二维电子气中量子态的自旋极化研究

Many interesting phenomena can be observed in the two-dimensional electron gas, such as quantum Hall effect, fractional quantum Hall effect, Wigner crystal, electron bubble state and stripe state. Although among those quantum states, fractional quantum Hall effect has attracted great attention, the spin polarization of most fractional states has not been determined experimentally. For example, the spin polarization of the even denominator state 5/2 is still under debate. The information of the spin polarization will help with the confirmation of 5/2 state’s wave function for its potential application in topological quantum computation. In addition, the spin polarization studies in the electron bubble state and the stripe state may also partially clarify the emergence of the quantum states and the competition between the states. Through the in-plane magnetic field, the Zeeman energy from the spin can be adjusted experimentally, while maintaining a constant filling factor from the perpendicular magnetic field. Therefore, the spin polarization can be studied through the stability of the quantum states as a function of in-plane magnetic field. We propose to probe the spin polarization status and the phase competition through the energy gap and tunneling measurements in the two-dimensional electron gas within GaAs heterostructure, in order to learn more about the many body effect in such a system. We plan to focus on the second and third Landau levels, which contain many interesting states, including the even denominator states.

低温强磁场下的二维电子气具有丰富的量子现象，如整数量子霍尔效应、分数量子霍尔效应、Wigner晶格、电子气泡相、各向异性态等。以较被人关注的分数量子霍尔效应为例，许多分数态依然缺乏足够的与自旋极化相关的实验研究。譬如，可用于拓扑量子计算的5/2态中有多个可能的波函数，如果能判定其自旋极化状态则有助于甄别其波函数，而5/2态的自旋极化与否目前尚未有定论。不仅如此，在电子气泡相和各向异性相中的自旋极化研究也有助于理解这个体系中量子态的产生与量子态间的竞争。通过引入二维电子气面内的磁场，实验上可以在维持垂直磁场所引起的朗道能级不变的条件下，调节总磁场所引起的塞曼能，因而一个量子态是否自旋极化可以通过其稳定度随面内磁场的变化予以研究。我们计划在砷化镓异质结的二维电子气中，通过能隙和隧穿测量等手段，探索多体相互作用所产生的量子态的自旋极化现象和相竞争，重点将关注量子现象最丰富的第二和第三朗道能级。

压电驱动的旋转样品台对于倾斜场实验有控制精度高的优势，但是因为技术原因难以降温。我们通过搭建旋转样品台和合理滤波，实现了最低电子温度25 mK、角分辨 < 0.1°的倾斜场实验条件[Review of Scientific Instruments 90, 023905 (2019)]，并以此研究偶数分母分数量子霍尔态的自旋极化状态。通过对不同二维下量子态的能隙随角度依赖关系的测量，我们发现了有限尺寸效应的实验证据，并且实验结果支持自旋极化的5/2和7/2分数态[Physical Review Research 2, 022056(R) (2020)]。此外，在研究中我们还意外发现了3/2分数量子霍尔平台 [Nature Communications 10, 4351 (2019)]，利用本项目积累的部分降低电子温度的技术进行了10微eV量级能带变化的实验观测 [Physical Review Letters 123, 206602 (2019)]，并且在项目经费的支持开展了计划外的量子反常霍尔效应体系中量子相变与标度行为研究 [Nature Communications 11, 4532 (2020)]。