How strong is localization in the integer quantum Hall effect: Relevant quantum corrections to conductivity in non-zero magnetic field

By considering the degeneracies of the localized and extended states separately we have investigated the integer quantum Hall effect (IQHE) in terms of fraction of extended states in a Landau subband. The IQHE is found to manifest itself as saw-tooth oscillations in the number density of the extended electrons as a function of magnetic field. Preliminary results of an experiment are also presented that support this picture. It is found that contrary to the traditional theoretical belief, the extended states form a non-vanishing fraction of the states in a Landau subband. Significantly it is shown that if this was not so, the IQHE would not arise in the first place. This result is relevant in connection with the long standing question of nature of transition between plateaus, and also the recent discovery of intriguing electron density driven metal–insulator transition in two-dimensional systems. The results also show that extended states float up in energy in addition to being systematically destroyed as the magnetic field is reduced, and that the system can become completely localized at a nonzero magnetic field.

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Quantum corrections to conductivity under conditions of the integer quantum Hall effect

Semiconductors ◽

10.1134/s1063782612060115 ◽

2012 ◽

Vol 46 (6) ◽

pp. 759-768 ◽

Cited By ~ 1

Author(s):

A. A. Greshnov

Keyword(s):

Hall Effect ◽

Quantum Hall Effect ◽

Quantum Hall ◽

Quantum Corrections ◽

Integer Quantum Hall Effect ◽

Integer Quantum

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An all-epitaxial nitride heterostructure with concurrent quantum Hall effect and superconductivity

Science Advances ◽

10.1126/sciadv.abf1388 ◽

2021 ◽

Vol 7 (8) ◽

pp. eabf1388

Author(s):

Phillip Dang ◽

Guru Khalsa ◽

Celesta S. Chang ◽

D. Scott Katzer ◽

Neeraj Nepal ◽

...

Keyword(s):

Hall Effect ◽

Quantum Hall Effect ◽

Electron Gas ◽

Quantum Hall ◽

High Electron Mobility Transistor ◽

High Electron ◽

2D Electron Gas ◽

Integer Quantum Hall Effect ◽

Topological Quantum ◽

Integer Quantum

Creating seamless heterostructures that exhibit the quantum Hall effect and superconductivity is highly desirable for future electronics based on topological quantum computing. However, the two topologically robust electronic phases are typically incompatible owing to conflicting magnetic field requirements. Combined advances in the epitaxial growth of a nitride superconductor with a high critical temperature and a subsequent nitride semiconductor heterostructure of metal polarity enable the observation of clean integer quantum Hall effect in the polarization-induced two-dimensional (2D) electron gas of the high-electron mobility transistor. Through individual magnetotransport measurements of the spatially separated GaN 2D electron gas and superconducting NbN layers, we find a small window of magnetic fields and temperatures in which the epitaxial layers retain their respective quantum Hall and superconducting properties. Its analysis indicates that in epitaxial nitride superconductor/semiconductor heterostructures, this window can be significantly expanded, creating an industrially viable platform for robust quantum devices that exploit topologically protected transport.

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