层状磁性拓扑绝缘体VBi_(2)Te_(4)的第一性原理研究

A First-Principles Study on Magnetic Topological Insulator of VBi_(2)Te_(4)

层状磁性拓扑绝缘体MnBi_(2)Te_(4)的发现为探索新颖的量子现象(例如,量子反常霍尔效应和轴子绝缘态等)提供了新的契机。本文利用第一性原理软件VASP系统研究了与MnBi_(2)Te_(4)具有相同构型的新型磁性材料VBi_(2)Te_(4)的磁学、电学以及拓扑特性。研究结果发现VBi_(2)Te_(4)可以稳定存在,并且该材料可以很容易剥离至单层。计算结果表明块体VBi_(2)Te_(4)的层间耦合为反铁磁排列,当不考虑自旋轨道耦合作用时,该体系具有约为0.7 eV的能隙;而考虑自旋轨道耦合作用后,体系的能隙变为0.12 eV且伴随有能带的翻转。进一步的拓扑不变量(Z_(2))和边界态计算表明反铁磁VBi_(2)Te_(4)是三维磁性拓扑绝缘体。对于块体铁磁的VBi_(2)Te_(4),当不考虑自旋轨道耦合作用时,体系的能隙约为0.66 eV;同样地,自旋轨道耦合作用可以引起能带的翻转。随后的边界态计算证明铁磁的VBi_(2)Te_(4)也具有拓扑特性。该研究工作表明,与层状磁性拓扑绝缘体MnBi_(2)Te_(4)一样,磁性VBi_(2)Te_(4)块体材料也具有拓扑特性,其有望来实现各种有趣的拓扑量子态。

The recently discovered magnetic topological insulator(TI) of MnBi_(2)Te_(4) had provided unprecedented opportunities to explore emerging quantum phenomena,such as quantum anomalous Hall effect(QAHE) and axion insulating state.Different from randomly doping magnetic atoms in TIs,bulk MnBi_(2)Te_(4) could be seen as that the antiferromagnetic(AFM) MnTe was intercalated into the threedimensional(3D) TI of Bi_(2)Te_(3),where the intralayer Mn atoms in a septuple layer(SL)(e.g.,Te-Bi-Te-Mn-Te-Bi-Te) were magnetically ordered and hosted the long range ferromagnetic(FM) order.Latest theoretical and experimental results had shown that bulk MnBi_(2)Te_(4) was a 3DTI,and the interlayer coupling of two nearest SLs MnBi_(2)Te_(4) was AFM.Such intriguing magnetic properties thus resulted in two distinct quantum phenomena,where odd SLs of MnBi_(2)Te_(4) hosted QAHE,while even SLs of MnBi_(2)Te_(4) exhibited axion insulator state.In particular,the observed temperatures of QAHE in layered MnBi_(2)Te_(4) could be significantly enhanced up to 45 K under an external magnetic field.Most recently,the magnetic material of MnSb_(2)Te_(4) had been experimentally fabricated,and it was found that FM and ferrimagnetic states could be achieved due to the site mixing of Mn and Sb atoms.Moreover,it was predicted that magnetic MnSb_(2)Te_(4) hosted topologically nontrivial states.Therefore,the search for more magnetic materials that hosted intriguingly magnetic topological properties was of great scientific and experimental interest.Here,the structural,electronic and magnetic properties of VBi_(2)Te_(4) were investigated by using the projector augmented wave(PAW) formalism in the Vienna ab initio simulation package(VASP).The Perdew-Burke-Ernzerhof(PBE) approximation was used to describe the exchange and correlation functional.And GGA+U method was employed to better describe the 3d electrons of V atoms in the system,in which the moderate on-site Coulomb interaction(U) and exchange interaction(J) were,respectively,set to 4.0 eV and 1.0 eV.The plane-wave cutoff energy was set to 500 eV and all the atoms in the supercells were allowed to move until the Hellmann Feynman force on each atom is smaller than 0.1 eV·nm^(-1).The gamma-centered Monkhorst-Pack K-point mesh of 15×15×1 was adopted in our calculations.The van der Waals(vdW) correction with the Grimme(DFT-D3) method was included in the calculation of the layered systems.The topological properties of bulk and layered systems were identified by using Wannier 90 and WannierTools.The calculated results revealed that bulk VBi_(2)Te_(4) hosted the same crystal structure as MnBi_(2)Te_(4),whose lattice constant was slightly larger than that of MnBi_(2)Te_(4).Then,it was found that bulk and layered VBi_(2)Te_(4) were dynamically stable,and VBi_(2)Te_(4) monolayer was thermodynamically stable even at room temperature,which indicated that VBi_(2)Te_(4) could be fabricated experimentally.The detailed magnetic calculations showed that the ground state of layered VBi_(2)Te_(4) was AFM coupling,while the magnetic order of VBi_(2)Te_(4) monolayer preferred in-plane FM order.The intriguing magnetic properties might induce abundant magnetic topological states,which was confirmed by later electronic and topological calculations.The AFM VBi_(2)Te_(4) exhibited insulating state with a bandgap of ~0.7 eV without including spin-orbit coupling(SOC) by calculating electronic band structure.While the bandgap of this system became to be 0.12 eV after SOC was considered.Due to the elements of Bi and Te hosting very strong SOC effect,it suggested that there might exist topological phase transition.The projected band clearly showed that the band inversion happened between Bi p_(z) and Te p_(z) with SOC including.The calculated Z_(2) invariant with Z_(2)=1 demonstrated that bulk AFM VBi_(2) Te_(4) was a three-dimensional topological insulator.Further edge state calculations showed that two helical edge states existed in the bulk gap,confirming the AFM topological properties of VBi_(2)Te_(4).When external magnetic field applied to VBi_(2)Te_(4),FM order could be realized in VBi_(2)Te_(4).Thus,the electronic and topological properties of FM VBi_(2) Te_(4) were then investigated.The band gap of this FM system was-0.66 eV,which was slightly smaller than that of AFM structure.Similarly,SOC could induce the band inversion between Bi p_(z) and Te p_(z) in such a FM system.The detailed edge state calculations confirmed that FM VBi_(2)Te_(4) hosted topologically nontrivial states.The magnetic,electronic,and topological properties of VBi_(2)Te_(4) by considering different effective U effect and vdW corrections were also investigated.The calculated results showed that although effective U and vdW corrections quantitatively affected the size of band gap,magnetic,electronic,and topological properties of AFM and FM VBi_(2)Te_(4) were not qualitatively affected.It demonstrated the robustness of physical properties in such a system.How to achieve FM coupling in layered VBi_(2)Te_(4)-like materials was also an important issue,especially for realizing the intriguing quantum phenomenon of QAHE in such layered systems.By doping Sb atoms in VBi_(2)Te_(4) or building FM heterostructures was a promising way to realize FM order in VBi_(2)Te_(4).According to the above analyses,it was expected that two-dimensional topological states of QAHE and axion insulating states might be achieved in VBi_(2)Te_(4) thin films.All those results demonstrated that layered magnetic material of VBi_(2)Te_(4) was also an ideal candidate to realize many intriguing topological states.