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Orbital Landau level dependence of the fractional quantum Hall effect in quasi-two dimensional electron layers: finite-thickness effects

机译:轨道兰道水平依赖于分数量子霍尔效应   准二维电子层:有限厚度效应

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摘要

The fractional quantum Hall effect (FQHE) in the second orbital Landau levelat filling factor 5/2 remains enigmatic and motivates our work. We consider theeffect of the quasi-2D nature of the experimental FQH system on a number of FQHstates (fillings 1/3, 1/5, 1/2) in the lowest, second, and third Landau levels(LLL, SLL, TLL,) by calculating the overlap, as a function of quasi-2D layerthickness, between the exact ground state of a model Hamiltonian and theconsensus variational wavefunctions (Laughlin wavefunction for 1/3 and 1/5 andthe Moore-Read Pfaffian wavefunction for 1/2). Using large overlap as astability, or FQHE robustness, criterion we find the FQHE does not occur in theTLL (for any thickness), is the most robust for zero thickness in the LLL for1/3 and 1/5 and for 11/5 in the SLL, and is most robust at finite-thickness(4-5 magnetic lengths) in the SLL for the mysterious 5/2 state and the 7/3state. No FQHE is found at 1/2 in the LLL for any thickness. We examine theorbital effects of an in-plane (parallel) magnetic field finding itsapplication effectively reduces the thickness and could destroy the FQHE at 5/2and 7/3, while enhancing it at 11/5 as well as for LLL FQHE states. Thein-plane field effects could thus be qualitatively different in the LLL and theSLL by virtue of magneto-orbital coupling through the finite thickness effect.In the torus geometry, we show the appearance of the threefold topologicaldegeneracy expected for the Pfaffian state which is enhanced by thicknesscorroborating our findings from overlap calculations. Our results haveramifications for wavefunction engineering--the possibility of creating anoptimal experimental system where the 5/2 FQHE state is more likely describedby the Pfaffian state with applications to topological quantum computing.
机译:第二轨道朗道能级在填充因子5/2上的分数量子霍尔效应(FQHE)仍然是令人迷惑的,并激发了我们的工作。我们考虑了实验性FQH系统的准2D性质对最低,第二和第三级Landau级别(LLL,SLL,TLL,FLL,SLL和TLL)中的许多FQH状态(填充1 / 3、1 / 5、1 / 2)的影响),通过计算准汉密尔顿模型的精确基态与共识变分波函数(1/3和1/5的劳克林波函数和1/2的摩尔-读普法夫波函数)之间的重叠(作为准2D层厚度的函数)) 。使用较大的重叠作为稳定性或FQHE鲁棒性,我们发现FQHE在TLL中不发生(对于任何厚度),对于LLL中零厚度的1/3和1/5以及11/5中的11/5来说最坚固SLL,对于神秘的5/2状态和7/3状态,在SLL的有限厚度(4-5磁长度)下最坚固。任何厚度的LLL处均未发现FQHE。我们检查了平面内(平行)磁场的轨道效应,发现其应用有效地减小了厚度,并可能破坏5/2和7/3时的FQHE,同时在11/5以及LLL FQHE状态下增强了FQHE。由于有限厚度效应的磁轨道耦合,因此在LLL和SLL中面内场效应可能在质量上有所不同。在环面几何中,我们展示了对Pfaffian态预期的三重拓扑简并性的出现,该简并性得到了增强厚度证实了我们从重叠计算中得出的结论。我们的结果对波函数工程产生了影响-有可能创建一个最优的实验系统,在该系统中5/2 FQHE状态更可能由Pfaffian状态描述,并应用于拓扑量子计算。

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