Low-energy theory for electron-phonon scattering in topological insulators

该项目旨在推进三维强拓扑绝缘体，特别是Bi 2Se 3和Bi 2 Te 3中表面狄拉克费米子的电子-声子散射效应的低能理论。 我们将考虑不同的几何形状，包括圆柱形和/或矩形纳米线，薄膜，和半无限样品。三个子项目总结和结构我们的主要目标：1）我们将研究电子-声子耦合效应对表面狄拉克费米子在拓扑绝缘体纳米线。特别是，我们将定量确定有效电子-声子耦合强度、声子感生磁电阻率贡献、准粒子寿命和相位相干长度。 我们将考虑具有圆形和/或矩形横截面的纳米线，研究任意温度的情况，并充分考虑磁场效应和费米能级的变化。2）我们将分析由于与声学声子的耦合，强拓扑绝缘体中自旋相关的弹道表面态输运的内在限制。 我们计划通过计算自旋弛豫率和自旋电阻率作为温度、掺杂水平和磁场的函数来研究半无限和薄膜几何结构。3）到目前为止，拓扑绝缘体中的电子-声子散射仅讨论了有限掺杂的情况，即，远离狄拉克点 当费米能量接近狄拉克点时，需要非微扰方法。 我们将在半无限几何的泛函积分方法中处理这个多体问题。 使用由此产生的有效的低能量理论的表面狄拉克费米子，我们将研究的电阻率和准粒子寿命的温度依赖性。磁场效应将包括在我们的分析中，我们将探讨是否可以实现电荷和/或自旋密度波相位。我们还计划研究表面超导性的前景。

This project is aimed at advancing the low-energy theory of electron-phonon scattering effects for the surface Dirac fermions in three-dimensional strong topological insulators, in particular in Bi2Se3 and Bi2Te3. We will consider different geometries, including cylindrical and/or rectangular nanowires, thin films, and semi-infinite samples.Three subprojects summarize and structure our main objectives:1) We will study electron-phonon coupling effects on the surface Dirac fermions in topological insulator nanowires. In particular, we will quantitatively determine the effective electron-phonon coupling strength, the phonon-induced magneto-resistivity contribution, the quasiparticle lifetime, and the phase coherence length. We shall consider nanowires with circular and/or rectangular cross-section, study the case of arbitrary temperatures, and fully take into account magnetic field effects and variations of the Fermi level.2) We will analyze intrinsic limits on spin-dependent ballistic surface state transport in strong topogical insulators due to the coupling to acoustic phonons. We plan to study the semi-infinite and the thin-film geometry by computing the spin relaxation rate and the spin resistivity as a function of temperature, doping level, and magnetic field.3) Electron-phonon scattering in topological insulators so far has only been discussed the case of finite doping, i.e., away from the Dirac point. When the Fermi energy is close to the Dirac point, non-perturbative approaches are needed. We will approach this many-body problem within a functional integral approach for the semi-infinite geometry. Using the resulting effective low-energy theory for the surface Dirac fermions, we will study the temperature dependence of the resistivity and of the quasiparticle lifetime. Magnetic field effects will be included in our analysis, and we shall explore whether charge- and/or spin-density wave phases could be realized. We also plan to investigate the prospects for surface superconductivity.