The Dirac Composite Fermion of the Fractional Quantum Hall Effect
29
Citation
45
Reference
10
Related Paper
Citation Trend
Abstract:
We review the recently proposed Dirac composite fermion theory of the half-filled Landau level.Keywords:
Composite fermion
Landau quantization
We generalize the fractional quantum Hall hierarchy picture to apply to arbitrary, possibly non-Abelian, fractional quantum Hall states. Applying this to the nu=5/2 Moore-Read state, we construct explicit trial wave functions to describe the fractional quantum Hall effect in the second Landau level. The resulting hierarchy of states, which reproduces the filling fractions of all observed Hall conductance plateaus in the second Landau level, is characterized by electron pairing in the ground state and an excitation spectrum that includes non-Abelian anyons of the Ising type. We propose this as a unifying picture in which p-wave pairing characterizes the fractional quantum Hall effect in the second Landau level.
Landau quantization
Composite fermion
Cite
Citations (2)
In the standard hierarchical scheme the daughter state at each step results from the fractional quantum Hall effect of the quasiparticles of the parent state. In this paper a new possible approach for understanding the fractional quantum Hall effect is presented. It is proposed that the fractional quantum Hall effect of electrons can be physically understood as a manifestation of the integer quantum Hall effect of composite fermionic objects consisting of electrons bound to an even number of flux quanta.
Composite fermion
Cite
Citations (2,204)
Unlike regular electron spin, the pseudospin degeneracy of Fermi points in graphene does not couple directly to magnetic field. Therefore graphene provides a natural vehicle to observe the integral and fractional quantum Hall physics in an elusive limit analogous to zero Zeeman splitting in GaAs systems. This limit can exhibit new integral plateaus arising from interactions, large pseudoskyrmions, fractional sequences, even/odd numerator effects, composite-fermion pseudoskyrmions, and a pseudospin-singlet composite-fermion Fermi sea. It is stressed that the Dirac nature of the $B=0$ spectrum, which induces qualitative changes in the overall spectrum, has no bearing on the fractional quantum Hall effect in the $n=0$ Landau level of graphene. The second Landau level of graphene is predicted to show more robust fractional quantum Hall effect than the second Landau level of GaAs.
Composite fermion
Landau quantization
Cite
Citations (137)
We numerically study the fractional quantum Hall effect at filling factors $\nu=12/5$ and 13/5 (the particle-hole conjugate of 12/5) in high-quality two-dimensional GaAs heterostructures via exact diagonalization including finite well width and Landau level mixing. We find that Landau level mixing suppresses $\nu=13/5$ fractional quantum Hall effect relative to $\nu=12/5$. By contrast, we find both $\nu=2/5$ and (its particle-hole conjugate) $\nu=3/5$ fractional quantum Hall effects in the lowest Landau level to be robust under Landau level mixing and finite well-width corrections. Our results provide a possible explanation for the experimental absence of the 13/5 fractional quantum Hall state as caused by Landau level mixing effects.
Cite
Citations (34)
We generalize the fractional quantum Hall hierarchy picture to apply to arbitrary, possibly non-Abelian, fractional quantum Hall states. Applying this to the $\ensuremath{\nu}=5/2$ Moore-Read state, we construct explicit trial wave functions to describe the fractional quantum Hall effect in the second Landau level. The resulting hierarchy of states, which reproduces the filling fractions of all observed Hall conductance plateaus in the second Landau level, is characterized by electron pairing in the ground state and an excitation spectrum that includes non-Abelian anyons of the Ising type. We propose this as a unifying picture in which $p$-wave pairing characterizes the fractional quantum Hall effect in the second Landau level.
Landau quantization
Composite fermion
Cite
Citations (127)
Composite fermion
Landau quantization
Cite
Citations (0)
The history and the experimental conditions leading to the discovery of the quantum Hall effect are discussed with a view to compare and contrast with the classical version of the effect. Landau levels are obtained for electrons confined in two dimensions (2D) in the presence of a strong transverse magnetic field. Their characteristics, such as, huge degeneracy, conductance properties, incompressibility etc. are discussed. The role of conduction via the edge modes in quantum Hall samples, and that it earned them the nomenclature of topological insulators, is emphasized. The Hall resistivity is computed using the Kubo formula, and the quantization of the hall plateaus is shown to be directly related to a topological invariant called the Chern number. A comparison of the above scenario observed in a 2D electron gas is performed by computing the Landau levels in graphene which yields feasibility of realizing the quantum Hall effect at the room temperature. Subsequently, the above discussion of the integer quantum Hall effect is supplemented by introducing the fractional quantum Hall effect, where the quantization of the hall plateaus is observed at fractional values which underscores the role of electronic interactions. We have stated the properties of the variational wavefunction due to Laughlin, and its success in explaining the odd-denominator fractions observed in experiments. Next, the idea of composite fermions due to Jain is shown to yield a much simpler and significantly intuitive picture of an enormously complicated many-particle problem. Eventually, to explain a lot of other fractions observed in the experiments, a discussion of the hierarchy scenario is invoked.
Landau quantization
Composite fermion
Cite
Citations (0)
I demonstrate that the wavefunction for a nu = n+ tilde{nu} quantum Hall state with Landau levels 0,1,...,n-1 filled and a filling fraction tilde{nu} quantum Hall state with 0 < tilde{nu} \leq 1 in the nth Landau level can be obtained hierarchically from the nu = n state by introducing quasielectrons which are then projected into the (conjugate of the) tilde{nu} state. In particular, the tilde{nu}=1 case produces the filled Landau level wavefunctions hierarchically, thus establishing the hierarchical nature of the integer quantum Hall states. It follows that the composite fermion description of fractional quantum Hall states fits within the hierarchy theory of the fractional quantum Hall effect. I also demonstrate this directly by generating the composite fermion ground-state wavefunctions via application of the hierarchy construction to fractional quantum Hall states, starting from the nu=1/m Laughlin states.
Composite fermion
Landau quantization
Cite
Citations (10)
At low Landau level filling of a two-dimensional electron system, typically associated with the formation of an electron crystal, we observe local minima in Rxx at filling factors nu = 2/11, 3/17, 3/19, 2/13, 1/7, 2/15, 2/17, and 1/9. Each of these developing fractional quantum Hall (FQHE) states appears only above a filling-factor-specific temperature. This can be interpreted as the melting of an electron crystal and subsequent FQHE liquid formation. The observed sequence of FQHE states follows the series of composite fermion states emanating from nu = 1/6 and nu = 1/8.
Composite fermion
Landau quantization
Filling factor
Wigner crystal
Sequence (biology)
Cite
Citations (125)
We have studied the fractional quantum Hall effect in higher Landau levels following Jain's composite-fermion theory. Our framework provides numerical calculations for the gaps in a range of electron densities typically used in experiments. As expected, the gaps diminish as the Landau level index increases. Surprisingly, however, they become negative in the third and higher Landau levels, indicating an absence of the fractional quantum Hall effect beyond the second Landau level.
Landau quantization
Composite fermion
Shubnikov–de Haas effect
Cite
Citations (5)