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Advanced Solid State Physics, Second Edition by Philip Phillips

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15  Quantum Hall and other topological states

When an electron gas is confined to move at the interface between two semiconductors and a magnetic field is applied perpendicular to the plane, a new state of matter (TSG1982) arises at sufficiently low temperatures. This state of matter is unique in condensed matter physics in that it has a gap to all excitations and exhibits fractional statistics. It is generally referred to as an incompressible quantum liquid or as a Laughlin liquid (L1983), in reference to the architect of this state. While the Laughlin state is mediated by the mutual repulsions among the electrons, it is the presence of the large perpendicular magnetic field that leads to the incompressible nature of this new many-body state. ...

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