搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

不同方向局域交换场对锡烯自旋输运的影响

郑军 马力 相阳 李春雷 袁瑞旸 陈箐

郑军, 马力, 相阳, 李春雷, 袁瑞旸, 陈箐. 不同方向局域交换场对锡烯自旋输运的影响. 物理学报, 2022, 71(14): 147201. doi: 10.7498/aps.71.20220277
引用本文: 郑军, 马力, 相阳, 李春雷, 袁瑞旸, 陈箐. 不同方向局域交换场对锡烯自旋输运的影响. 物理学报, 2022, 71(14): 147201. doi: 10.7498/aps.71.20220277
Zheng Jun, Ma Li, Xiang Yang, Li Chun-Lei, Yuan Rui-Yang, Chen Jing. Effects of local exchange field in different directions on spin transport of stanene. Acta Phys. Sin., 2022, 71(14): 147201. doi: 10.7498/aps.71.20220277
Citation: Zheng Jun, Ma Li, Xiang Yang, Li Chun-Lei, Yuan Rui-Yang, Chen Jing. Effects of local exchange field in different directions on spin transport of stanene. Acta Phys. Sin., 2022, 71(14): 147201. doi: 10.7498/aps.71.20220277

不同方向局域交换场对锡烯自旋输运的影响

郑军, 马力, 相阳, 李春雷, 袁瑞旸, 陈箐

Effects of local exchange field in different directions on spin transport of stanene

Zheng Jun, Ma Li, Xiang Yang, Li Chun-Lei, Yuan Rui-Yang, Chen Jing
Article Text (iFLYTEK Translation)
PDF
HTML
导出引用
  • 利用非平衡格林函数方法, 理论研究了多种组合形式的局域交换场对锡烯纳米带自旋输运性质的影响. 研究表明锡烯自旋相关电导、边缘态和体能带都显著地依赖于不同区域交换场的方向和强度. 在[I: ±Y, II: +Z, III: ±Y]方向交换场的共同作用下, 边缘态受Y方向交换场影响形成带隙, 禁带宽度与交换场强度M 成正比, 在M<E<M能量范围电导值为0. 对上下边缘区域同时施加+ZZ方向的交换场时, 边缘态和体能带都发生较强的自旋劈裂, 自旋向上和向下能带沿相反方向向高能量区域移动, 增大交换场的强度电导自旋极化的范围将从高能量扩展到低能量区域. 当交换场方向为[I: Z, II: ±Y, III: ±Z]时, 低能区自旋相关的电导保持电子空穴对称性, 不同交换场强度条件下, 自旋相关电导都在相同的能量范围λso<E<λso保持电导平台Gσ=e2/h.
    Topological insulator is a new quantum state of matter in which spin-orbit coupling gives rise to topologically protected gapless edge or surface states. The nondissipation transport properties of the edge or surface state make the topological device a promising candidate for ultra-low-power consumption electronics. Stanene is a type of two-dimensional topological insulator consisting of Sn atoms arranged similarly to graphene and silicene in a hexagonal structure. In this paper, the effects of various combinations of local exchange fields on the spin transport of stanene nanoribbons are studied theoretically by using the non-equilibrium Green's function method. The results show that the spin-dependent conductance, edge states, and bulk bands of stanene are significantly dependent on the direction and strength of the exchange field in different regions. Under the joint action of the exchange fields in [I: ±Y, II: +Z, III: ±Y] direction, the edge states form a band-gap under the influence of the Y-direction exchange field. The band-gap width is directly proportional to the exchange field strength M, and the conductance is zero in an energy range of M<E<M. When the exchange fields in the direction of +Z or Z are applied, respectively, to the upper edge region and the lower edge region at the same time, the spin-up energy band and the spin-down energy band move to a high energy region in opposite directions, and strong spin splitting occurs in the edge state and bulk bands. Increasing the strength of the exchange field, the range of spin polarization of conductance spreads from the high energy region to the low energy region. When the directions of the exchange field are [I: Z, II: ±Y, III: ±Z], the edge states are spin degenerate, but the weak spin splitting occurs in the bulk bands. Under the condition of different exchange field strengths, the spin-dependent conductance maintains a conductance platform of Gσ=e2/h in the same energy range of λso<E<λso.
      PACS:
      72.25.-b(Spin polarized transport)
      73.63.-b(Electronic transport in nanoscale materials and structures)
      通信作者: 郑军, zhengjun@bhu.edu.cn ; 李春雷, licl@cnu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 12174038, 11604021)、辽宁省“兴辽英才”青年拔尖人才项目(批准号: XLYC2007141)和北京市教育委员会科技计划面上项目(批准号: KM201810028022)资助的课题
      Corresponding author: Zheng Jun, zhengjun@bhu.edu.cn ; Li Chun-Lei, licl@cnu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12174038, 11604021), the Revitalization Talents Program of Liaoning Province, China (Grant No. XLYC2007141), and the Science Technology Foundation from Education Commission of Beijing, China (Grant No. KM201810028022)

    自石墨烯在2004年被成功制备以来[1,2], 伴随着体系维度降低所带来的新奇特性, 长程有序的二维纳米材料引起科研人员广泛关注[3]. 锡烯是锡原子以蜂窝状翘曲结构排列而成的二维单原子层薄膜. 2009年Cahangirov等[4]利用第一性原理计算明确了原子之间较大的成键间距会削弱π电子交叠, 具有D3d点群对称性的六角蜂窝状翘曲结构在能量上最稳定. 同年Sahin 等[5]理论研究了锡烯的晶格结构特征, 研究发现锡原子可形成稳定的低翘曲蜂窝状结构. 2011年Liu等[6]的理论计算结果表明sp2sp3杂化轨道混合构成的低翘曲结构可增强自旋-轨道耦合, 锡烯具有非平庸的拓扑特性[7]. 2013 年Xu等[8] 通过第一性原理计算研究了应变和边缘修饰对锡烯拓扑能隙的影响, 发现通过化学修饰可以调控锡烯拓扑态的自由度, 锡烯的拓扑能隙可以达到300 meV. 较大的体能隙使得基于锡烯等类石墨烯结构可以用于较高温度条件下的二进制逻辑操作, 实现“开”与“关”两种状态, 多种基于IV主族拓扑绝缘体的晶体管模型已被提出并得到研究[9-16].

