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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.
One very important feature of the Hall effect is that it differentiates between positive charges moving in one direction and negative charges moving in the opposite. In the diagram above, the Hall effect with a negative charge carrier (the electron) is presented. But consider the same magnetic field and current are applied but the current is ...
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.
In quantum mechanics, fractionalization is the phenomenon whereby the quasiparticles of a system cannot be constructed as combinations of its elementary constituents. One of the earliest and most prominent examples is the fractional quantum Hall effect, where the constituent particles are electrons but the quasiparticles carry fractions of the electron charge.
2005 – Charles Kane and Gene Mele propose the quantum spin Hall effect. [97] 2008-2010 – Andreas P. Schnyder, Shinsei Ryu, Akira Furusaki and Andreas W. W. Ludwig; [98] [99] and well as Alexei Kitaev, [100] develop the periodic table of topological matter. 2013 – The quantum anomalous Hall effect is first observed by the team of Xue Qikun ...
After the advent of quantum mechanics, Lev Landau in 1930 developed the theory of Landau quantization and laid the foundation for a theoretical explanation of the quantum Hall effect which was discovered half a century later. [29]: 458–460 [30] Magnetism as a property of matter has been known in China since 4000 BC.
Quantum anomalous Hall effect (QAHE) is the "quantum" version of the anomalous Hall effect. While the anomalous Hall effect requires a combination of magnetic polarization and spin-orbit coupling to generate a finite Hall voltage even in the absence of an external magnetic field (hence called "anomalous"), the quantum anomalous Hall effect is ...
The Chern–Simons term can also be added to models which aren't topological quantum field theories. In 3D, this gives rise to a massive photon if this term is added to the action of Maxwell's theory of electrodynamics. This term can be induced by integrating over a massive charged Dirac field. It also appears for example in the quantum Hall ...