Sample interview questions: Can you explain the concept of quantum Hall effect and its applications in condensed matter physics?
Sample answer:
Quantum Hall Effect
The Quantum Hall Effect (QHE) is a remarkable phenomenon observed in two-dimensional electron systems (2DESs) at low temperatures and high magnetic fields. It manifests as a series of well-defined plateaus in the Hall resistance versus magnetic field plot, each corresponding to a different Landau level filling factor.
Mechanism
In a 2DES subjected to a strong magnetic field, the electron energy spectrum becomes discrete and forms Landau levels. The QHE occurs when the Fermi energy of the electrons lies within a Landau level, and the electrons are confined to the lowest energy states within that level. The magnetic field quantizes the electron motion in one direction, leading to the formation of extended states in the perpendicular direction.
Integer Quantum Hall Effect (IQHE)
In the IQHE, the Hall resistance becomes independent of the magnetic field and takes on quantized values given by:
R_H = h/(e^2 * ν)
where h is Planck’s constant, e is the charge of an electron, and ν is the Landau level filling factor. This quantized Hall resistance is an intrinsic property of the 2DES and arises from the topological nature of the electron states.
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