    块体锡材料中的原子是以sp3杂化的金刚石结构排序, 原子之间的共价键很难被破坏, 无法通过简单的机械剥离方法获得单原子层锡薄膜. 超高真空环境下, 在衬底上利用分子束外延生长是制备锡烯采用的主要方法. 2015年Zhu等[17] 在Bi2Te3(111)衬底上成功制备了锡烯. 2017年Gou等[18] 在Sb(111)表面实现了锡烯的制备. 2018年基于PbTe(111), InSb(111), Ag(111) 以及Cu(111)衬底, Zang等[19]、Xu等[20]、Yuhara等[21]、Deng 等[22]相继成功制备了翘曲和平面结构的锡烯. 目前科研人员已经在不同的金属和半导体表面实现了锡烯的生长制备[23-26], 尽管耦合相互作用以及能带杂化引起了不同周期的结构重构, 但实验结果依然在一定程度上证实了理论上所预言的拓扑绝缘体本征物性.

    近些年, 人们对锡烯的电学[27-34]、光学[15,35-37]、磁学[38-42]以及热学[43-47] 性质进行了一系列研究. 本文从理论上研究局域铁磁交换场对锡烯纳米带边缘态和体能带自旋输运性质的影响. 如图1(a)所示, 将锡烯纳米带的中间区域分成上(I)、中(II)、下(III) 3个区域, 对3个区域分别施加YZ轴方向的交换场, 重点讨论不同方向局域交换场的组合形式和强度对电导和能带的调控.

    图 1 (a) 交换场作用下的锡烯纳米带俯视图. 图中沿Y轴方向将锡烯等分为I, II, III 3个区域, 并分别对这3个区域施加[I: $ +Z $, II: $ +Y $, III: $ -Z $]和[I: $ -Z $, II: $ -Y $, III: $ +Z $]方向组合的交换场; (b) 无外场作用时锡烯的电子能带结构; 铁磁交换场按照(c) [I: $ \pm Y $, II: $ +Z $, III: $ \pm Y $]和(e) [I: $ \pm Y $, II: $ -Z $, III: $ \pm Y $]分布时自旋相关电导随费米能E的变化; (d)交换场强度为$ M=\lambda_{{\rm{so}}}/2 $, 方向为(d) [I: $ \pm Y $, II: $ +Z $, III: $ \pm Y $]及(f) [I: $ \pm Y $, II: $ -Z $, III: $ \pm Y $]时的电子能带结构, 图中红色圈线和蓝色实线分别对应自旋向上和自旋向下的电子\r\nFig. 1. (a) Top view of a stanene nanoribbon with local exchange field, where stanene is equally divided into three regions, (i.e., I, II, and III) along the Y-axis, and exchange fields in the directions of [I: $ + Z $, II: $ + Y $, III: $ - Z $] and [I: $ - Z  $, II: $ - Y $, III: $ + Z $] are applied to these three regions respectively. (b) Energy-band diagram of stanene without external field. Spin dependent conductance $ G_\sigma $ as a function of the Fermi energy E with the ferromagnetic exchange fields distributed according to (c) [I: $ \pm Y  $, II: $ + Z  $, III: $ \pm Y $] and (e) [I: $ \pm Y  $, II: $ - Z $, III: $ \pm Y $]. Energy-band diagram of stanene with the strength of external field $ M=\lambda_{{\rm{so}}}/2 $, the exchange field directions are (d) [I: $ \pm Y $, II: $ +Z $, III: $ \pm Y $] and (f) [I: $ \pm Y $, II: $ +Z $, III: $ \pm Y $]. The red circle-lines and blue solid-lines correspond to spin-up and spin-down electrons, respectively
    图 1  (a) 交换场作用下的锡烯纳米带俯视图. 图中沿Y轴方向将锡烯等分为I, II, III 3个区域, 并分别对这3个区域施加[I: +Z, II: +Y, III: Z]和[I: Z, II: Y, III: +Z]方向组合的交换场; (b) 无外场作用时锡烯的电子能带结构; 铁磁交换场按照(c) [I: ±Y, II: +Z, III: ±Y]和(e) [I: ±Y, II: Z, III: ±Y]分布时自旋相关电导随费米能E的变化; (d)交换场强度为M=λso/2, 方向为(d) [I: ±Y, II: +Z, III: ±Y]及(f) [I: ±Y, II: Z, III: ±Y]时的电子能带结构, 图中红色圈线和蓝色实线分别对应自旋向上和自旋向下的电子
    Fig. 1.  (a) Top view of a stanene nanoribbon with local exchange field, where stanene is equally divided into three regions, (i.e., I, II, and III) along the Y-axis, and exchange fields in the directions of [I: +Z, II: +Y, III: Z] and [I: Z, II: Y, III: +Z] are applied to these three regions respectively. (b) Energy-band diagram of stanene without external field. Spin dependent conductance Gσ as a function of the Fermi energy E with the ferromagnetic exchange fields distributed according to (c) [I: ±Y, II: +Z, III: ±Y] and (e) [I: ±Y, II: Z, III: ±Y]. Energy-band diagram of stanene with the strength of external field M=λso/2, the exchange field directions are (d) [I: ±Y, II: +Z, III: ±Y] and (f) [I: ±Y, II: +Z, III: ±Y]. The red circle-lines and blue solid-lines correspond to spin-up and spin-down electrons, respectively

    在紧束缚近似下, 基于Kane-Mele模型在3个区域分别施加±Y 轴和±Z轴方向交换场的锡烯哈密顿量可以表示为[7,48-51]

    H=tij,σciσcjσ+iλso33ijσˉσvijciσσzσˉσcjˉσ+MNy/3i=1σciσ(+σy)ciσ+M2Ny/3i=Ny/3+1σciσ(σz)ciσ+MNyi=2Ny/3+1σciσ(σy)ciσ,
    (1)

    式中前两项表示未受外场作用的锡烯, tλso为最近邻锡原子之间的电子跃迁能和有效自旋轨道耦合强度; ciσcjσ分别为电子的产生和湮灭算符, ciσ(cjˉσ)表示在第i(j) 个晶格格点产生(湮灭)一个自旋向上σ=+1(向下σ=1)的电子; ijij表示求和遍布所有最近邻和次近邻格点; 符号函数υij是与位置相关的Haldane相因子[52,53], 在数值计算中当次近邻相互作用沿顺时针方向时υij=+1, 反之υij=1. (1)式中的第3—5项分别表示对上(i[1,Ny/3]), 中(i[Ny/3+1,2Ny/3]), 下(i[2Ny/3+1,Ny]) 3个区域分别施加方向为+Y, –Z和–Y, 强度为M的铁磁交换场, 其中Ny为纳米带边界沿Y轴方向的锡原子数, σyσzσz表象的泡利矩阵. 局部交换场可以通过铁磁体的邻近效应引入[54], 如I区域的交换场, 可以通过将Fe原子沉积到硅烯纳米带上边缘的表面或将硅烯纳米带部分沉积到铁磁绝缘衬底上, 交换场的方向可通过外场调节. 利用Bloch-Wannier变换将(1)式中的产生和湮灭算符变换到Bloch表象, cjyσ=1NykBZckσeikjy, cjyσ=1NykBZckσeikjy, 其中jy对应Y轴方向的晶格格点位置. 通过求解本征值方程可以计算得到不同方向铁磁交换场条件下的锡烯电子能带结构.

