标题： 磁场诱导的螺旋模式和准弹道拓扑绝缘体纳米带中周向量子化表面态子带的拓扑转变 显示英文标题

标题： Magnetic field induced helical mode and topological transitions in a quasi-ballistic topological insulator nanoribbon with circumferentially quantized surface state sub-bands

摘要： 一种拓扑绝缘体（TI）纳米线（NW），其中心是绝缘的，而二维自旋螺旋狄拉克费米子拓扑表面态（TSS）在周围被量化为一系列一维子带，有望带来新颖的拓扑物理和应用。 轴向磁通（{\Phi }）通过中心驱动表面子带中的周期性拓扑转变，从所有双简并态且在整数（包括零）通量量子（{\Phi }$_0$ = h/e，其中h是普朗克常数，e是电子电荷）时具有间隙狄拉克点（DP），转变为在半整数通量量子时包含一个拓扑保护的非简并一维自旋螺旋模态且恢复狄拉克点。 所产生的磁电导预计会表现出阿哈罗诺夫-玻姆振荡（ABO），其最大值在半整数或整数通量量子处交替出现（称为{\pi }-ABO或0-ABO），这取决于费米波矢（k$_F$，周期为2{\pi }/C，C为纳米线周长）。 这里，我们报告了在Bi$_2$Te$_3$ TI纳米线（NR，矩形横截面NW）场效应器件中，0-ABO和{\pi }-ABO之间清晰的k$_F$-周期性交替现象，这些器件表现出约2 {\mu }m的准弹道传输（表现为与长度无关的电导、随着温度(T)增加的ABO振幅指数衰减以及提取的相位相干长度与1/T成正比）。 导电率作为栅极电压的函数，在半通量量子和零通量量子下也表现出清晰但反相关的振荡，周期性地依赖于k$_F$(周期为 2{\pi }/C，等效于当C包含整数倍的费米波长 2{\pi }/k$_F$)，这与环向量化表面子带一致。 我们还提取了TSS从体价带中出现的最小费米能量和动量，这与已知的Bi$_2$Te$_3$带结构一致。 显示英文摘要

摘要： A topological insulator (TI) nanowire (NW), where the core is insulating and the 2D spin-helical Dirac fermion topological surface states (TSS) are circumferentially quantized into a series of 1D sub-bands, promises novel topological physics and applications. An axial magnetic flux ({\Phi}) through the core drives periodic topological transitions in the surface sub-bands, changing from being all doubly-degenerate with a gapped Dirac point (DP) at integer (including zero) flux quanta ({\Phi}$_0$ = h/e, with h being the Planck constant and e the electron charge), to contain a topologically-protected, non-degenerate 1D spin helical mode with restored DP at half-integer flux quanta. The resulting magnetoconductance is predicted to exhibit Aharonov-Bohm oscillations (ABO) with maxima occurring alternatively at half-integer or integer flux quanta (referred to as {\pi}-ABO or 0-ABO), depending periodically on the Fermi wavevector (k$_F$, with period 2{\pi}/C, C being the NW circumference). Here, we report a clear observation of such k$_F$-periodic alternations between 0-ABO and {\pi}-ABO in Bi$_2$Te$_3$ TI nanoribbon (NR, a rectangular cross sectional NW) field effect devices, which exhibit quasi-ballistic transport over ~2 {\mu}m (as manifested in length-independent conductance, exponential decaying ABO amplitude with increasing temperature (T), and an 1/T dependence of the extracted phase coherence length). The conductances as functions of the gate voltage at half and zero flux quanta also exhibit clear, but anti-correlated oscillations periodic in k$_F$ (with period 2{\pi}/C, equivalently when C encloses an integer multiples of Fermi wavelength 2{\pi}/k$_F$), consistent with the circumferentially quantized surface sub-bands. We also extract the minimal Fermi energy and momentum for TSS to emerge out of the bulk valence band, in agreement with the known Bi$_2$Te$_3$ bandstructure.