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中的行为，观察到Fibonacci横向超晶格的复杂公度振荡和开放轨道的几何共振。通过详细的傅立叶分析，发现调制电势的分布可以很好地用周期调制的叠加来描述，这些周期调制的周期被黄金比例连续标度。在费米波长附近的短单元长度的斐波纳契LSL中，观察到零场电阻率的强烈增强，紧接着是急剧的负磁电阻。它们分别可以用斐波那契晶格绕射增强的背向散射率和磁击穿效应来解释。在周期LSL中，研究了Shubnikov-de Haas振荡的幅度和相位的调制。调制方式如…所示考虑到碰撞和扩散对电导率的贡献与磁场的关系，更能定量地解释这一点。对Shubnikov-de Haas振荡线形的详细分析表明，费米能量随磁场的变化而振荡，朗道能级的无序展宽可以很好地用高斯近似。周期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大而减小。观察到奇数分子分数量子霍尔效应随着调制的引入而消失，而偶数分子量子霍尔效应被保留或增强。分数量子霍尔态的消失可能预示着在最低朗道能级处发生了向新的条纹态的相变。较少

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