    利用非平衡格林函数和Landauer-Buttiker公式, 零温度条件下与半无限长锡烯导线耦合的锡烯纳米带自旋相关电导可以表示为[55,56]

    Gσ(E)=e2hTr[ΓLσ(E)Grσ(E)ΓRσ(E)Gaσ(E)],
    (2)

    式中Γασ(E)=i[Σrασ(E)Σaασ(E)]为线宽函数, α=L,R分别对应左右导线区域. 自能函数Σr(a)ασ(E)=Hcαgr(a)ασ(E)Hαc可以在求解表面格林函数gr(a)ασ(E)的基础上计算得出. 在计算表面格林函数时, 本文假定导线半无限长且具有周期性, 将导线沿着Y轴方向划分成层. 与器件相连的导线末端锡原子层的哈密顿量用矩阵H00表示, 用矩阵H01表示层间耦合的哈密顿量, 并以此构造一个2N×2N的矩阵[H101(EIH00)H101H01I0], 求解矩阵的本征值和本征矢量, 并按本征值绝对值从小到大排列本征矢(e1,e2,,e2N)=[S1S2S3S4], 则表面格林函数可表示为grασ(E)=[(EIH00)H01S1S12]1[57-59], 式中I为单位矩阵. (2)式中的Grσ(E)=[Gaσ(E)]=[EIHΣrLσΣrRσ]1为整个系统对应的推迟格林函数, H为(1)式给出的不同方向交换场作用区域的哈密顿量矩阵.

    在数值计算中交换场作用区域的X轴方向和Y轴方向的锡原子数固定为Nx=Ny=256. 最近邻锡原子之间的电子跃迁能和有效自旋轨道耦合强度分别为t=1.3 eV 和λso=100 meV[7,8]. 不同方向交换场的强度和系统温度分别为M=λso/2=50 meV和T=0 K.

    首先讨论I (III)区域施加沿Y轴方向, II区域施加沿Z轴方向的交换场对自旋相关电导和电子能带结构的影响. 图1(c)图1(e)分别给出了中间区域交换场沿着+ZZ两种情况下自旋相关电导随费米能E的变化. 通过两幅图的对比可以看出, 当费米能E位于M+M窗口时, 自旋向上和向下电导值都为0, 此时的锡烯可以看成禁带宽度为2M的半导体. 能量E>+M的范围内σ方向自旋电导Gσ与能量E<M的范围内ˉσ方向自旋电导Gˉσ都关于能量E=0对称, 虽然局域交换场按照[±Y, +Z, ±Y]和[±Y, Z, ±Y]两种组合形式分布时总电导G=G+G始终保持电子空穴对称G(E)=G(E), 但是深能级区域相同能量条件下的自旋相关电导明显不同. 当交换场按照[±Y, +Z, ±Y]分布时, E>M (E<M)区域的自旋极化率为P=(GG)/(G+G)>0 (P<0). 交换场方向为[I: ±Y, II: Z, III: ±Y]时, E>0能量范围的极化率与[I: ±Y, II: +Z, III: ±Y]条件下E<0能量范围的极化率相同.

    为了更好地理解图1(c)图1(e)中电子自旋的输运特性, 图1(b)图1(d)图1(f)分别给出了不受外场作用的锡烯电极和施加交换场的中心区域的电子能带图. 从图1(b)可以看出, 不受外场影响时, 电子能带在Dirac点KK' 处形成宽度为2λso的体带隙, 体带隙内的边缘态自旋简并, 并在(π,0)点相交. 在局域交换场作用下, 电子的能带结构发生显著改变, 图1(b)图1(c)分别对应交换场按照[±Y, +Z, ±Y][±Y, Z, ±Y]分布时锡烯的能带图. 磁化矢量方向垂直于纳米带的反铁磁交换场, 能够破坏时间反演对称性, 当仅有中间(II)区域存在交换场时, 体能带受到+Z方向交换场影响发生劈裂, 但边缘态不受外场影响保持自旋简并. Y轴方向的铁磁交换场不仅可以破坏时间反演对称性, 还可以破坏自旋对称性, 在I和III区域引入Y轴方向的交换场并不会破坏电子能级的二重简并, 但是可以使边缘态在体带隙内打开宽度为2M的带隙. 因为±Y轴方向外场对能带的作用没有区别, 所以[+Y, +Z, +Y], [+Y, +Z, Y], [Y, +Z, +Y], [Y, +Z, Y] 4种外场组合形式的能带结构是等价的. 在对图1(a)所示的I—III 3个区域施加[±Y, +Z, ±Y][±Y, Z, ±Y]方向的交换场时体能带发生自旋劈裂, 边缘态保持简并形成大小为2M的能隙(如图1(b)图1(c) 所示). 因此当能量处于M<E<+M时电子无法通过纳米带, 自旋相关电导Gσ=0. 当E>ME<M时, GG, 并且由于导线区域(图1(b))与交换场作用区域(图1(b)图1(c))能带不匹配, 阶梯状电导平台退变成一系列共振峰.

    接下来讨论在I (III)区域引入沿±Z轴方向, II区域引入沿Y轴方向交换场对电导和能带的影响. 图2(a)为交换场按照[+Z, ±Y, +Z][Z, ±Y, Z]分布时锡烯的能带图. 通过与图1(d)图1(f)比较易见, I (III)与II区域交换场互换方向后, 边缘态和体能带都将发生自旋劈裂. 当I (III) 区域交换场为+Z方向时自旋向上电子形成的能带整体上移, 边缘态交叉点由(π,0)移动到(π,M), 而自旋向下电子对应的能带整体向下移动, 边缘态交叉点由(π,0)移动到(π,M). 虽然边缘态发生自旋劈裂, 但是在体带隙范围依然存在自旋向上和自旋向下的边缘态, 因此图2(c)M<E<M能量窗口出现G=G=e2/hG=G+G=2e2/h的电导平台. 通过调整交换场的方向可以改变电子自旋输运性质, 将I (III)区域的交换场调节到Z方向, 图2(c)中红色虚线(蓝色点线)则对应自旋向下(自旋向上)电导.

