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The fractional quantum Hall effect is more complicated and still considered an open research problem. [2] Its existence relies fundamentally on electron–electron interactions. In 1988, it was proposed that there was a quantum Hall effect without Landau levels. [3] This quantum Hall effect is referred to as the quantum anomalous Hall (QAH) effect.
Due to the cosine function's properties, the pattern is periodic on with period 1 (it repeats for each quantum flux per unit cell). The graph in the region of α {\displaystyle \alpha } between 0 and 1 has reflection symmetry in the lines α = 1 2 {\displaystyle \alpha ={\frac {1}{2}}} and ϵ = 0 {\displaystyle \epsilon =0} . [ 1 ]
The Goos–Hänchen effect (named after Hermann Fritz Gustav Goos (1883–1968) and Hilda Hänchen (1919–2013) is an optical phenomenon in which linearly polarized light undergoes a small lateral shift when totally internally reflected. The shift is perpendicular to the direction of propagation in the plane containing the incident and ...
Haldane is known for a wide variety of fundamental contributions to condensed matter physics including the theory of Luttinger liquids, the theory of one-dimensional spin chains, the theory of fractional quantum hall effect, exclusion statistics, entanglement spectra and much more. [11] [12]
The most promising applications of topological insulators are spintronic devices and dissipationless transistors for quantum computers based on the quantum Hall effect [14] and quantum anomalous Hall effect. [62] In addition, topological insulator materials have also found practical applications in advanced magnetoelectronic and optoelectronic ...
Quantum Hall transitions are the quantum phase transitions that occur between different robustly quantized electronic phases of the quantum Hall effect. The robust quantization of these electronic phases is due to strong localization of electrons in their disordered, two-dimensional potential. But, at the quantum Hall transition, the electron ...
The fractional quantum Hall effect (FQHE) is a collective behavior in a 2D system of electrons. In particular magnetic fields, the electron gas condenses into a remarkable liquid state, which is very delicate, requiring high quality material with a low carrier concentration, and extremely low temperatures.
Specific applications of quantum mechanics in electronics is researched within semiconductor physics. The term also encompassed the basic processes of laser operation, which is today studied as a topic in quantum optics. Usage of the term overlapped early work on the quantum Hall effect and quantum cellular automata.