Engineering Future Quantum Technologies in Low-Dimensional Systems

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.