    图 2 交换场强度$M=\lambda_{{\rm{so}}}/2$, 方向为(a) [I: $ +Z $, II: $ \pm Y $, III: $ +Z $]及(b) [$ -Z $, II: $ \pm Y $, III: $ +Z $]时电子能带结构;  交换场按照(c) [I: $ +Z $, II: $ \pm Y $, III: $ +Z $]和(d) [$ -Z $, II: $ \pm Y $, III: $ +Z $]分布时电导G随费米能E 的变化, 图中红色圈线、蓝色三角线和黑色点线分别对应自旋向上、自旋向下以及总的电导\r\nFig. 2. Energy-band diagram of stanene with the strength of external field $ M=\lambda_{{\rm{so}}}/2 $, the exchange field directions (a) [I: $ +Z $, II: $ \pm Y $, III: $ +Z $] and (b) [$ -Z $, II: $ \pm Y $, III: $ +Z $]. Conductance G as a function of the Fermi energy E with the ferromagnetic exchange fields distributed according to (c)  [I: $ +Z $, II: $ \pm Y $, III: $ +Z $] and (d) [$ -Z $, II: $ \pm Y $, III: $ +Z $]. The red circle-lines, blue triangle-lines and black dot-lines correspond to spin-up, spin-down, and total conductance, respectively
    图 2  交换场强度M=λso/2, 方向为(a) [I: +Z, II: ±Y, III: +Z]及(b) [Z, II: ±Y, III: +Z]时电子能带结构; 交换场按照(c) [I: +Z, II: ±Y, III: +Z]和(d) [Z, II: ±Y, III: +Z]分布时电导G随费米能E 的变化, 图中红色圈线、蓝色三角线和黑色点线分别对应自旋向上、自旋向下以及总的电导
    Fig. 2.  Energy-band diagram of stanene with the strength of external field M=λso/2, the exchange field directions (a) [I: +Z, II: ±Y, III: +Z] and (b) [Z, II: ±Y, III: +Z]. Conductance G as a function of the Fermi energy E with the ferromagnetic exchange fields distributed according to (c) [I: +Z, II: ±Y, III: +Z] and (d) [Z, II: ±Y, III: +Z]. The red circle-lines, blue triangle-lines and black dot-lines correspond to spin-up, spin-down, and total conductance, respectively

    图2(b)给出交换场按照[Z, ±Y, +Z]分布时锡烯的能带图. 可以看出I (III) 区域交换场方向相反时, 边缘态保持自旋简并, 边缘态交点仍对应能量E=0但是向K点偏移, 当交换场按照[Z, ±Y, +Z]分布时边缘态交点则向K'点偏移, 偏移的程度与交换场强度M有关, 当M=λso时交叉点位于KK'点. ±Y方向交换场可以引起深能级区域能带发生自旋劈裂, 但同等场强条件下能带劈裂程度弱于Z方向交换场的作用. 因此如图2(d)所示, 体带隙及其附近区域不同自旋方向的电导值近似相等, 自旋极化率P0, 不同自旋方向的电导Gσ及总电导G关于E=0对称.

    图3以自旋向上电导为例, 讨论交换场强度M 变化对自旋电子输运的影响. 图3(a)交换场方向为[I: +Y, II: +Z, III: +Y], 交换场强度分别为M=0.025,0.05,0.075,0.1 eV, 从图3(a)可以看出, 改变 I和III区域+Y方向交换场强度可以有效地调节带隙大小, 随着场强的增强, 边缘态带隙的宽度随之增加, 在M<E<M的能量范围自旋相关电导Gσ=0. 图3(b)对应的交换场方向为[I: +Z, II: +Y, III: +Z], 此时随着交换场的增强, 自旋向上电子对应的能谷向能量E=0区间移动的程度加强, 逐渐进入无外场作用时的体带隙, 在M<E<0的范围自旋向上的电导平台逐渐被破坏, 形成一系列的共振峰, 但是能量在0<E<M范围内的自旋向上电导平台不受影响. 图3(c)给出了交换场方向为[I: Z, II: +Y, III: +Z]条件下的自旋向上电导. 可以看出, 当交换场按[I: Z, II: +Y, III: +Z]分布时电导平台并不受交换场强度变换影响, 在0.1+0.1 eV 范围保持Gσ=e2/h. 随着交换场强度的增强, 体能带的劈裂程度增大, 外场作用区间与左右电极的能带失配程度提高, E<ME>M能量范围的电导值随着交换场强度的增加而降低.

    图 3 交换场方向为(a) [I: $ + Y $, II: $ + Z $, III: $ +Y $], (b) [I: $ + Z $, II: $ + Y $, III: $ +Z $], (c) [I: $ - Z $, II: $ + Y $, III: $ +Z $], 交换场强度参数M分别取0.025, 0.050, 0.075, 0.100 eV 时, 自旋向上电导$ G_\uparrow $随费米能E的变化\r\nFig. 3. Conductance G as a function of the Fermi energy E with different values of exchange field parameter $ M=0.025 $, 0.050, 0.075, 0.100 eV for the exchange field directions are (a) [I: $ + Y $, II: $ + Z $, III: $ +Y $], (b) [I: $ + Z $, II: $ + Y $, III: $ +Z $], (c) [I: $ - Z $, II: $ + Y $, III: $ +Z $]
    图 3  交换场方向为(a) [I: +Y, II: +Z, III: +Y], (b) [I: +Z, II: +Y, III: +Z], (c) [I: Z, II: +Y, III: +Z], 交换场强度参数M分别取0.025, 0.050, 0.075, 0.100 eV 时, 自旋向上电导G随费米能E的变化
    Fig. 3.  Conductance G as a function of the Fermi energy E with different values of exchange field parameter M=0.025, 0.050, 0.075, 0.100 eV for the exchange field directions are (a) [I: +Y, II: +Z, III: +Y], (b) [I: +Z, II: +Y, III: +Z], (c) [I: Z, II: +Y, III: +Z]

    本文理论研究了交换场按[I: ±Y, II: +Z, III: ±Y], [I: ±Y, II: Z, III: ±Y], [I: +Z, II: ±Y, III: +Z], [I: Z, II: ±Y, III: +Z]分布时锡烯纳米带的自旋输运. 研究表明通过改变不同区域交换场的方向和强度可以有效调节边缘态和体能带电子的输运性质和强度. 当交换场方向为[I: ±Y, II: +Z, III: ±Y]时, 边缘态保持简并打开能隙, 边缘态能隙的宽度随着交换场强度的增加而增大, 在M<E<M的能量范围Gσ=0, 此时锡烯可以看成禁带宽度为2M的半导体. II区域+Z方向的交换场可以使得体能带发生较强的自旋劈裂, 能量E>M范围自旋极化率P>0. 当交换场方向为[I: ±Y, II: Z, III: ±Y]时, 能隙宽度保持不变, E>M条件下的自旋极化率P<0. 施加[I: +Z, II: ±Y, III: +Z]方向的交换场可以使得自旋向上和向下电子的能带整体向高能量和低能量区域移动, 提高交换场的强度KK' 谷能带进入无外场作用时的体带隙, Gσ=e2/h的电导平台被破坏形成一系列小的共振峰. 当交换场方向为[I: Z, II: ±Y, III: +Z]时, 边缘态向K'点移动, 体能带发生自旋劈裂, 但是II区域相同强度Y方向的交换场引起的劈裂程度明显弱于+Z方向的交换场, 体带隙附近区域自旋极化率近似为0. 增大交换场强度M, λso<E<λso能量窗口内的电导平台不受影响, 但是E<ME>M能量范围的电导受到抑制.

