| Topological materials are one of the most popular materials in the field of condensed matter physics over the past decade.Because the properties of topological materials are very distinct from those of topologically trivial materials,and some of those properties are very promising for future technical applications,therefore,the research of topological materials has attracted an intensive attention from physicists and material scientists all over the world.Topological insulator is an important ingredient of topological material.The bulk band of topological insulator is gapped out,but there are gapless surface states on its boundary.The surface states are topologically protected by its bulk band topology,highly spin polarized and spin-momentum locked.This surface states can be used in spintronic devices to transmit and process information with electron spin.The coupling of topological surface states with superconducting states can create Majorana fermions,which satisfies Abelian statistics and can be used in topological quantum computation.Topological surface state is an important part of topological insulator theory,and it is also the key for the technical application of topological insulators.Due to its cubic symmetry and unique order of energy bands,the properties of the recently identified topological material,?-Sn,are quite different from those previously studied topological materials.The energy bands of s and p with opposite parities of ?-Sn are inverted comparing to those of Si and Ge.Therefore,?-Sn has a topologically non-trivial energy band structure.At the same time,the cubic symmetry of ?-Sn makes its conduction band and valence band degenerate and results in a semiconducting state with zero band gap in ?-Sn.By applying strain to reduce the symmetry,the degeneracy of conduction band and valence band can be removed,and its non-trivial band structure can show abundant topological properties.However,the research on its topological phase is not enough at present,and the effect of the strength of spin-orbit coupling on its topological order has not been thoroughly investigated yet.In particular,studies on the topological surface states of topological phase ?-Sn are very limited.The topological surface states confirmed by experiments are located in the deep valence band,while the surface states in the band gap between the conduction band and valence band have not been reported experimentally up to now,meanwhile,the existing results of theoretical studies on surface states of ?-Sn are inconsistent.Therefore,in order to study the effect of spin-orbit coupling and strain on the topological order of ?-Sn and the properties of its topological surface states,we calculated the bulk energy band of ?-Sn under different spin-orbit coupling strengths and different strains by using the first-principles method,and analyzed the evolution of its topological properties.The energy band structure of topologically insulating state ?-Sn thin film is calculated,the constitution and properties of its surface states are analyzed,and some significant results are achieved:(1)By adjusting the spin-orbit coupling and strain,we observed the topological phase transformation of ?-Sn between ordinary semimetal,topological insulator,Dirac semimetal,ordinary metal;(2)The semi metallic state of ?-Sn in cubic symmetry also has a surface state,which exhibits properties similar to topological surface states such as spin polarization and robustness.(3)The surface state of topological state ?-Sn thin film is composed of two Dirac cones,the upper Dirac cone is located in the band gap between the conduction band and valence band,and the lower Dirac cone is located in the valence band.These two Dirac cones are robust and cannot be removed by surface hydrogen passivation.Our results enrich people's knowledge about the topology properties of ?-Sn,and offer a valuable reference for the future application of ?-Sn in spintronic devices and topological quantum computation. |
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