Study of high Landau levels by spatial modulation technique

制备了单向周期、单向准周期（Fibonacci）和二维三角形横向超晶格（LSL），详细研究了它们在磁场下的行为，观察到Fibonacci LSL的复杂可伸缩振荡和开轨道的几何共振.通过详细的傅里叶分析，调制电位的轮廓被发现是很好地描述了叠加的周期调制与其周期连续缩放的黄金分割比。在零场电阻率的强烈增强，然后由尖锐的负磁阻观察斐波那契LSL与接近费米波长的短单位长度。它们可以分别用斐波那契晶格衍射引起的反向散射率增强和磁击穿效应来解释。在周期性LSL中，研究了Shubnikov-de哈斯振荡的振幅和相位调制。调制显示为 关于我们 o可以通过考虑碰撞和扩散对电导率的贡献的磁场依赖性来定量解释。对Shubnikov-de哈斯振荡的线形分析表明，费米能级随磁场的变化而振荡，朗道能级的无序展宽可以用高斯近似表示.周期性调制提高了朗道能级的简并度，导致朗道带宽度随磁场振荡。奇整数量子霍尔效应的激活能随朗道带宽度的增加而减小。奇数分子的分数量子霍尔效应在调制作用下消失，而偶数分子的分数量子霍尔效应则存在甚至增强。分数量子霍尔态的消失可能是在最低朗道能级上向新条纹态相变的信号。少

Unidirectional periodic, unidirectional quasiperiodic (Fibonacci) and two-dimensional triangular lateral superlattices (LSLs) are prepared for detailed investigation of their behavior under magnetic fields.Complicated commensurability oscillation and the geometric resonance of the open orbits are observed for Fibonacci LSLs. By detailed Fourier analyses, the profile of the modulated potential is found to be well-described by the superposition of periodic modulations with their periods scaled consecutively by the golden ratio. Strong enhancement in the zero-field resistivity, followed by sharp negative magnetoresistance is observed for Fibonacci LSL with short unit lengths close to the Fermi wave length. They can be explained by enhanced back-scattering rate by the diffraction from the Fibonacci lattice, and magnetic breakdown effect, respectively.In periodic LSLs, the modulation of the amplitude and the phase of the Shubnikov-de Haas oscillations is studied. The modulations are shown t … More o be quantitatively explicable by taking the magnetic-field dependence of the collisional and diffusion contributions to the conductivity into account. Detailed analyses of the line shape of the Shubnikov-de Haas oscillation reveal that the Fermi energy oscillates with the magnetic field and that the disorder broadening of the Landau levels is well approximated by Gaussians.Integral and Fractional quantum Hall effects under periodic modulation are also investigated. The periodic modulation lifts the degeneracy of the Landau levels, resulting in the Landau bands with the width oscillating with the magnetic field. The activation energies for odd-integer quantum Hall effects are found to decrease responding to the width acquired by the Landau bands. Odd numerator fractional quantum Hall effects are observed to vanish by the introduction of the modulation, while those with even numerator are found to survive or even to be enhanced. The disappearance of the fractional quantum Hall state may be signaling the phase transition into novel stripe state in the lowest Landau level. Less