The remarkable world of quantum physics continues to astound us with its ability to transform our understanding of low-dimensional systems. Through the confinement of low-dimensional electrons in narrow constrictions formed in high-quality semiconductor heterostructures like GaAs/AlGaAs, we have unlocked new frontiers in the field of solid-state physics - both fundamentally and technologically. As we subject electrons to strong perpendicular magnetic fields, their energy becomes quantized through the formation of Landau Levels, resulting in quantisation in the transverse resistance. This phenomenon, known as the Quantum Hall Effect, with its mysterious filling factor v taking on both integer and fractional values, has paved the way for remarkable advancements in producing high-quality semiconductor heterostructures [1].
Through experiments, over a hundred fractional quantum Hall states have been discovered, with the 5/2 state generating significant interest due to its non-Abelian statistics and its role in upcoming quantum computing schemes. But it's not just the 2D electrons that captivate us - when confined to move along a direction, they give rise to quasi-1D electrons that provide an important playground to investigate interaction effects between neighbouring 1D electrons. Conductance measurement through them results in 1D quantisation as N2e^2/h, where N=1,2,3... represents the number of occupied 1D subbands. Recently, 1D electrons were shown to exhibit fractional quantised conductance, a counterpart of the Fractional Quantum Hall Effect, though without any magnetic field [2]!
In this talk, I will present experiment results utilising both the 2D and 1D electrons, and their importance for both fundamental quantum physics and emerging quantum technologies.
References:
[1] Shevyrin et al, “Nonequilibrium phenomena in bilayer electron systems”, Phys Rev B, 107, L041302 (2023).
[2] Kumar et al, “Zero-magnetic field fractional quantum states”, Phys Rev Lett, 122, 086803 (2019).