key points: 1. The quantum Hall effect is a remarkable physical phenomenon in which electrons flow in a two-dimensional plane subjected to a perpendicular magnetic field, resulting in unique electrical properties. 2. In the classical Hall effect, the magnetic field causes electrons to accumulate on one side of the sample, creating a Hall voltage perpendicular to the current flow. This leads to a resistivity matrix with both longitudinal and Hall components. 3. Classical physics predicts that the Hall resistivity should be directly proportional to the magnetic field, and the longitudinal resistivity should be independent of it. 4. Quantum mechanics introduces two crucial concepts: the flux quantum (hc/e) and the dimensionless number "nu" (the ratio of electron density to flux quanta). 5. The quantum Hall effect deviates from classical expectations. Instead of a linear relationship, it exhibits quantized steps in the Hall resistivity as a function of magnetic field or nu. 6. These steps are extremely precise, with the resistivity remaining constant to one part in a billion across each step. 7. The most striking feature is that the resistivity values at the steps are quantized to universal values, particularly h/e^2. 8. The quantum Hall effect is observed across various materials and under specific conditions, including low temperatures and strong magnetic fields, making it a universal phenomenon. 9. There are two types of quantum Hall effect: integer values of nu (integer quantum Hall effect) and fractional values of nu (fractional quantum Hall effect). 10. Key differences between these two types include the role of electron-electron interactions and the emergence of fractional excitations in the fractional quantum Hall effect. 11. Research directions in understanding the quantum Hall effect include exploring its underlying physics, implications, mathematical aspects (topology), and potential applications such as quantum computing. 12. Topological states of matter, like topological insulators and superconductors, also exhibit unique properties without the need for magnetic fields. 13. The quantum Hall effect's precision and universality have practical applications, such as calibrating measurement units, and hold promise for future technologies, including topological quantum computing. (if wrong anything, please clarify it)
So they ran some oms though a flat wire with a magnet next to it. They thought the resistance would change evenly. But it changed in steps. How is this proof of anything other than some preferred energy levels for electons? I am deep into an argument about the lack of hard proof for extra dimensional space. Just factors without a visible source. If you could point in the right direction I would appreciate it.
1) What do you mean by "running a few Ohms"? You run a current, not a resistance. 2) There is nothing here involving extra dimensions. Why would there be? If anything, the QHE involves effectively lower-dimensional systems, since you restrict your electrons to a flat material sample.
@@alexanderfagerlund2669 search for "Photonic topological boundary pumping as a probe of 4D quantum Hall physics" on nature website. "Physically, we don’t have a 4D spatial system, but we can access 4D quantum Hall physics using this lower-dimensional system because the higher-dimensional system is coded in the complexity of the structure.” Professor Mikael Rechtsman. I agree on the other parts of your counter-arguments.
