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（LSLs），用于详细研究它们在磁场作用下的行为。研究了Fibonacci LSLs的复杂可通约性振荡和开放轨道的几何共振。通过详细的傅里叶分析，发现调制电位的分布可以用周期调制的叠加来很好地描述，它们的周期按黄金比例连续缩放。对于接近费米波长的短单位长度的斐波那契LSL，观察到零场电阻率的强增强，随后是急剧的负磁阻。它们可以分别用斐波那契晶格衍射增强的后向散射率和磁击穿效应来解释。在周期性LSLs中，研究了舒布尼科夫-德哈斯振荡振幅和相位的调制。考虑到对电导率贡献的碰撞和扩散对磁场的依赖，更能定量地解释这些调制。对舒布尼科夫-德哈斯振荡线形的详细分析表明，费米能量随磁场而振荡，并且朗道能级的无序展宽很好地近似于高斯能级。研究了周期调制下的积分和分数量子霍尔效应。周期调制提高了朗道能级的简并性，导致朗道带宽度随磁场振荡。奇整数量子霍尔效应的活化能随朗道带宽度的增大而减小。引入调制后，奇数分子分数量子霍尔效应消失，而偶数分子分数量子霍尔效应存在或增强。分数阶量子霍尔态的消失可能是在最低朗道能级上向新型条纹态相变的信号。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