Theoretical Study Of Multiple Dirac Cones And High Carrier Mobility In Two-dimensional Materials

Graphene,a two-dimensional(2D)honeycomb framework of sp2-hybridized carbon atoms,is the most representative 2D Dirac material.It displays a linear energy-momentum dispersion relationship(referred to as Dirac cones)near the Fermi level with the valence and conduction bands meeting at a single point(Dirac point).These Dirac cones originate from the pz orbitals,which constitute a conjugated ?orbital throughout the graphene,giving rise to many unique characteristics,such as high electronic and thermal conductivity,large mechanical strength,and so on.The carriers near the Dirac cones have high mobilities(?1/300 of the velocity of light),which hold great promise in building high-speed nanoscale electronic devices.Also,many theoretical and experimental studies indicate that Dirac cones in graphene can lead to some interesting scenarios,such as massless Dirac fermions,quantum Hall effect,and topological aspects.The detect of Hawking evaporation of gravitational black holes(BHs)is prohibited because of the extremely low Hawking temperature.However,the Coulomb field and electrostatic interaction can simulate the gravitational field and gravity,respectively.Thus,quasi-particles in low-energy excitation behave similarly to particles in high-energy physics.For example,quantum tunneling effect in condensed matter physics can simulate Hawking radiation in astrophysics,leading to much higher Hawking temperatures than those of gravitational BHs.Pristine graphene does not possess a band gap,which results in a low on/off ratio of FET devices.In order to find more stable Dirac semimetals,we considered two kinds of 2D materials:2D Cairo lattice(penta-MX2 monolayer)and graphene-like MXenes.In addition,to overcome the limits of zero-band-gap in graphene,2D materials with direct band gaps and ultrahigh carrier mobilities are highly desirable.The research of Dirac semimetals and direct-band-gap semiconductors with high carrier mobility has important scientific significances and good prospects in relevant applications.In this thesis,we adopted first-principles calculations within density functional theory(DFT)in combination with the tight-binding(TB)method to reveal the origins of Dirac cones and high carrier mobilities of 2D materials.We also employed the basic theories of general relativity to describe the propagation of quasi-particles in low-energy excitation,which can mimic the properties of Dirac fermions in high-energy physics.The main contents and representative results are as follows:(1)Using a tight-binding approach,we demonstrated the multiple Dirac cones(type-?/?/?)inherited in a 2D Cairo lattice.The ?-? interactions between the d?and pz orbitals which are characterized by a set of TB parameters are responsible for the multiple Dirac cones.The phase diagram in the TB parameter space with equations of phase boundaries were established.On the basis of first-principles calculations,we also proposed a candidate material,penta-NiSb2 monolayer,to achieve these multiple Dirac cones.Unstrained penta-NiSb2 monolayer has a type-III Dirac cone with the Fermi velocities ranging from zero to 105 m/s.The Lifshitz transition between the three types of Dirac cones can be realized by applying external biaxial strains.According to the general theory of relativity,it is proved that an inhomogenous penta-NiSb2 system offers a solid-state platform to simulate Hawking evaporation,called fermionic analogue of BH horizon.The BH size is dertermined by the size of the material.When it is set at 20 nm,a high Hawking temperature of 4.6 K can be achieved,which is much higher than that of a gravitational BH with one solar mass(?10-8K).The multiple Dirac cones revealed in the Cairo lattice pave a way for the design of 2D Dirac materials to achieve specific applications.(2)Based on first-principles calculations,we built a database containing 312 kinds of MXenes and proposed a new Zr2Si MXene with high stability and an antiferromagnetic ground state.Our results indicates that the spins of Zr2Si MXene align in a ferromagnetic(parallel)way within the upper/lower Zr plane,but the coupling between the two Zr planes is antiferromagnetic(anti-parallel).Zr2Si MXene has a linear energy-momentum relationship featured by Dirac cones near the Fermi level without considering the spin-orbit coupling(SOC)effect and the Coulomb interaction(U)between Zr-4d electrons.The Dirac cones are determined to originate from the d x2-y2 and dz 2 orbitals of Zr and to be anisotropic in the momentum space.These Fermi velocities are estimated to be about one third of that in graphene.By taking SOC and U into account,the Dirac point opens a topologically trivial band gap,which possesses an opportune on/off ratio of FET devices and opens an avenue for using Zr2Si MXene for electronic applications.A transition between the AFM and FM states of Zr2Si MXene leads to the switching between semiconducting and metallic states.These interesting properties suggest the applications of Zr2Si MXene for electronic devices to be quite promising.(3)From a tight-binding(TB)model of the 2D Cairo lattice,we demonstrated that the p-d ? conjugation can lead to an intrinsic band gap and ultrahigh carrier mobilities.On the basis of first-principles calculations,we proposed a stable candidate material:penta-NiP2,with a robust direct band gap of about 0.818 eV for monolayer and 0.635 eV for bilayer.By means of an acoustic phonon-limited scatting stratege,the carrier mobility of penta-NiP2 monolayer is in the range of 105-106 cm2 V-1 s-1,which is comparable to that of graphene.These properties are quite desired for high-speed electronic devices.The synthetic approach of penta-NiP2 monolayer was also discussed.