# Current and Quantum Hall Effect

• Benevito
In summary, the Hall Effect is a phenomenon where a magnetic field perpendicular to an electric current causes a voltage difference across a conductor. It was discovered in 1879 by Edwin Hall and has practical applications in various industries. The Quantum Hall Effect, a quantum mechanical version observed in two-dimensional electron systems, earned Klaus von Klitzing the Nobel Prize in Physics in 1985. The Hall Effect is caused by the Lorentz force, and it is measured using a Hall probe. Its applications include measuring magnetic fields, speed and position sensing, and the development of the SI unit for electrical resistance.
Benevito
Why does the presence of an energy gap in QHE guarantee dissipationless current flow?

Because of the gap the system is an insulator in the bulk but has conducting surface states on the edge. These states are chiral with the chirality depending on the direction of the magnetic field: they cannot backscatter. If there is are impurities in the sample they will just go around them.

## What is the Current Hall Effect?

The Current Hall Effect is a phenomenon in which a magnetic field perpendicular to an electric current causes a voltage difference across a conductor. This effect was discovered by Edwin Hall in 1879.

## What is the Quantum Hall Effect?

The Quantum Hall Effect is a quantum mechanical version of the Hall Effect, observed in two-dimensional electron systems at very low temperatures and strong magnetic fields. It was discovered by Klaus von Klitzing in 1980 and earned him the Nobel Prize in Physics in 1985.

## What causes the Hall Effect?

The Hall Effect is caused by the Lorentz force, which is the force experienced by a charged particle moving in a magnetic field. In the case of the Hall Effect, this force causes a separation of charges in the conductor, resulting in a voltage difference.

## How is the Hall Effect measured?

The Hall Effect is measured using a Hall probe, which consists of a thin strip of conductive material with a voltage measuring device attached. When placed in a magnetic field and subjected to an electric current, the probe will detect a voltage difference across its edges.

## What are the applications of the Hall Effect?

The Hall Effect has many practical applications, including measuring magnetic fields in electronic devices, such as smartphones and computers, and in scientific instruments, such as mass spectrometers. It is also used in the automotive industry for speed and position sensing in vehicles. Additionally, the Quantum Hall Effect has led to the development of the International System of Units (SI) for electrical resistance.

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