Signatures of neutral quantum Hall modes in transport through low-density constrictions

Constrictions in fractional quantum Hall (FQH) systems not only facilitate backscattering between counter-propagating edge modes, but also may reduce the constriction filling fraction $\nu_c$ with respect to the bulk filling fraction $\nu_b$. If both $\nu_b$ and $\nu_c$ correspond to incompressible FQH states, at least part of the constriction region is surrounded by composite edges, whose low energy dynamics is characterized by a charge mode and one or several neutral modes. In the incoherent regime, decay of neutral modes describes the equilibration of composite FQH edges, while in the limit of coherent transport, the presence of neutral modes gives rise to universal conductance fluctuations. In addition, neutral modes renormalize the strength of scattering across the constriction, and thus can determine the relative strength of forward and backwards scattering.Comment: corrected description of the results of Ref. [10], Ref. [17] adde

Are Microwave Induced Zero Resistance States Necessarily Static?

We study the effect of inhomogeneities in Hall conductivity on the nature of the Zero Resistance States seen in the microwave irradiated two-dimensional electron systems in weak perpendicular magnetic fields, and we show that time-dependent domain patterns may emerge in some situations. For an annular Corbino geometry, with an equilibrium charge density that varies linearly with radius, we find a time-periodic non-equilibrium solution, which might be detected by a charge sensor, such as an SET. For a model on a torus, in addition to static domain patterns seen at high and low values of the equilibrium charge inhomogeneity, we find that, in the intermediate regime, a variety of nonstationary states can also exist. We catalog the possibilities we have seen in our simulations. Within a particular phenomenological model, we show that linearizing the nonlinear charge continuity equation about a particularly simple domain wall configuration and analyzing the eigenmodes allows us to estimate the periods of the solutions to the full nonlinear equation.Comment: Submitted to PR

Interference, Coulomb blockade, and the identification of non-abelian quantum Hall states

We examine the relation between different electronic transport phenomena in a Fabry-Perot interferometer in the fractional quantum Hall regime. In particular, we study the way these phenomena reflect the statistics of quantum Hall quasi-particles. For two series of states we examine, one abelian and one non-abelian, we show that the information that may be obtained from measurements of the lowest order interference pattern in an open Fabry-Perot interferometer is identical to the one that may be obtained from the temperature dependence of Coulomb blockade peaks in a closed interferometer. We argue that despite the similarity between the experimental signatures of the two series of states, interference and Coulomb blockade measurements are likely to be able to distinguish between abelian and non-abelian states, due to the sensitivity of the abelian states to local perturbations, to which the non-abelian states are insensitive.Comment: 10 pages. Published versio

Driven nonlinear dynamics of two coupled exchange-only qubits

Inspired by creation of a fast exchange-only qubit (Medford et al., Phys. Rev. Lett., 111, 050501 (2013)), we develop a theory describing the nonlinear dynamics of two such qubits that are capacitively coupled, when one of them is driven resonantly at a frequency equal to its level splitting. We include conditions of strong driving, where the Rabi frequency is a significant fraction of the level splitting, and we consider situations where the splitting for the second qubit may be the same or different than the first. We demonstrate that coupling between qubits can be detected by reading the response of the second qubit, even when the coupling between them is only of about $1\%$ of their level splittings, and calculate entanglement between qubits. Patterns of nonlinear dynamics of coupled qubits and their entanglement are strongly dependent on the geometry of the system, and the specific mechanism of inter-qubit coupling deeply influences dynamics of both qubits. In particular, we describe the development of irregular dynamics in a two-qubit system, explore approaches for inhibiting it, and demonstrate existence of an optimal range of coupling strength maintaining stability during the operational time.Comment: 11 pages, 6 figures; One additional figure with changes to the text about the results. Additional references include

Spin Order in Paired Quantum Hall States

We consider quantum Hall states at even-denominator filling fractions, especially $\nu=5/2$, in the limit of small Zeeman energy. Assuming that a paired quantum Hall state forms, we study spin ordering and its interplay with pairing. We give numerical evidence that at $\nu = 5/2$ an incompressible ground state will exhibit spontaneous ferromagnetism. The Ginzburg-Landau theory for the spin degrees of freedom of paired Hall states is a perturbed CP$^2$ model. We compute the coefficients in the Ginzburg-Landau theory by a BCS-Stoner mean field theory for coexisting order parameters, and show that even if repulsion is smaller than that required for a Stoner instability, ferromagnetic fluctuations can induce a partially or fully polarized superconducting state

The Physical Significance of Singularities in the Chern--Simons Fermi Liquid Description of a Partially Filled Landau Level

We analyze the linear response of a half filled Landau level to long wavelength and low frequency driving forces, using Fermi liquid theory for composite fermions. This response is determined by the composite fermions quasi--particle effective mass, $m^*$, and quasi--particle Landau interaction function $f(\theta-\theta')$. Analyzing infra--red divergences of perturbation theory, we get an exact expression for $m^*$, and conjecture the form of the $f(\theta-\theta')$. We then conclude that in the limit of infinite cyclotron frequency, and small ${\bf q},\omega$, the composite fermion excitation spectrum is continuous for $0<\omega<\gamma \frac{e^2}{\epsilon h}q$, with $\gamma$ an unknown number. For fractional quantum Hall states near a half filled Landau level, we derive an exact expression for the energy gap.Comment: 4 pages, RevTeX. This paper, being short and non-technical, could serve as a useful starting point for reading our manuscript cond-mat/9502032. The present paper does, however, include results not published in the forme