    [1]

    Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666Google Scholar

    [2]

    Geim A K, Novoselov K S 2007 Nat. Mater. 6 183Google Scholar

    [3]

    Chang H, Wang H, Song K K, Zhong M, Shi L B, Qian P 2021 J. Phys.: Condens. Matter 34 013003

    [4]

    Cahangirov S, Topsakal M, Akturk E, Sahin H, Ciraci S 2009 Phys. Rev. Lett. 102 236804Google Scholar

    [5]

    Sahin H, Cahangirov S, Topsakal M, Bekaroglu E, Ciraci S 2009 Phys. Rev. B 80 155453Google Scholar

    [6]

    Liu C C, Feng W X, Yao Y G 2011 Phys. Rev. Lett. 107 076802Google Scholar

    [7]

    Liu C C, Jiang H, Yao Y G 2011 Phys. Rev. B 84 195430Google Scholar

    [8]

    Xu Y, Yan B H, Zhang H J, Wang J, Xu G, Tang P Z, Duan W H, Zhang S C 2013 Phys. Rev. Lett. 111 136804Google Scholar

    [9]

    Ni Z, Liu Q, Tang K, Zheng J, Zhou J, Qin R, Gao Z, Yu D, Lu J 2012 Nano Lett. 12 113Google Scholar

    [10]

    Ezawa M 2013 Appl. Phys. Lett. 102 172103Google Scholar

    [11]

    Kaneko S, Tsuchiya H, Kamakura Y, Mori N, Ogawa M 2014 Appl. Phys. Express 7 035102Google Scholar

    [12]

    Ni Z Y, Zhong H X, Jiang X H, Quhe R G, Luo G F, Wang Y Y, Ye M, Yang J B, Shi J J, Lu J 2014 Nanoscale 6 7609Google Scholar

    [13]

    Zhai X C, Jin G J 2016 J. Phys.: Condens. Matter 28 355002Google Scholar

    [14]

    Katayama Y, Yamauchi R, Yasutake Y, Fukatsu S, Ueno K 2019 Appl. Phys. Lett. 115 122101Google Scholar

    [15]

    Zheng J, Xiang Y, Li C L, Yuan R Y, Chi F, Guo Y 2020 Phys. Rev. Appl. 14 034027Google Scholar

    [16]

    Zheng J, Xiang Y, Li C L, Yuan R Y, Chi F, Guo Y 2021 Phys. Rev. Appl. 16 024046Google Scholar

    [17]

    Zhu F F, Chen W J, Xu Y, Gao C L, Guan D D, Liu C H, Qian D, Zhang S C, Jia J F 2015 Nat. Mater. 14 1020Google Scholar

    [18]

    Gou J, Kong L J, Li H, Zhong Q, Li W B, Cheng P, Chen L, Wu K H 2017 Phys. Rev. Mater. 1 054004Google Scholar

    [19]

    Zang Y Y, Jiang T, Gong Y, Guan Z Y, Liu C, Liao M H, Zhu K J, Li Z, Wang L L, Li W, Song C L, Zhang D, Xu Y, He K, Ma X X, Zhang S C 2018 Adv. Funct. Mater. 28 1802723Google Scholar

    [20]

    Xu C Z, Chan Y H, Chen P, Wang X X, Flototto D, Hlevyack J A, Bian G, Mo S K, Chou M Y, Chiang T C 2018 Phys. Rev. B 97 035122Google Scholar

    [21]

    Yuhara J, Fujii Y, Nishino K, Isobe N, Nakatake M, Xian L, Rubio A, Le-Lay G 2018 2D Mater. 5 025002

    [22]

    Deng J L, Xia B Y, Ma X C, Chen H Q, Shan H, Zhai X F, Li B, Zhao A D, Xu Y, Duan W H, Zhang S C, Wang B, Hou J G 2018 Nat. Mater. 17 1081Google Scholar

    [23]

    Liu Y, Gao N, Zhuang J, Liu C, Wang J, Hao W, Dou S X, Zhao J, Du Y 2019 J. Phys. Chem. Lett. 10 1558Google Scholar

    [24]

    Pang W, Nishino K, Ogikubo T, Araidai M, Nakatake M, Le Lay G, Yuhara J 2020 Appl. Surf. Sci. 517 146224Google Scholar

    [25]

    Li J, Lei T, Wang J, Wu R, Qian H, Ibrahim K 2020 Appl. Phys. Lett. 116 101601Google Scholar

    [26]

    Dhungana D S, Grazianetti C, Martella C, Achilli S, Fratesi G, Molle A 2021 Adv. Funct. Mater. 31 2102797Google Scholar

    [27]

    Ezawa M 2015 J. Phys. Soc. Jpn. 84 121003Google Scholar

    [28]

    Wang D, Chen L, Wang X, Cui G, Zhang P 2015 Phys. Chem. Chem. Phys. 17 26979Google Scholar

    [29]

    Kuang Y D, Lindsay L, Shi S Q, Zheng G P 2016 Nanoscale 8 3760Google Scholar

    [30]

    van den Broek B, Houssa M, Iordanidou K, Pourtois G, Afanas’ev V V, Stesmans A 2016 2D Mater. 3 015001

    [31]

    Nakamura Y, Zhao T, Xi J, Shi W, Wang D, Shuai Z 2017 Adv. Electron. Mater. 3 1700143Google Scholar

    [32]

    Shen L, Lan M, Zhang X, Xiang G, 2017 RSC Adv. 7 9840Google Scholar

    [33]

    Hattori A, Tanaya S, Yada K, Araidai M, Sato M, Hatsugai Y, Shiraishi K, Tanaka Y 2017 J. Phys.: Condens. Matter 29 115302Google Scholar

    [34]

    Fadaie M, Shahtahmassebi N, Roknabad M R, Gulseren O 2018 Phys. Lett. A 382 180Google Scholar

    [35]

    Chaves A J, Ribeiro R M, Frederico T, Peres N M R 2017 2D Mater. 4 025086

    [36]

    M. Ezawa 2012 Phys. Rev. B 86 161407Google Scholar

    [37]

