Quantum Hall Effect and Hall Voltage

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SUMMARY

The Quantum Hall Effect describes the relationship between transverse and longitudinal resistance in a conductor subjected to a magnetic field. Hall resistance is defined as the ratio of Hall voltage (Vhall) to current (I), expressed as Rhall = Vhall/I. This relationship highlights that Hall resistance arises from the charge flow across the conductor, influenced by the magnetic field, rather than being a direct application of Ohm's Law. Understanding this distinction clarifies the behavior of charge carriers in a magnetic field.

PREREQUISITES
  • Quantum mechanics fundamentals
  • Electromagnetism principles
  • Understanding of resistance and voltage concepts
  • Basic knowledge of Ohm's Law
NEXT STEPS
  • Study the derivation of the Quantum Hall Effect
  • Explore the mathematical formulation of Hall voltage
  • Investigate the implications of magnetic fields on charge carriers
  • Learn about applications of the Quantum Hall Effect in modern physics
USEFUL FOR

Physics students, researchers in condensed matter physics, and anyone interested in the principles of magnetoresistance and its applications in technology.

Salamon
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I understand that the Quantum Hall Effect explains how both the transverse and longitudinal resistance vary with magnetic field strength.

I don’t get why the hall resistance is equal to the hall voltage over the current .


I know current isn’t a vector quantity but isn’t the hall resistance an opposition to the charge flow that goes across the conductor due to the magnetic field?

I have read that Ohm’s Law has nothing to do with Hall Voltage but I can’t understand why Rhall=Vhall/I

I would only think the longitudinal resistance would be an opposition to the current I.

What is wrong with the way I am visualizing this?
 

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