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Register a new userFinite frequency noise spectroscopy for fractional Hall states at { u} = 5/2
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We investigate the finite frequency noise of a quantum point contact at filling factor { u} = 5/2 using a weakly coupled resonant LC circuit as a detector. We show how one could spectroscopically address the fractional charged excitations inspecting separately their charge and scaling dimensions. We thus compare the behaviour of the Pfaffian and the anti-Pfaffian non-Abelian edge states models in order to give possible experimental signatures to identify the appropriate model for this fractional quantum Hall states. Finally we investigate how the temperature of the LC resonant circuit can be used in order to enhance the sensibility of the measurement scheme.
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We investigate the nature of the fractional quantum Hall (FQH) state at filling factor $ u=13/5$, and its particle-hole conjugate state at $12/5$, with the Coulomb interaction, and address the issue of possible competing states. Based on a large-scale density-matrix renormalization group (DMRG) calculation in spherical geometry, we present evidence that the physics of the Coulomb ground state (GS) at $ u=13/5$ and $12/5$ is captured by the $k=3$ parafermion Read-Rezayi RR state, $text{RR}_3$. We first establish that the state at $ u=13/5$ is an incompressible FQH state, with a GS protected by a finite excitation gap, with the shift in accordance with the RR state. Then, by performing a finite-size scaling analysis of the GS energies for $ u=12/5$ with different shifts, we find that the $text{RR}_3$ state has the lowest energy among different competing states in the thermodynamic limit. We find the fingerprint of $text{RR}_3$ topological order in the FQH $13/5$ and $12/5$ states, based on their entanglement spectrum and topological entanglement entropy, both of which strongly support their identification with the $text{RR}_3$ state. Furthermore, by considering the shift-free infinite-cylinder geometry, we expose two topologically-distinct GS sectors, one identity sector and a second one matching the non-Abelian sector of the Fibonacci anyonic quasiparticle, which serves as additional evidence for the $text{RR}_3$ state at $13/5$ and $12/5$.
We study the nature of the u=5/2 quantum Hall state in wide quantum wells under the mixing of electronic subbands and Landau levels. We introduce a general method to analyze the Moore-Read Pfaffian state and its particle-hole conjugate, the anti-Pfaffian, under periodic boundary conditions in a quartered Brillouin zone scheme containing both even and odd numbers of electrons. We examine the rotational quantum numbers on the torus, and show spontaneous breaking of the particle-hole symmetry can be observed in finite-size systems. In the presence of electronic-subband and Landau-level mixing the particle-hole symmetry is broken in such a way that the anti-Pfaffian is unambiguously favored, and becomes more robust in the vicinity of a transition to the compressible phase, in agreement with recent experiments.
We report a reliable method to estimate the disorder broadening parameter from the scaling of the gaps of the even and major odd denominator fractional quantum Hall states of the second Landau level. We apply this technique to several samples of vastly different densities and grown in different MBE chambers. Excellent agreement is found between the estimated intrinsic and numerically obtained energy gaps for the $ u=5/2$ fractional quantum Hall state. Futhermore, we quantify, for the first time, the dependence of the intrinsic gap at $ u=5/2$ on Landau level mixing.
Parafermions are non-Abelian anyons which generalize Majorana fermions and hold great promise for topological quantum computation. We study the braiding of $mathbb{Z}_{2n}$ parafermions which have been predicted to emerge as bound states in fractional quantum Hall systems at filling factor $ u = 1/n$ ($n$ odd). Using a combination of bosonization and refermionization, we calculate the energy splitting as a function of distance and chemical potential for a pair of parafermions separated by a gapped region. Braiding of parafermions in quantum Hall edge states can be implemented by repeated fusion and nucleation of parafermion pairs. We simulate the conventional braiding protocol of parafermions numerically, taking into account the finite separation and finite chemical potential. We show that a nonzero chemical potential poses challenges for the adiabaticity of the braiding process because it leads to accidental crossings in the spectrum. To remedy this, we propose an improved braiding protocol which avoids those degeneracies.
The nature of the fractional quantum Hall effect at $ u=1/2$ observed in wide quantum wells almost three decades ago is still under debate. Previous studies have investigated it by the variational Monte Carlo method, which makes the assumption that the transverse wave function and the gap between the symmetric and antisymmetric subbands obtained in a local density approximation at zero magnetic field remain valid even at high perpendicular magnetic fields; this method also ignores the effect of Landau level mixing. We develop in this work a three-dimensional fixed phase Monte Carlo method, which gives, in a single framework, the total energies of various candidate states in a finite width quantum well, including Landau level mixing, directly in a large magnetic field. This method can be applied to one-component states, as well two-component states in the limit where the symmetric and antisymmetric bands are nearly degenerate. Our three-dimensional fixed-phase diffusion Monte Carlo calculations suggest that the observed 1/2 fractional quantum Hall state in wide quantum wells is likely to be the one-component Pfaffian state supporting non-Abelian excitations. We hope that this will motivate further experimental studies of this state.
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