Conductivity of Paired Composite Fermions

Foster, K.; Bonesteel, N. E.; Simon, Steven H.

doi:10.1103/physrevlett.91.046804

Cited by 5 publications

(4 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The MR state has been studied in great detail [8][9][10][11] and interpreted by two complementary 12 pictures: as a Laughlin state of tightly bound electron pairs 13,14 or a superfluid of weakly bound CF pairs. [15][16][17] The first numerical calculations for interacting electrons in a partially filled LL 1 were carried out by Morf. 18 They seemed to confirm that a half-filled LL 1 has a spin-polarized incompressible ground state accurately described by the MR wave function.…”

Section: Introductionmentioning

confidence: 99%

Landau level mixing in theν=5∕2fractional quantum Hall state

Wójs¹,

Quinn²

2006

Phys. Rev. B

View full text Add to dashboard Cite

The effect of Landau level ͑LL͒ mixing on the =5/2 fractional quantum Hall state is studied directly in a minimal, yet still numerically tractable, approximation. Specifically, the inter-LL excitations with one unit of cyclotron energy are included in the exact diagonalization of a small yet representative number of electrons on a sphere. Significant reduction of the excitation gap found already in this simple model indicates that LL mixing must play an important role in more realistic systems, with a full spectrum of allowed inter-LL excitations. This suggests a possible route to the explanation of the troubling discrepancy between earlier calculations and experiments. On the other hand, even within our limited approach the LL mixing is found to considerably reduce overlaps with the Moore-Read wave function, raising the question of the actual realization of non-Abelian quasiparticles ͑QPs͒ at =5/2. In view of the discussed limitations of exact numerics, conclusive resolution of this question will probably require an experiment directly probing the QP statistics.

show abstract

Section: Introductionmentioning

confidence: 99%

Landau level mixing in theν=5∕2fractional quantum Hall state

Wójs¹,

Quinn²

2006

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…Exactly at ν = 5/2, if we treat the CS gauge field at mean-field level, the electrons form a Fermi sea of composite fermions in zero net field [7]. Following the lead of previous studies [12], we add an explicit p−wave attraction between the composite fermions (which in a more complete treatment should properly be derived by integrating out high energy degrees of freedom in some fashion). At T = 0, a further BCS mean-field decoupling of this attraction produces a p + ip superconducting state with coherence length ξ and a gap to creating Bogoliubov quasiparticles ('Bogolons') ∆ = v F /ξ.…”

mentioning

confidence: 99%

Weakly Coupled Pfaffian as a Type I Quantum Hall Liquid

Parameswaran¹,

Kivelson²,

Sondhi³

et al. 2011

Phys. Rev. Lett.

View full text Add to dashboard Cite

The Pfaffian phase in the proximity of a half-filled Landau level is understood to be a p+ip superconductor of composite fermions. We consider the properties of this paired quantum Hall phase when the pairing energy is small, i.e., in the weak-coupling, BCS limit, where the coherence length is much larger than the charge screening length. We find that, as in a type I superconductor, vortices attract so that, upon varying the magnetic field from its magic value at ν=5/2, the system exhibits Coulomb frustrated phase separation. We propose that the weakly and strongly coupled Pfaffians exemplify a general dichotomy between type I and type II quantum Hall fluids.

show abstract

“…Excitations in this superconductor are vortices carrying half a flux quantum and an electric charge of e /4, and fermions created in twos by breaking pairs with an appropriate energy gap. 2,3 The Bogoliubov-de Gennes ͑BdG͒ equation describing the fermionic excitations of a twodimensional ͑2D͒ p-wave superconductor admits zero-energy solutions in the presence of well-separated vortices, one solution near each vortex' core; these solutions are Majorana fermions ␥, satisfying ␥ † = ␥. As a consequence, the ground state is degenerate; for 2N well-separated vortices, the ground state degeneracy is 2 N .…”

mentioning

confidence: 99%

Electronic transport in an array of quasiparticles in theν=5∕2non-Abelian quantum Hall state

Grosfeld

Stern²

2006

Phys. Rev. B

View full text Add to dashboard Cite

The Moore-Read Pfaffian =5/2 quantum Hall state is a p-wave superconductor of composite fermions. Small deviations from =5/2 result in the formation of an array of vortices within this superconductor, each supporting a Majorana zero mode near its core. We consider how tunneling between these cores is reflected in the electronic response to an electric field of a nonzero wave-vector q and frequency . We find a mechanism for dissipative transport at frequencies below the =5/2 gap, and calculate the q , dependence of the dissipative conductivity. The contributions we find depend exponentially on ͉ −5/2͉ −1/2 .

show abstract

Conductivity of Paired Composite Fermions

Cited by 5 publications

References 23 publications

Landau level mixing in theν=5∕2fractional quantum Hall state

Landau level mixing in theν=5∕2fractional quantum Hall state

Weakly Coupled Pfaffian as a Type I Quantum Hall Liquid

Electronic transport in an array of quasiparticles in theν=5∕2non-Abelian quantum Hall state

Contact Info

Product

Resources

About