> The fractional quantum Hall effect is more complicated and still considered an open research problem. [2] Its existence relies fundamentally on electron–electron interactions. In 1988, it was proposed that there was quantum Hall effect without Landau levels. [3] This quantum Hall effect is referred to as the quantum anomalous Hall (QAH) effect. There is also a new concept of the quantum spin Hall effect which is an analogue of the quantum Hall effect, where spin currents flow instead of charge currents. [4]

Fractional quantum Hall effect: https://en.wikipedia.org/wiki/Fractional_quantum_Hall_effect :

> The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2-dimensional (2D) electrons shows precisely quantized plateaus at fractional values of e^{2}/h, where e is the electron charge and h is the Planck constant. It is a property of a collective state in which electrons bind magnetic flux lines to make new quasiparticles, and excitations have a fractional elementary charge and possibly also fractional statistics

westurner.github .io/hnlog/#story-38139569 ctrl-f "quantum Hall", "hall effect" :

- "Electrical switching of the edge current chirality in quantum Hall insulators" (2023) https://www.nature.com/articles/s41563-023-01694-y ( https://news.ycombinator.com/item?id=38139569 )

But that's not elementary charge.

"Inside the proton, the ‘most complicated thing you could possibly imagine’" (2024) https://www.quantamagazine.org/inside-the-proton-the-most-co... https://news.ycombinator.com/item?id=39374020 :

> Despite this difference in complexity, an electron has a charge of -e and a proton has a charge of +e. They are exactly complementary regarding charge (if I am understanding right, I am not a smart person).

> my question is... why? why must protons and electrons be perfectly complementary regarding charge? if the proton is this insanely complex thing, by what rule does it end up equaling exactly the opposite charge of an electron? why not a charge of +1.8e, or +3e, or 0.1666e, etc? Certainly it is convenient that a proton and electron complement each other, but what makes that the case?