Absence of the Aharonov-Bohm effect of chiral Majorana fermion edge states

In 1983, Laughlin reported a wave function which while using the first-principles kinetic energy and Coulomb interactions fractionalizes the charge of the electron so that a charge such as 1/3 occurs. Since then this wave function has been applied to many problems in condensed matter physics. An effort is made to review the literature dealing with Aharonov–Bohm effect, ground state, confinement, phase transitions, Wigner and Luttinger solids, edge states, Anderson's theory, statistics and anyons, etc. The importance of the angular momentum is pointed out and it is shown that Landau levels play an important role in understanding the fractions at which the plateaus occur in the quantum Hall effect.

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ARE AHARONOV–BOHM EFFECT AND QUANTIZED HALL REGIME COMPATIBLE?

International Journal of Nanoscience ◽

10.1142/s0219581x03001656 ◽

2003 ◽

Vol 02 (06) ◽

pp. 535-541

Author(s):

B. CHENAUD ◽

C. CHAUBET ◽

B. JOUAULT ◽

L. SAMINADAYAR ◽

D. MAILLY ◽

...

Keyword(s):

Quantum Hall ◽

Quantum Point Contacts ◽

Edge States ◽

Point Contacts ◽

Quantum Oscillations ◽

Fabry Perot ◽

Hall Regime ◽

Quantum Point ◽

Bohm Effect ◽

Aharonov Bohm

We present calculations of the quantum oscillations appearing in the transmission of a mesoscopic GaAs / GaAlAs ring isolated by quantum point contacts. We show that the device acts as an electronic Fabry–Perot spectrometer in the quantum Hall effect regime, and discuss the effect of the coherence length of edge states.

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Phenomena and devices at the quantum scale and the mesoscale

10.1093/oso/9780198759874.003.0003 ◽

2017 ◽

Author(s):

Sandip Tiwari

Keyword(s):

Coulomb Blockade ◽

Secure Communication ◽

Quantum Hall ◽

Nanoscale Device ◽

Self Energy ◽

Stability Diagrams ◽

Charge Stability ◽

Bohm Effect ◽

Aharonov Bohm ◽

Non Locality

Unique nanoscale phenomena arise in quantum and mesoscale properties and there are additional intriguing twists from effects that are classical in origin. In this chapter, these are brought forth through an exploration of quantum computation with the important notions of superposition, entanglement, non-locality, cryptography and secure communication. The quantum mesoscale and implications of nonlocality of potential are discussed through Aharonov-Bohm effect, the quantum Hall effect in its various forms including spin, and these are unified through a topological discussion. Single electron effect as a classical phenomenon with Coulomb blockade including in multiple dot systems where charge stability diagrams may be drawn as phase diagram is discussed, and is also extended to explore the even-odd and Kondo consequences for quantum-dot transport. This brings up the self-energy discussion important to nanoscale device understanding.

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