【作者】 王丹；

【导师】 张敏；

【作者基本信息】 西华师范大学 ， 凝聚态物理， 2020， 硕士

【摘要】 拓扑绝缘体（Topological insulator,TI）和传统意义上的金属和绝缘体不同,内部结构是有带隙的绝缘态,表面是无间隙的金属态,受时间反演对称保护。拓扑绝缘体本身的能带结构和拓扑保护决定了体系不受晶体的缺陷、非磁性杂质等外界环境的影响,电子可以无散耗地运输。其中Bi₂Se₃是最接近理想状态的三维（3D）强拓扑绝缘体,化学计量比可控,易合成纯的化学相,化学成分毒性不强,体能带的Fermi能级位于能隙之中,能隙（0.3eV）远大于室温的能量尺度,只拥有一个相互交替的狄拉克表面态,这使它成为潜在的自旋电子学和技术应用的理想候选者。在体系中引入磁性,通过拓扑有序和铁磁有序之间的复杂相互作用可以破坏时间反演对称性,在Dirac点打开能隙,有望实现量子反常霍尔效应（QAHE）、磁光效应、磁单极子和Majorana费米子等奇特性质,推动新器件的发展。本文采用基于密度泛函理论（DFT）的平面波赝势方法系统地研究了非磁性元素X（B、C、N）掺杂Bi₂Se₃的Bi位、Se1位、Se2位和间隙的几何结构、电子结构和磁性。计算结果如下:（1）在计算Bi₂Se₃的几何结构时,考虑范德华修正是非常必要的。对所有掺杂后的结构和原子进行弛豫,发现掺杂后体系的晶格常数均变小,键长变短,原子之间距离变小,相互作用增强。形成能大小与键长对应,键长越长,形成能越小,结构越稳定。B和C原子掺杂间隙位时形成能最低,是最稳定最可能形成的结构;N原子掺杂Se1位时形成能最低。所有X原子掺杂Bi₂Se₃的Bi位形成能最大,掺杂取代Bi原子的可能性最小。（2）考虑自旋轨道耦合效应（SOC）能准确描述Bi₂Se₃的电子结构,特别是费米能级附近的能带结构。X原子掺杂Bi₂Se₃后的能带整体上与无掺杂一致,价带主要来源Se原子的4p轨道,导带主要来源于Bi原子的6p轨道。（3）在B原子掺杂Bi位和Se2位,C原子掺杂所有位置,N原子掺杂Se2位和间隙位时,引入的杂质态会与时间反演对称的态发生耦合,导致体系的电子结构发生改变,在费米能级附近出现了杂质能带,并在Dirac点引入带隙。（4）与过渡金属元素掺杂类似,非磁性元素X掺杂能够引入自旋极化的铁磁序,破坏时间反演对称性,引入的磁矩大小与掺杂原子和周围原子的键长相关。在C原子掺杂的所有位置和所有X原子掺杂Se2位时,都能诱导产生磁矩,而引入稳定铁磁序的关键就在于掺杂的X原子有局域化的2p轨道,能够形成杂质能带,在Dirac点引入带隙。这就为X原子掺杂调控Bi₂Se₃拓扑绝缘性提供了可行的方法,可以促进拓扑绝缘体在自旋电子学器件中的应用。更多还原

【Abstract】 The discovered Topological insulator（TI）with a bulk energy gap and gapless metallic surface state is different from metal and insulator.The band structures are spin split and protected by the time-reversal symmetry（resistant to defects and nonmagnetic impurities）.Bi₂Se₃ is the ideal three dimensional（3D）topological insulator materials in bulk,with controllable stoichiometric ratio,easy synthesize and low toxicity.Its Fermi energy is located in the energy gap and there is one single Dirac cone at Dirac point in Brillouin zone.Particularly,it is ideal device for potential spintronic and technological application because its bulk band gap is much larger than the energy scale of room temperature.The time-reversal symmetry can be destroyed by the complex interaction between the topological order and the ferromagnetic order.The energy gap appears at the Dirac point with the magnetism introduced.TI is expected to realize the quantized anomalous Hall Effect（QAHE）,magneto-optical effect,magnetic monopole and Majorana fermion,and promote the development of new devices.Thus,in this paper,the geometrical structure,electronic structure and magnetic properties of the non-magnetic elements X（B、C、N）doping at Bi、Se1、Se2 and gap sites of Bi₂Se₃ are calculated using first-principles pseudo-potential plane wave method based on density functional theory（DFT）.The calculated results are as follows:（1）The van der Waals（vdw）density-function D2 correction is quite necessary for structure optimizing.All structures and atoms are relaxed.The optimized results show that the lattice parameters of the structures and the distance between atoms with X doping become small,the bond length becomes short,and the interaction is enhanced.The formation energy corresponds to the bond length.The structure is stable with small formation energy.The structures of B and C doping at gap site is the most stable and likely to be formed with the minimum formation energy.The formation energy of N atom doping at Se1 site is lowest.The formation energy of X atoms doping at Bi site is the largest,and the possibility of replacing Bi atoms is the least.（2）Due to the spin-orbit coupling（SOC）,the electronic structure of Bi₂Se₃ can be accurately described,especially the energy band near the Fermi level.The energy band of X-doping is consistent with Bi₂Se₃.The valence band is mainly from Se-4p states and the conduction band is mainly from Bi-6p states.（3）The electronic structures of B atom doping at Bi site and Se2 site,C atom doping at all sites,N atom doping at Se2 site and gap site are changed due to the coupling of impurity state and time-reversal symmetry state.The impurity energy band appears near the Fermi level,and the band gap is introduced at the Dirac point.（4）It is similar to the transition metals,non-magnetic atom X doping Bi₂Se₃ can induce spin-polarized ferromagnetic states and destroy the time inversion symmetry.Further research reveals that the magnetic moments are related to the covalent bond length between X and surrounding atoms.C atoms doping at all sites and all X atoms doping at Se2 site can induce magnetic moments.In order to have a stable magnetic state,the 2p state of the X atom must be sufficiently localized,which form impurity energy bands and open band gaps at the Dirac point.This provides a feasible method for X-atom doping to manipulate the topological properties of Bi₂Se₃ and promote the application of topological insulators in spintronic devices.更多还原