively.Our analysis shows that the SOCinduced switching of the ground state is attributed to a more asymmetric surface charge distribution in the H₃ structure compared to the T₄ structure,which is associated with the hybridization of the Pb px,py,and pz orbitals.This asymmetry of surface charge distribution gives rise to a relatively larger Rashba spin splitting of surface states as well as a relatively larger pseudogap opening in the H₃ structure.By the nudged elasticband calculation,we obtain a sizable energy barrier from the H₃ to the T₄ structure as ⁰.59 and ⁰.27 e V for Pb/Si?111?and Pb/Ge?111?,respectively.Based on the predicted thermodynamics and kinetics of Pb/Si?111?and Pb/Ge?111?,we suggest not only the coexistence of the two energetically competing structures at low temperatures,but also the order-disorder transition at high temperatures.3.The Sn overlayer on the Si?111?surface has been considered as a prototypical system for exploring twodimensional?2D?correlated physics on the triangular lattice.Most of the previous theoretical studies were based on the presumption that the surface state dominantly originates from Sn dangling-bond?DB?electrons,leading to a strongly correlated 2D electronic system.By contrast,our density-functional theory calculations show that the Sn DB state significantly hybridizes with Si substrate states to form a resonant state.The strong resonance between the Sn 5pz and Si 3pz orbitals facilitates the recently observed antiferromagnetic order through superexchange interactions,giving rise to a band-gap opening.It is thus demonstrated that the insulating ground state of Sn/Si?111?can be characterized as a Slater-type insulator via band magnetism.4.Here,the energetics and kinetic properties of a single Cu atom and previously reported Cu magic clusters on the Si?111?-?7×7?surface are re-examined by the stateof-the-art first-principles calculations based on density-functional theory.First of all,the diffusion path and high diffusion rate of a Cu atom on the Si?111?-?7×7?surface are identified by mapping out the total potential energy surface of the Cu atom as a function of its positions on the surface,supporting previous experimental hypothesis that the apparent triangular light spots observed by scanning tunneling microscopy?STM?are resulted from a single Cu atom frequently hopping among adjacent adsorption sites.Furthermore,our findings confirm that in the low coverage of 0.15 monolayer?ML?the previously proposed hexagonal ring-like Cu6 cluster configuration assigned to the STM pattern is considerably unstable.Importantly,the most stable Cu6/Si?111?complex also possesses distinct simulated STM pattern with the experimentally observed ones.Instead,an energetically preferred solid-centered Cu7 structure exhibits a reasonable agreement between the simulated STM patterns and the experimental images.Therefore,the present findings convincingly rule out the tentative six-atom model and provide new insights into understanding the well-defined Cu nanocluster arrays on the Si?111?-?7×7?surface.