First-principles And Theoretical Studies On Dirac Materials

Dirac materials is a novel class of crystal materials, whose low-energy electronicexcitation is described by Dirac equations in relativistic quantum mechanics. Takinggraphene as an example, we introduce the basic concepts and characteristics of Diracmaterials. Based on the manipulation of Dirac states in graphene, a large numberof novel phenomena are proposed and realized, such as valleytronics, quantum spinHall efect and quantum anomalous Hall (QAH) efect. Subsequently，we describethe developments and point out problems in these related felds.Density functional theory (DFT) plays an important role in the study of Diracmaterials. We introduce the basic principles and implementations of DFT. Wealso describe the calculation methods of topological invariants of Dirac materials.Combining theoretical analysis and frst-principles calculation based on DFT, wedevelop the related physics of Dirac systems and the corresponding material discov-ery. These novel fndings are shown in four parts:We develop the spin and valley physics of an antiferromagnetic honeycomblattice. We show that by coupling the valley degree of freedom to antiferromag-netic order, there is an emergent electronic degree of freedom characterized by theproduct of spin and valley indices, which leads to spin-valley dependent optical selection rule and anomalous Hall efect. These properties will enable optical polar-ization in the spin-valley space, and electrical detection/manipulation through theinduced spin, valley and charge fuxes. The domain walls of an antiferromagnetichoneycomb lattice harbors valley-protected edge states that support spin-dependenttransport. We then employ frst-principles calculations to show that the proposedoptoelectronic properties can be realized in antiferromagnetic MnPX3(X=S, Se)in monolayer form.We propose a novel mechanism to tailor-make various topological insulatingphases. We establish that valley-dependent dimerization of Dirac surface states canbe exploited to induce topological quantum phase transitions, in a binary super-lattice bearing symmetry-unrelated interfacial Dirac states. This mechanism leadsto a rich phase diagram and allows for rational design of strong, weak, and crys-talline topological insulators. Our frst-principles simulations further demonstratethis mechanism in and superlattices of calcium and tin tellurides.We propose a realization of single-spin Dirac states and QAH states in simple,non-topological oxides. Our frst-principles calculations show that in heterostruc-ture of CrO2with TiO2, four single-spin Dirac points emerge in momentum-spaceband structure. Owing to spin-orbit coupling, these single-spin Dirac cones arefeld-tunable, and exhibit quantum anomalous Hall efect with out-of-plane magne-tization, which enjoys symmetry-protected topological gaps equivalent to43Kelvinand quantization of Hall conductance to2. Recent advances in the topolog-ical quantum phases are combined with technologically relevant simple oxides inthis chapter, which will signifcantly broaden the scope of studies Dirac Fermionand topological phases.Based on frst-principles simulations, we show the signifcant efects of thechemical decoration on edge states of topological Bi(111) bilayer nanoribbon, whichremove the trivial edge state and recover the Dirac linear dispersion of topologicaledge state. By comparing the edge states with and without chemical decoration,the Bi(111) bilayer nanoribbon ofers a simple system for assessing conductancefuctuation of edge states. The chemical decoration can also modify the penetration depth and the spin texture of edge states. A low-energy efective model is proposedto explain the distinctive spin texture of Bi(111) bilayer nanoribbon, which breaksthe spin-momentum orthogonality along the armchair edge.