Quantifying the effects of finite sample thicknesses and disorder will help researchers find agreement between predicted and observed energy gaps.
量化有限之樣本厚度及無秩序的影響，將有助於研究人員們找到，被預測及被觀察到之能隙間的一致性。
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.
在分數量子霍爾效應(FQHE：一種物理現象，其中二維(2D)電子的霍爾電導，在e2/h的分數值處，精確地展現出量化的平台.它是集體狀態的一個特性，其中電子結合磁通量線以產生新的準粒子，且激發具有分數的基本電荷，因此可能也具有分數的統計量)中，二維電子氣體，在低溫及高磁場下，形成一種具有分數電荷之準粒子的不可壓縮液體。
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，其霍爾阻抗，以分數而非整數的區間被量化。該體系的一個基本屬性，是其不可壓縮之基態與其激發態之間的能隙。不過，儘管近40年的研究，有關此間隙大小的理論預測，始終比實驗測定的大。
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.
那種差異的諸多主要原因，是眾所周知的。其中包括電子層的非零厚度，及實際樣本中的異質性、缺陷與其他形式的無秩序。雖然，理論家們一直試圖，說明那些及其他的影響。不過，他們的模型仍然預測過大的能隙。
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及其美國普林斯頓大學的同僚們已經進行了，電子層厚度與FQHE能隙間之關係的首度實驗分析。他們的測量為試圖縮小能隙預測差距的理論家們，提供了一種基準。
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 w̃. 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及其團隊製作了，諸多寬度從20 nm到80 nm的砷化鎵量子阱，概略地設定電子層厚度。研究人員們測量了，此些裝置的縱向阻抗，作為實用磁場的一種函數，此些阻抗顯示了，大約十幾個符合具有不同ν(朗道填充因子)分數值之FQHE狀態的極小值。
圖1.當溫度接近零時，特定填充因子的縱向阻抗，以取決於能隙的速率，呈指數下降至零。實驗測量的能隙(紅色)，定性但不定量地與先前的理論模型(綠色、藍色及橙色)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).
如圖顯示，此些研究人員，在一系列量子阱寬度(紅色)處，測到了ν= 1/3 能隙(1/3Δ)。正如由理論預期般，間隙隨著厚度增加而減小。不過，此些被測定的能隙，仍然始終低於理論估算的能隙(綠色、藍色及橙色)。
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.
不過，此些模型考量了，非零電子層厚度而不是無秩序的角色。對每個量子阱厚度，此些研究人員探究了，一系列填充因子的實驗能隙，且發現了一種使推測趨勢，與ν範圍中點處之預期相符的能量抵消(一種無秩序的能量)。
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.
相對上，此些樣本是高質量的；就70 nm阱而言，無秩序能量是1.2 ± 0.2 K，這是先前對類似及其他FQHE體系之研究中，測量值的一半到十分之一。總體上，無秩序能量具有一種分散的可比值範圍，且與厚度無明確的關係。
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.
當被無秩序能量抵消時，較厚樣本的能隙，大致上與理論值相一致。雖然，較薄樣本的能量仍然達不到理論值。要在理論與實驗之間取得更佳的一致性，將需要無秩序的更精確分析，並與Shayegan及其團隊收集的數據，進行直接比較。
網址：https://physicstoday.scitation.org/do/10.1063/PT.6.1.20210820a/full/
翻譯: 許東榮
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