Engineering Future Quantum Technologies in Low-Dimensional Systems

低维半导体纳米结构中的量子输运是一个成熟的研究领域，在过去的几十年里，它已经在固态物理学中产生了几个里程碑式的发现。在各种发现中，最突出的是1980年量子霍尔效应（QHE）的发现。QHE是著名的经典霍尔效应的量子性质的第一个实验证明。在QHE中，二维电子气的横向电导表示为（e^2/h）.v，其中v是填充因子。的电导显示出显着的填充因子的整数值的平坦平台。可以注意到，横向电导或QHE与基本常数（e^2/h）成比例，并且不依赖于样品的几何形状或尺寸，因此是不变的。作为一个先驱理论家，R Laughlin提出了一个用拓扑不变量Chern数来描述整数态的理论。1982年，贝尔实验室的物理学家在QHE测量中报告说，新的量子化平台出现在填充因子的分数值，如1/3。这一非凡的发现催生了分数量子霍尔效应（Fractional Quantum Hall Effect，缩写为FWHE）。这是由于在强量子化磁场的影响下，高质量半导体中二维电子气中的电子-电子相互作用。爱因斯坦是固体物理学中第一个证明在极高磁场和极低温度下形成的准粒子将拥有一个电子电荷的一小部分，比如说，1/3。在发现了量子化学后，几项实验研究发现了100多个新的分数态。虽然QHE/QHE在80年代受到了相当大的关注，但当1988年Halfman使用蜂窝晶格上的紧束缚模型提出没有任何磁场的QHE的想法时，一个令人兴奋的发展已经形成。他认为量子霍尔态的存在并不一定需要外部磁场，而是取决于系统的对称性及其拓扑相。这一重要贡献的知识导致了各种发现，包括反常和霍尔效应和拓扑绝缘体。 1988年，人们发现通过一维通道的电导可以量化为（2e^2/h）。N，其中N是整数。这是一个了不起的观察，也是固态物理学中的重大发现之一，二维电子的电导在被限制在一维时会以基本常数（2e^2/h）为单位量子化，这种行为类似于QHE，尽管没有任何磁场。当电子-电子相互作用被引入时，量子化是对量子化的补充，物理学家想知道是否有一个分数对应的一维整数电导量子化。实验物理学中的这个关键问题一直没有答案，直到2018/2019年，基于GaAs的高质量半导体中的电子在2/5、1/6、1/2等数值上表现出以e^2/h为单位的分数电导量子化，当1D通道中的电子配置成锯齿形时，这些新的量子态就形成了，从而实现了“环形路径”和“循环电流”。这些复杂的量子现象导致分数激发，这表明拓扑量子计算方案的承诺。该提案旨在研究弱限制的1D量子线中形成的分数量子态，其中几个参数在实现这种意想不到的量子行为中起着重要作用。我们的目标是研究这些新的分数量子态的性质，以及如何测量和操纵它们的自旋和电荷相位。这些新的量子态将被用来研究通过Aharonov-Bohn干涉法的纠缠，自旋阻塞现象，通过电子聚焦的分数态选择，通过量子散粒噪声测量的电子电荷等。

Quantum transport in low-dimensional semiconductor nanostructures is a well-established field of research that has resulted in several landmark discoveries in solid-state physics over the past several decades. Among various findings, the one which stands out is the discovery of the Quantum Hall Effect (QHE) in 1980. The QHE was the first experimental demonstration of the quantum nature of the celebrated classical Hall effect. In the QHE, the transverse conductance of a two-dimensional electron gas is represented as (e^2/h).v, where v is the filling factor. The conductance shows remarkably flat plateaus for integer values of the filling factor. It may be noted that the transverse conductance or QHE is proportional to fundamental constants (e^2/h), and does not depend on the sample geometry or size, so is invariant. A pioneering theorist, R Laughlin proposed a theory describing the integer states in terms of a topological invariant, Chern number. In 1982, physicists working at Bell labs reported in the QHE measurements that new quantised plateaus appeared at fractional values of the filling factor, like 1/3. This remarkable discovery gave birth to the Fractional Quantum Hall Effect (FQHE). The observation was due to electron-electron interactions in the two-dimensional electron gas in high-quality semiconductors under the influence of a strong quantising magnetic field. FQHE was the first demonstration in solid state physics that the quasiparticles formed at the extremely high magnetic field and very low temperatures would possess a fraction of an electronic charge, say, 1/3. Following the discovery of the FQHE, several experimental studies resulted in the discovery of more than 100 new fractional states. While FQHE/QHE was receiving considerable attention in the 80s, an exciting development took shape when Haldane in 1988 proposed the idea of QHE without any magnetic field using the tight-binding model on a honeycomb lattice. He suggested that the existence of quantum Hall states do not necessarily require an external magnetic field, but depends on the symmetries of the system and its topological phases. This important contribution to the knowledge led to various discoveries, including the anomalous and Hall effects and topological insulators. It was shown in 1988 that conductance through a one-dimensional channel was quantised as (2e^2/h). N, where N is an integer. This was a remarkable observation and one of the significant discoveries in solid-state physics, that the conductance of 2D electrons, when confined to one dimension would quantise in units of fundamental constants (2e^2/h), a behaviour similar to the QHE although without any magnetic field. As FQHE was complementing the IQHE when electron-electron interactions were introduced, physicists wondered if there could be a fractional counterpart of the 1D integer conductance quantisation. This critical question in experimental physics remained unanswered until 2018/2019, when electrons in high-quality semiconductors based on GaAs showed fractional conductance quantisation in units of e^2/h at values 2/5,1/6, 1/2, etc. These new quantum states form when electrons in a 1D channel configure into a zigzag, enabling "ring paths" and "cyclic currents". These complex quantum phenomena result in fractional excitations which show promise for topological quantum computing schemes. This proposal aims to investigate the fractional quantum states formed in weakly confined 1D quantum wires, where several parameters play a significant role in achieving this unexpected quantum behaviour. We aim to investigate the nature of these new fractional quantum states and how their spin and charge phases could be measured and manipulated. These novel quantum states would be utilised to investigate entanglement via Aharonov-Bohn interferometry, spin blockage phenomena, fractional state selection via electron focusing, electronic charge via quantum shot noise measurements, etc.