Fractional quantum Hall effect in semiconductor systems

Papić, Zlatko; Balram, Ajit C.

doi:10.48550/arxiv.2205.03421

Cited by 1 publication

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References 183 publications

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“…Another very popular approach is the composite fermion (CF) theory [61,62] and the parton theory [63][64][65][66]. A CF is a composite quasiparticle formed by attachment of an even number of flux on to every electron in the system.…”

Section: Modern Approaches To the Fqhementioning

confidence: 99%

Dynamical and statistical properties of anyons in fractional quantum hall effect

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The quantum Hall effect has been the prototypical example for many emerging fields of Physics, including the study of topological phases of matter, topological order, and topological insulators. The objects of interest in this thesis are anyons, which are elementary excitations in fractional quantum Hall (FQH) fluids. Anyons are quasiparticles with fractional charge and fractional statistics. The latter property makes it a subject of immense interest due to application in fault-tolerant quantum computing. Here, we employ a perspective that anyons are the appropriate degree of freedom to describe the relevant physics of FQH systems. This is because when a topological phase is assumed and the energy gap goes to infinity, anyons ("quasiholes") are the only possible elementary excitations, since they are not energetically punished by the correspondng model Hamiltonian. With respect to a realistic Hamiltonian, however, this choice of degree of freedom depends on the exact effective interaction in the system. For example, while the Laughlin state is the model state at filling factor n + 1/3 (where n is some integer), when the effective electron-electron interaction is more long-ranged, the quasiholes of a Gaffnian state may be excited and become the better degree of freedom to describe physics in the same filling factor. This perspective results in a surprising observation that a Laughlin quasihole may fractionalize under certain conditions, leading to a quasiparticle of charge e/6 that can potentially be detected in experiments.Another important aspect of anyons is their intrinsic spin and the corresponding spin-statistics relation, which must account for the fact that FQH anyons are not point particles, but objects with finite sizes and intricate internal structures. Our investigation leads to a rigorous derivation of the general spin-statistics relation for anyons in Abelian FQH phases. Furthermore, we show it is possible to fully capture the important features of the statistics by a conformal Hilbert space (CHS) description. Our analysis provides the necessary tools to study such geometric effects, which we use to investigate how disorder in a realistic system may affect different experimental schemes for measuring anyon statistics.

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Section: Modern Approaches To the Fqhementioning

confidence: 99%

Dynamical and statistical properties of anyons in fractional quantum hall effect

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Fractional quantum Hall effect in semiconductor systems

Cited by 1 publication

References 183 publications

Dynamical and statistical properties of anyons in fractional quantum hall effect

Dynamical and statistical properties of anyons in fractional quantum hall effect

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