Quasiparticle Interference Effect In Semi-dirac Electron System

The low-energy dispersion around a two-dimensional（2D）semi-Dirac point（SDP）is linear in one momentum direction and parabolic in the perpendicular direction.This highly anisotropic band structure gives SD electrons the properties of both Dirac electrons and Schr¨odinger electrons.Meanwhile,SD electrons also exhibit some unique new characteristics,such as the power-law with index 2/3in Landau-level.Quasi-particle interference（QPI）induced by disorder gives an oscillation pattern of the local density of states（LDOS）in the vicinity of the imperfections,i.e.,the Friedel oscillations.Those LDOS oscillations can be directly probed using the scanning tunneling microscope,and the information of the Fermi surface can be extracted from the LDOS.The decay index of Friedel oscillation is different for different electronic systems or different types of disorder.For example,in 2D system with isotropic Dirac points such as graphene or the surface states of three dimensional topological insulators,the Friedel oscillations of the LDOS near a nonmagnetic impurity or a line defect are predicted to show an r^-2or r^-3/2asymptotic power-law decay,which is much faster than r^-1or r^-1/2in conventional two-dimensional electron gas,with r the distance from the imperfection.These decay indexes serve as fingerprints to characterize related physical systems.In this dissertation,we study the QPI effect when there are point impurities or line defects in the SD system,which is divided into the following chapters:We theoretically study the power-law decay behavior of the local density of states（LDOS）oscillations near a line defect in system with semi-Dirac points by using a low-energy k·p Hamiltonian.We find that the LDOS oscillations are strongly anisotropic and sensitively depend on the orientation of the line defect.We analytically obtain the decay indexes of the LDOS oscillations near a line defect running along different directions by using the stationary phase approximation.Specifically,when the line defect is perpendicular to the linear dispersion direction,the decay index is-5/4 whereas it becomes-1/4 if the system is gapped,both of which are different from the decay index-3/2 in isotropic Dirac systems.This unique decay index originates from the unique anisotropic band structure around SDP.In contrast,when the line defect is perpendicular to the parabolic dispersion direction,the decay index is always-1/2 regardless of whether the system is gapped or not,which is the same as that in a conventional semimetal because both of them have a parabolic dispersion.In general,when the defect runs along an arbitrary direction,the decay index sensitively depends on the incident energy for a certain orientation of the line defect.It varies from-5/4 to-1/2 due to the absence of strict stationary phase point.Our results indicate that the decay index-5/4 provides a fingerprint to identify semi-Dirac points in 2D electron systems.Based on the low-energy effective k·p Hamiltonian,we study the power-law decay behavior of the LDOS oscillations near a line defect in monolayer black phosphorus（BP）.We find that the power-law of LDOS oscillations is isotropic and independent on the orientation of the line defect.We first calculate the LDOS near a line defect running along different directions based on the two-band model.The fitted results all give a power-law with decay index-1/2,which is the same as the result in the conventional two-dimensional electron gas.Using the stationary phase approximation method combined with the single-band model,we analyti-cally obtain that the power-law of LDOS is-1/2,independent of the direction of the defect.This result originates from the fact that the low-energy dispersion of BP is parabolic in all directions.Our results show that the highly anisotropic BP also has isotropic properties,providing further understanding of the electronic structure of BP.Based on the tight-binding model of anisotropic honeycomb lattice,we study the impurity scattering effect in semi-Dirac system.Using the T matrix approxi-mation method combined with Green’s function,we obtain the LDOS induced by a single impurity has an elliptical contour around the semi-Dirac point,and the scat-tering mainly occurs on the contour.In real space,the power-law index of Friedel oscillation is anisotropy.For the direction of linear dispersion,the decay index is-1/2,which is different from the result of the isotropic Dirac system and the con-ventional two-dimensional electron gas.For the direction of parabolic dispersion,the decay index is-1,which is consistent with the result of conventional two-dimensional electron gas.For the system without a gap,the Hamiltonian satisfies the chiral symmetry,and impurity scattering will induce zero-energy defect state,and the stronger the impurity potential,the larger the DOS corresponding to the defect state.For the system with a gap,the chiral symmetry of the Hamiltonian is broken,and the defect state deviates from the zero-energy position.