    Salazar C, Muniz R A, Sipe J E 2017 Phys. Rev. Mater. 1 054006Google Scholar

    [38]

    Rachel S, Ezawa M 2014 Phys. Rev. B 89 195303Google Scholar

    [39]

    Lado J L, Fernandez-Rossier J 2014 Phys. Rev. Lett. 113 027203Google Scholar

    [40]

    Li S S, Zhang C W 2016 Mater. Chem. Phys. 173 246Google Scholar

    [41]

    W. Xiong, C. Xia, T. Wang, Y. Peng, Y. Jia 2016 J. Phys. Chem. C 120 10622Google Scholar

    [42]

    Krompiewski S, Cuniberti G 2017 Phys. Rev. B 96 155447Google Scholar

    [43]

    Zhou H, Cai Y, Zhang G, Zhang Y W 2016 Phys. Rev. B 94 045423Google Scholar

    [44]

    Peng B, Zhang H, Shao H, Xu Y, Ni G, Zhang R, Zhu H 2016 Phys. Rev. B 94 245420Google Scholar

    [45]

    Peng X F, Zhou X, Jiang X T, Gao R B, Tan S H, Chen K Q 2017 J. Appl. Phys. 122 054302Google Scholar

    [46]

    Noshin M, Khan A I, Subrina S 2018 Nanotechnology 29 185706Google Scholar

    [47]

    郑军, 李春雷, 王小明, 袁瑞旸 2021 物理学报 70 147301Google Scholar

    Zheng J, Li C L, Wang X M, Yuan R Y 2021 Acta Phys. Sin. 70 147301Google Scholar

    [48]

    Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802Google Scholar

    [49]

    Ezawa M 2012 Phys. Rev. Lett. 109 055502Google Scholar

    [50]

    Zheng J, Chi F, Guo Y 2018 Appl. Phys. Lett. 113 112404Google Scholar

    [51]

    Zheng J, Chi F, Guo Y 2018 Phys. Rev. Appl. 9 024012Google Scholar

    [52]

    Haldane F D M 1988 Phys. Rev. Lett. 61 2015Google Scholar

    [53]

    Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801Google Scholar

    [54]

    Williams J R, Carlo L D, Marcus C M 2007 Science 317 638Google Scholar

    [55]

    Pastawski H M 1991 Phys. Rev. B 44 6329Google Scholar

    [56]

    Datta S 1992 Phys. Rev. B 45 1347

    [57]

    Lee D H, Joannopoulos J D 1981 Phys. Rev. B 23 4997Google Scholar

    [58]

    Sancho M P L, Sancho J M L, Rubio J 1984 J. Phys. F: Met. Phys. 14 1205Google Scholar

    [59]

    Sancho M P L, Sancho J M L, Sancho J M L, Rubio J 1985 J. Phys. F: Met. Phys. 15 851Google Scholar

  • 图 1  (a) 交换场作用下的锡烯纳米带俯视图. 图中沿Y轴方向将锡烯等分为I, II, III 3个区域, 并分别对这3个区域施加[I: +Z, II: +Y, III: Z]和[I: Z, II: Y, III: +Z]方向组合的交换场; (b) 无外场作用时锡烯的电子能带结构; 铁磁交换场按照(c) [I: ±Y, II: +Z, III: ±Y]和(e) [I: ±Y, II: Z, III: ±Y]分布时自旋相关电导随费米能E的变化; (d)交换场强度为M=λso/2, 方向为(d) [I: ±Y, II: +Z, III: ±Y]及(f) [I: ±Y, II: Z, III: ±Y]时的电子能带结构, 图中红色圈线和蓝色实线分别对应自旋向上和自旋向下的电子

    Fig. 1.  (a) Top view of a stanene nanoribbon with local exchange field, where stanene is equally divided into three regions, (i.e., I, II, and III) along the Y-axis, and exchange fields in the directions of [I: +Z, II: +Y, III: Z] and [I: Z, II: Y, III: +Z] are applied to these three regions respectively. (b) Energy-band diagram of stanene without external field. Spin dependent conductance Gσ as a function of the Fermi energy E with the ferromagnetic exchange fields distributed according to (c) [I: ±Y, II: +Z, III: ±Y] and (e) [I: ±Y, II: Z, III: ±Y]. Energy-band diagram of stanene with the strength of external field M=λso/2, the exchange field directions are (d) [I: ±Y, II: +Z, III: ±Y] and (f) [I: ±Y, II: +Z, III: ±Y]. The red circle-lines and blue solid-lines correspond to spin-up and spin-down electrons, respectively

    图 2  交换场强度M=λso/2, 方向为(a) [I: +Z, II: ±Y, III: +Z]及(b) [Z, II: ±Y, III: +Z]时电子能带结构; 交换场按照(c) [I: +Z, II: ±Y, III: +Z]和(d) [Z, II: ±Y, III: +Z]分布时电导G随费米能E 的变化, 图中红色圈线、蓝色三角线和黑色点线分别对应自旋向上、自旋向下以及总的电导

    Fig. 2.  Energy-band diagram of stanene with the strength of external field M=λso/2, the exchange field directions (a) [I: +Z, II: ±Y, III: +Z] and (b) [Z, II: ±Y, III: +Z]. Conductance G as a function of the Fermi energy E with the ferromagnetic exchange fields distributed according to (c) [I: +Z, II: ±Y, III: +Z] and (d) [Z, II: ±Y, III: +Z]. The red circle-lines, blue triangle-lines and black dot-lines correspond to spin-up, spin-down, and total conductance, respectively

    图 3  交换场方向为(a) [I: +Y, II: +Z, III: +Y], (b) [I: +Z, II: +Y, III: +Z], (c) [I: Z, II: +Y, III: +Z], 交换场强度参数M分别取0.025, 0.050, 0.075, 0.100 eV 时, 自旋向上电导G随费米能E的变化

    Fig. 3.  Conductance G as a function of the Fermi energy E with different values of exchange field parameter M=0.025, 0.050, 0.075, 0.100 eV for the exchange field directions are (a) [I: +Y, II: +Z, III: +Y], (b) [I: +Z, II: +Y, III: +Z], (c) [I: Z, II: +Y, III: +Z]

  • [1]

    Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666Google Scholar

    [2]

    Geim A K, Novoselov K S 2007 Nat. Mater. 6 183Google Scholar

    [3]

    Chang H, Wang H, Song K K, Zhong M, Shi L B, Qian P 2021 J. Phys.: Condens. Matter 34 013003

    [4]

    Cahangirov S, Topsakal M, Akturk E, Sahin H, Ciraci S 2009 Phys. Rev. Lett. 102 236804Google Scholar

    [5]

