Detecting non-Abelian statistics in the nu = 5/2 fractional quantum hall state

In this Letter we propose an interferometric experiment to detect non-Abelian quasiparticle statistics--one of the hallmark characteristics of the Moore-Read state expected to describe the observed fractional quantum Hall effect plateau at nu = 5/2. The implications for using this state for constructing a topologically protected qubit as has been recently proposed by Das Sarma et al. are also addressed.     

Proposed experiments to probe the non-Abelian nu = 5/2 quantum hall state

We propose several experiments to test the non-Abelian nature of quasiparticles in the fractional quantum Hall state at nu = 5/2. In a simplified version of the experiment suggested by [S. Das Sarma, M. Freedman, and C. Nayak, Phys. Rev. Lett. 94, 166802 (2005).], interference is turned on and off when the number of localized quasiparticles between the interfering paths varies between even and odd. We find analogous effects in the thermodynamic properties of closed systems.     

Phase diagram of interacting composite fermions in the bilayer nu=2/3 quantum hall effect

We study the phase diagram of composite fermions (CFs) in the presence of spin and pseudospin degrees of freedom in the bilayer nu=2/3 quantum Hall (QH) state. Activation studies elucidate the existence of three different QH states with two different types of hysteresis in the magnetotransport. While a noninteracting CF model provides a qualitative account of the phase diagram, the observed renormalization of tunneling gap and a non-QH state at high densities are not explained in the noninteracting CF model, and are suggested to be manifestations of interactions between CFs.     

Composite fermion hofstadter problem: partially polarized density wave states in the nu = 2/5 fractional quantum hall effect

It is well known that the nu = 2/5 state is unpolarized at zero Zeeman energy, while it is fully polarized at large Zeeman energies. A novel state with a charge/spin density wave order for composite fermions is proposed to exist at intermediate values of the Zeeman coupling for nu = 2/5. This state has half the maximum possible polarization, and can be extended to other incompressible fractions. A Hartree-Fock calculation based on the new approach for all fractional quantum Hall states developed by R. Shankar and the author is used to demonstrate the stability of this state to single-particle excitations and to compute gaps. A very recent experiment shows direct evidence for this state.     

Particle-hole symmetry and the nu=5/2 quantum Hall state

We discuss the implications of approximate particle-hole symmetry in a half-filled Landau level in which a paired quantum Hall state forms. We note that the Pfaffian state is not particle-hole symmetric. Therefore, in the limit of vanishing Landau-level mixing, in which particle-hole transformation is an exact symmetry, the Pfaffian spontaneously breaks this symmetry. There is a particle-hole conjugate state, which we call the anti-Pfaffian, which is degenerate with the Pfaffian in this limit. We observe that strong Landau-level mixing should favor the Pfaffian, but it is an open problem which state is favored for the moderate Landau-level mixing which is present in experiments. We discuss the bulk and edge physics of the anti-Pfaffian. We analyze a simplified model in which transitions between analogs of the two states can be studied in detail. Finally, we discuss experimental implications.     

Metamorphosis of the quantum Hall ferromagnet at nu=2/5

We report on the dramatic evolution of the quantum Hall ferromagnet in the fractional quantum Hall regime at nu=2/5 filling. A large enhancement in the characteristic time scale gives rise to a dynamical transition into a novel quantized Hall state. The observed Hall state is determined to be a zero-temperature phase distinct from the spin-polarized and spin-unpolarized nu=2/5 fractional quantum Hall states. It is characterized by a strong temperature dependence and puzzling correlation between temperature and time.     

Phase diagram for quantum hall bilayers at nu=1

We present a phase diagram for a double quantum well bilayer electron gas in the quantum Hall regime at a total filling factor nu=1, based on exact numerical calculations of the topological Chern number matrix and the (interlayer) superfluid density. We find three phases: a quantized Hall state with pseudospin superfluidity, a quantized Hall state with pseudospin "gauge-glass" order, and a decoupled composite Fermi liquid. Comparison with experiments provides a consistent explanation of the observed quantum Hall plateau, Hall drag plateau, and vanishing Hall drag resistance, as well as the zero-bias conductance peak effect, and suggests some interesting points to pursue experimentally.     

NMR evidence for spin canting in a bilayer nu=2 quantum hall system

We investigate the electron spin states in the bilayer quantum Hall system at total Landau level filling factor nu=2 exploiting current-pumped and resistively detected NMR. The measured Knight shift, K(S), of 75As nuclei reveals continuous variation of the out-of-plane electronic spin polarization between nearly full and zero as a function of density imbalance. Nuclear spin relaxation measurements indicate a concurrent development of an in-plane spin component. These results provide direct information on the spin configuration in this system and comprise strong evidence for the spin canting suggested by previous experiments.     

Intrinsic gap of the nu=5/2 fractional quantum Hall state

The fractional quantum Hall effect is observed at low magnetic field where the cyclotron energy is smaller than the Coulomb interaction energy. The nu=5/2 excitation gap at 2.63 T is measured to be 262+/-15 mK, similar to values obtained in samples with twice the electronic density. Examining the role of disorder on the 5/2 state, we find that a large discrepancy remains between theory and experiment for the intrinsic gap extrapolated from the infinite mobility limit. The observation of a 5/2 state in the low-field regime suggests that inclusion of nonperturbative Landau level mixing may be necessary to fully understand the energetics of half-filled fractional quantum Hall liquids.     

Splitting of long-wavelength modes of the fractional quantum hall liquid at nu = 1/3

Resonant inelastic light scattering experiments at nu = 1/3 reveal a novel splitting of the long-wavelength modes in the low energy spectrum of quasi-particle excitations in the charge degree of freedom. We find a single peak at small wave vectors that splits into two distinct modes at larger wave vectors. The evidence of well-defined dispersive behavior at small wave vectors indicates a coherence of the quantum fluid in the micron length scale. We evaluate interpretations of long-wavelength modes of the electron liquid.     

Bilayer quantum hall systems at filling factor nu = 2: An exact diagonalization study

We present an exact diagonalization study of bilayer quantum Hall systems at filling factor nu = 2 in the spherical geometry. We find the high-Zeeman-coupling phase boundary of the broken symmetry canted antiferromagnet is given exactly by previous Hartree-Fock mean-field theories, but that the state's stability at weak Zeeman coupling has been qualitatively overestimated. In the absence of interlayer tunneling, degeneracies occur between total spin multiplets due to the Hamiltonian's invariance under independent spin rotations in top and bottom two-dimensional electron layers.     

e/3 Laughlin quasiparticle primary-filling nu=1/3 interferometer

We report experimental realization of a quasiparticle interferometer where the entire system is in 1/3 primary fractional quantum Hall state. The interferometer consists of chiral edge channels coupled by quantum-coherent tunneling in two constrictions, thus enclosing an Aharonov-Bohm area. We observe magnetic flux and charge periods h/e and e/3, equivalent to the creation of one quasielectron in the island. Quantum theory predicts a 3h/e flux period for charge e/3, integer statistics particles. Thus, the observed periods demonstrate the anyonic braiding statistics of Laughlin quasiparticles.