小分量子霍效中的理差距 (文)＠PEREGRINE科滴

2023-04-06 20:08:35| 人80| 回0 | 上一篇 | 下一篇

小分量子霍效中的理差距 (文)

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Quantifying the effects of finite sample thicknesses and disorder will help researchers find agreement between predicted and observed energy gaps.

量化有限之本厚度及秩序的影，有助於研究人找到，被及被察到之能隙的一致性。

In the fractional quantum Hall effect (FQHE), a two-dimensional electron gas at low temperature and high magnetic field forms an incompressible liquid of quasiparticles that have fractional electric charge.

在分量子霍效(FQHE：一物理象，其中二(2D)子的霍，在e²/h的分值，精地展出量化的平台.它是集的一特性，其中子合磁通量以生新的粒子，且激具有分的基本荷，因此可能也具有分的量)中，二子，在低及高磁下，形成一具有分荷之粒子的不可液。

As a result, its Hall resistance is quantized at fractional rather than integer intervals. A basic property of the system is the energy gap between its incompressible ground state and its excited states. But despite nearly 40 years of study, the theoretical predictions for the gap’s size are consistently larger than what’s measured experimentally.

因此，其霍阻抗，以分而非整的被量化。系的一基本性，是其不可之基其激之的能隙。不，管近40年的研究，有此隙大小的理，始比定的大。

The primary reasons for that discrepancy are known. Among them are the nonzero thickness of the electron layer and the heterogeneity, defects, and other forms of disorder in real samples. Although theorists have tried to account for those and other effects, their models still predict too large an energy gap.

那差的多主要原因，是所周知的。其中包括子的非零厚度，及本中的性、缺陷其他形式的秩序。然，理家一直，明那些及其他的影。不，他的模型仍然大的能隙。

Mansour Shayegan and his colleagues at Princeton University have now conducted the first experimental analysis of the relationship between electron-layer thickness and the FQHE energy gap. Their measurements provide a benchmark for theorists trying to close the gap in energy gap predictions.

目前，Mansour Shayegan及其美普林斯大的同僚已行了，子厚度FQHE能隙之的首度分析。他的量小能隙差距的理家，提供了一基。

Shayegan and his team prepared gallium arsenide quantum wells whose widths w, ranging from 20 nm to 80 nm, roughly set the electron-layer thickness w. When the researchers measured the devices’ longitudinal resistances as a function of an applied magnetic field, the resistances showed about a dozen minima, which corresponded to FQHE states with different fractional values of ν, the Landau filling factor.

Shayegan及其作了，多度20 nm到80 nm的砷化量子阱，概略地定子厚度。研究人量了，此些置的向阻抗，作用磁的一函，此些阻抗示了，十符合具有不同ν(朗道填充因子)分值之FQHE的小值。

1.度接近零，特定填充因子的向阻抗，以取於能隙的速率，呈指下降至零。量的能隙(色)，定性但不定量地先前的理模型(色、色及橙色)一致。

As shown in the graph, the researchers measured the ν = 1/3 energy gap (1/3Δ) at an array of quantum well widths (red). As expected theoretically, the gap decreased with increasing thickness. But the measured energy gaps were still consistently lower than those calculated theoretically (green, blue, and orange).

如示，此些研究人，在一系列量子阱度(色)，到了ν= 1/3 能隙(1/3Δ)。正如由理期般，隙著厚度增加而小。不，此些被定的能隙，仍然始低於理估算的能隙(色、色及橙色)。

The models, however, consider the role of nonzero electron-layer thickness but not disorder. For each quantum-well thickness, the researchers looked at the experimental energy gaps for a series of filling factors and found an energy offset—a disorder energy—that made the extrapolated trend match what’s expected at the midpoint of the range of ν.

不，此些模型考量了，非零子厚度而不是秩序的角色。每量子阱厚度，此些研究人探究了，一系列填充因子的能隙，且了一使推，ν中之期相符的能量抵消(一秩序的能量)。

The samples were relatively high quality; the disorder energy for the 70 nm well was 1.2 ± 0.2 K, half to a 10th of the values measured in previous studies on similar and other FQHE systems. Overall, the disorder energies had a scattered range of comparable values and no clear relationship with thickness.

相上，此些本是高量的；就70 nm阱而言，秩序能量是1.2 ± 0.2 K，是先前似及其他FQHE系之研究中，量值的一半到十分之一。上，秩序能量具有一分散的可比值，且厚度明的。

When offset by the disorder energies, the energy gaps for thicker samples approximately matched the theoretical values, although thinner samples’ energies still fell short of theory. Getting better agreement between theory and experiment will require a more rigorous analysis of disorder and direct comparison with the data collected by Shayegan and his group.