    Sahin H, Cahangirov S, Topsakal M, Bekaroglu E, Ciraci S 2009 Phys. Rev. B 80 155453Google Scholar

    [6]

    Liu C C, Feng W X, Yao Y G 2011 Phys. Rev. Lett. 107 076802Google Scholar

    [7]

    Liu C C, Jiang H, Yao Y G 2011 Phys. Rev. B 84 195430Google Scholar

    [8]

    Xu Y, Yan B H, Zhang H J, Wang J, Xu G, Tang P Z, Duan W H, Zhang S C 2013 Phys. Rev. Lett. 111 136804Google Scholar

    [9]

    Ni Z, Liu Q, Tang K, Zheng J, Zhou J, Qin R, Gao Z, Yu D, Lu J 2012 Nano Lett. 12 113Google Scholar

    [10]

    Ezawa M 2013 Appl. Phys. Lett. 102 172103Google Scholar

    [11]

    Kaneko S, Tsuchiya H, Kamakura Y, Mori N, Ogawa M 2014 Appl. Phys. Express 7 035102Google Scholar

    [12]

    Ni Z Y, Zhong H X, Jiang X H, Quhe R G, Luo G F, Wang Y Y, Ye M, Yang J B, Shi J J, Lu J 2014 Nanoscale 6 7609Google Scholar

    [13]

    Zhai X C, Jin G J 2016 J. Phys.: Condens. Matter 28 355002Google Scholar

    [14]

    Katayama Y, Yamauchi R, Yasutake Y, Fukatsu S, Ueno K 2019 Appl. Phys. Lett. 115 122101Google Scholar

    [15]

    Zheng J, Xiang Y, Li C L, Yuan R Y, Chi F, Guo Y 2020 Phys. Rev. Appl. 14 034027Google Scholar

    [16]

    Zheng J, Xiang Y, Li C L, Yuan R Y, Chi F, Guo Y 2021 Phys. Rev. Appl. 16 024046Google Scholar

    [17]

    Zhu F F, Chen W J, Xu Y, Gao C L, Guan D D, Liu C H, Qian D, Zhang S C, Jia J F 2015 Nat. Mater. 14 1020Google Scholar

    [18]

    Gou J, Kong L J, Li H, Zhong Q, Li W B, Cheng P, Chen L, Wu K H 2017 Phys. Rev. Mater. 1 054004Google Scholar

    [19]

    Zang Y Y, Jiang T, Gong Y, Guan Z Y, Liu C, Liao M H, Zhu K J, Li Z, Wang L L, Li W, Song C L, Zhang D, Xu Y, He K, Ma X X, Zhang S C 2018 Adv. Funct. Mater. 28 1802723Google Scholar

    [20]

    Xu C Z, Chan Y H, Chen P, Wang X X, Flototto D, Hlevyack J A, Bian G, Mo S K, Chou M Y, Chiang T C 2018 Phys. Rev. B 97 035122Google Scholar

    [21]

    Yuhara J, Fujii Y, Nishino K, Isobe N, Nakatake M, Xian L, Rubio A, Le-Lay G 2018 2D Mater. 5 025002

    [22]

    Deng J L, Xia B Y, Ma X C, Chen H Q, Shan H, Zhai X F, Li B, Zhao A D, Xu Y, Duan W H, Zhang S C, Wang B, Hou J G 2018 Nat. Mater. 17 1081Google Scholar

    [23]

    Liu Y, Gao N, Zhuang J, Liu C, Wang J, Hao W, Dou S X, Zhao J, Du Y 2019 J. Phys. Chem. Lett. 10 1558Google Scholar

    [24]

    Pang W, Nishino K, Ogikubo T, Araidai M, Nakatake M, Le Lay G, Yuhara J 2020 Appl. Surf. Sci. 517 146224Google Scholar

    [25]

    Li J, Lei T, Wang J, Wu R, Qian H, Ibrahim K 2020 Appl. Phys. Lett. 116 101601Google Scholar

    [26]

    Dhungana D S, Grazianetti C, Martella C, Achilli S, Fratesi G, Molle A 2021 Adv. Funct. Mater. 31 2102797Google Scholar

    [27]

    Ezawa M 2015 J. Phys. Soc. Jpn. 84 121003Google Scholar

    [28]

    Wang D, Chen L, Wang X, Cui G, Zhang P 2015 Phys. Chem. Chem. Phys. 17 26979Google Scholar

    [29]

    Kuang Y D, Lindsay L, Shi S Q, Zheng G P 2016 Nanoscale 8 3760Google Scholar

    [30]

    van den Broek B, Houssa M, Iordanidou K, Pourtois G, Afanas’ev V V, Stesmans A 2016 2D Mater. 3 015001

    [31]

    Nakamura Y, Zhao T, Xi J, Shi W, Wang D, Shuai Z 2017 Adv. Electron. Mater. 3 1700143Google Scholar

    [32]

    Shen L, Lan M, Zhang X, Xiang G, 2017 RSC Adv. 7 9840Google Scholar

    [33]

    Hattori A, Tanaya S, Yada K, Araidai M, Sato M, Hatsugai Y, Shiraishi K, Tanaka Y 2017 J. Phys.: Condens. Matter 29 115302Google Scholar

    [34]

    Fadaie M, Shahtahmassebi N, Roknabad M R, Gulseren O 2018 Phys. Lett. A 382 180Google Scholar

    [35]

    Chaves A J, Ribeiro R M, Frederico T, Peres N M R 2017 2D Mater. 4 025086

    [36]

    M. Ezawa 2012 Phys. Rev. B 86 161407Google Scholar

    [37]

    Salazar C, Muniz R A, Sipe J E 2017 Phys. Rev. Mater. 1 054006Google Scholar

    [38]

    Rachel S, Ezawa M 2014 Phys. Rev. B 89 195303Google Scholar

    [39]

    Lado J L, Fernandez-Rossier J 2014 Phys. Rev. Lett. 113 027203Google Scholar

    [40]

    Li S S, Zhang C W 2016 Mater. Chem. Phys. 173 246Google Scholar

    [41]

    W. Xiong, C. Xia, T. Wang, Y. Peng, Y. Jia 2016 J. Phys. Chem. C 120 10622Google Scholar

    [42]

    Krompiewski S, Cuniberti G 2017 Phys. Rev. B 96 155447Google Scholar

    [43]

    Zhou H, Cai Y, Zhang G, Zhang Y W 2016 Phys. Rev. B 94 045423Google Scholar

    [44]

    Peng B, Zhang H, Shao H, Xu Y, Ni G, Zhang R, Zhu H 2016 Phys. Rev. B 94 245420Google Scholar

    [45]

    Peng X F, Zhou X, Jiang X T, Gao R B, Tan S H, Chen K Q 2017 J. Appl. Phys. 122 054302Google Scholar

    [46]

    Noshin M, Khan A I, Subrina S 2018 Nanotechnology 29 185706Google Scholar

    [47]

    郑军, 李春雷, 王小明, 袁瑞旸 2021 物理学报 70 147301Google Scholar

    Zheng J, Li C L, Wang X M, Yuan R Y 2021 Acta Phys. Sin. 70 147301Google Scholar

    [48]

    Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802Google Scholar

    [49]

    Ezawa M 2012 Phys. Rev. Lett. 109 055502Google Scholar

    [50]

    Zheng J, Chi F, Guo Y 2018 Appl. Phys. Lett. 113 112404Google Scholar

    [51]

    Zheng J, Chi F, Guo Y 2018 Phys. Rev. Appl. 9 024012Google Scholar

    [52]

    Haldane F D M 1988 Phys. Rev. Lett. 61 2015Google Scholar

    [53]

    Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801Google Scholar

    [54]

    Williams J R, Carlo L D, Marcus C M 2007 Science 317 638Google Scholar

    [55]

    Pastawski H M 1991 Phys. Rev. B 44 6329Google Scholar

    [56]

    Datta S 1992 Phys. Rev. B 45 1347

    [57]

    Lee D H, Joannopoulos J D 1981 Phys. Rev. B 23 4997Google Scholar

    [58]

    Sancho M P L, Sancho J M L, Rubio J 1984 J. Phys. F: Met. Phys. 14 1205Google Scholar

    [59]

    Sancho M P L, Sancho J M L, Sancho J M L, Rubio J 1985 J. Phys. F: Met. Phys. 15 851Google Scholar

  • [1] 彭淑平, 邓淑玲, 刘乾, 董丞骐, 范志强. N, B原子取代调控M-OPE分子器件的量子干涉与自旋输运. 物理学报, 2024, 73(10): 108501. doi: 10.7498/aps.73.20240174
    [2] 彭淑平, 黄旭东, 刘乾, 任鹏, 伍丹, 范志强. 二噻吩硼烷异构体分子结构测定的第一性原理研究. 物理学报, 2023, 72(5): 058501. doi: 10.7498/aps.72.20221973
    [3] 刘畅, 王亚愚. 磁性拓扑绝缘体中的量子输运现象. 物理学报, 2023, 72(17): 177301. doi: 10.7498/aps.72.20230690
    [4] 贾亮广, 刘猛, 陈瑶瑶, 张钰, 王业亮. 单层二维量子自旋霍尔绝缘体1T'-WTe2研究进展. 物理学报, 2022, 71(12): 127308. doi: 10.7498/aps.71.20220100
    [5] 许佳玲, 贾利云, 刘超, 吴佺, 赵领军, 马丽, 侯登录. Li(Na)AuS体系拓扑绝缘体材料的能带结构. 物理学报, 2021, 70(2): 027101. doi: 10.7498/aps.70.20200885
    [6] 王航天, 赵海慧, 温良恭, 吴晓君, 聂天晓, 赵巍胜. 高性能太赫兹发射: 从拓扑绝缘体到拓扑自旋电子. 物理学报, 2020, 69(20): 200704. doi: 10.7498/aps.69.20200680
    [7] 贾鼎, 葛勇, 袁寿其, 孙宏祥. 基于蜂窝晶格声子晶体的双频带声拓扑绝缘体. 物理学报, 2019, 68(22): 224301. doi: 10.7498/aps.68.20190951
    [8] 刘畅, 刘祥瑞. 强三维拓扑绝缘体与磁性拓扑绝缘体的角分辨光电子能谱学研究进展. 物理学报, 2019, 68(22): 227901. doi: 10.7498/aps.68.20191450
    [9] 向天, 程亮, 齐静波. 拓扑绝缘体中的超快电荷自旋动力学. 物理学报, 2019, 68(22): 227202. doi: 10.7498/aps.68.20191433
    [10] 相阳, 郑军, 李春雷, 郭永. 局域交换场和电场调控的锗烯纳米带自旋过滤效应. 物理学报, 2019, 68(18): 187302. doi: 10.7498/aps.68.20190817
    [11] 高艺璇, 张礼智, 张余洋, 杜世萱. 二维有机拓扑绝缘体的研究进展. 物理学报, 2018, 67(23): 238101. doi: 10.7498/aps.67.20181711
    [12] 敬玉梅, 黄少云, 吴金雄, 彭海琳, 徐洪起. 三维拓扑绝缘体antidot阵列结构中的磁致输运研究. 物理学报, 2018, 67(4): 047301. doi: 10.7498/aps.67.20172346
    [13] 邓小清, 孙琳, 李春先. 界面铁掺杂锯齿形石墨烯纳米带的自旋输运性能. 物理学报, 2016, 65(6): 068503. doi: 10.7498/aps.65.068503
    [14] 王青, 盛利. 磁场中的拓扑绝缘体边缘态性质. 物理学报, 2015, 64(9): 097302. doi: 10.7498/aps.64.097302
    [15] 李兆国, 张帅, 宋凤麒. 拓扑绝缘体的普适电导涨落. 物理学报, 2015, 64(9): 097202. doi: 10.7498/aps.64.097202
    [16] 白继元, 贺泽龙, 杨守斌. 平行耦合双量子点分子A-B干涉仪的电荷及其自旋输运. 物理学报, 2014, 63(1): 017303. doi: 10.7498/aps.63.017303
    [17] 陈艳丽, 彭向阳, 杨红, 常胜利, 张凯旺, 钟建新. 拓扑绝缘体Bi2Se3中层堆垛效应的第一性原理研究. 物理学报, 2014, 63(18): 187303. doi: 10.7498/aps.63.187303
    [18] 李平原, 陈永亮, 周大进, 陈鹏, 张勇, 邓水全, 崔雅静, 赵勇. 拓扑绝缘体Bi2Te3的热膨胀系数研究. 物理学报, 2014, 63(11): 117301. doi: 10.7498/aps.63.117301
    [19] 曾伦武, 张浩, 唐中良, 宋润霞. 拓扑绝缘体椭球粒子的电磁散射. 物理学报, 2012, 61(17): 177303. doi: 10.7498/aps.61.177303
    [20] 胡长城, 王刚, 叶慧琪, 刘宝利. 瞬态自旋光栅系统的建设及其在自旋输运研究中的应用. 物理学报, 2010, 59(1): 597-602. doi: 10.7498/aps.59.597
计量
  • 文章访问数:  4941
  • PDF下载量:  90
出版历程
  • 收稿日期:  2022-02-14
  • 修回日期:  2022-03-17
  • 上网日期:  2022-07-02
  • 刊出日期:  2022-07-20

/

返回文章
返回