Integer and fractional quantum Hall effects in bilayer electron systems

Integer and fractional quantum Hall (QH) effects are studied in bilayer electron systems both theoretically and experimentally, especially, at ν=2 and 2/3. Due to the spin and layer degrees of freedom, the SU(4) symmetry underlies the integer QH states, where quantum coherence develops spontaneously and quasiparticles are coherent excitations. It is intriguing that a pair of skyrmions makes one quasiparticle at ν=2. In the fractional QH regime, on the other hand, the composite-fermion cyclotron gap competes with the Zeeman and tunneling gaps, bringing in new phases and excitations. At ν=2/3 our experimental data suggest that a quasiparticle is not a coherent excitation but simply a composite fermion.     

Composite-Particles (Boson,Fermion) Theory of Fractional Quantum Hall Effect

A theory is developed for fractional quantum Hall effect in terms of composite (c)-bosons (fermions) without useing Laughlin’s results about the fractional charge. Here the c-particle (fermion, boson) is defined as a bound composite fermion (boson) containing a conduction electron and an even (odd) number of fluxons (elementary magnetic fluxes). The Bose-condensed c-bosons, each containing an electron and an odd number m of fluxons at the filling factor ν=1/m is shown to generate the Hall conductivity plateau value m e ²/h, where the density of c-particles, \(n_{\phi }^{(m)}\), either bosonic or fermionic, with m fluxons is given by \(n_{\phi }^{(m)}=n_{\mathrm {e}}/m\), n _e = electron density. The only assumption is that any c-fermion carries a charge magnitude equal to the electron charge e. The quantum Hall state is shown to be more stable at ν=1/3 than at ν=1.     

Charge neutral counterflow transport at filling factor 1 in GaAs hole bilayers

Interacting bilayers placed in perpendicular magnetic field exhibit a peculiar quantum Hall state (QHS) at total filling factor ν=1, owing to the carrier-carrier interaction in the two layers. The physics of the ν=1 QHS is similar to that of the many-particle ground state of a superconductor. Unlike conventional superconductors, however, in the ν=1 QHS carriers in one layer pair with vacancies in the opposite layer forming charge neutral particles which flow without dissipation at the lowest temperatures. Here we review the experimental evidence supporting this picture, with an emphasis on magnetotransport in interacting GaAs hole bilayers in a configuration where equal and opposite currents are passed in the two layers.     

Fractional statistics,Hanbury-Brown and Twiss correlations and the quantum Hall effect

The direct detection of the statistics of the quasiparticles in the quantum Hall effect has so far eluded experimental discovery. Here a quantum transport geometry is analyzed, which could provide a link to the fractional statistics via the measurement of low frequency noise correlations. The proposal constitutes an analog of the Hanbury-Brown and Twiss experiment, this time for three chiral edges – one injector edge and two collectors. Luttinger liquid theory reveals that the real time correlator decays much slower than in the case of fermions, and exhibits oscillations with a frequency scale corresponding to the applied bias multiplied by the quasiparticle charge. The zero frequency noise correlations are negative at filling factor 1/3 as for bare electrons (anti-bunching). However they are strongly reduced in amplitude, which constitutes a first evidence of unusual correlations. The noise correlations become positive (suggesting bunching) for ν⩽1/5, however with a much reduced amplitude, when one computes the noise assuming that only the most relevant operators contribute. To cite this article: R. Guyon et al., C. R. Physique 3 (2002) 697–707.     

Helical-edge transport near ν = 0 of monolayer graphene

The complex nature of filling factor ν = 0 of monolayer graphene is studied in magnetotransport experiments. As a function of perpendicular magnetic field a metal-insulator transition is observed, which is attributed to disorder-induced Landau level broadening in the canted antiferromagnetic phase. In the metallic regime a separation of the zeroth Landau level appears and signs of the quantum spin Hall effect are seen near ν = 0. In addition to local transport, nonlocal transport experiments show results being consistent with helical edge transport.     

Light scattering observations of spin reversal excitations in the fractional quantum Hall regime

Resonant inelastic light scattering experiments access the low lying excitations of electron liquids in the fractional quantum Hall regime in the range 2/5≥ν≥1/3. Modes associated with changes in the charge and spin degrees of freedom are measured. Spectra of spin reversed excitations at filling factor ν?1/3 and at ν?2/5 identify a structure of lowest spin-split Landau levels of composite fermions (CFs) that is similar to that of electrons. Observations of spin wave excitations enable determinations of energies required to reverse spin. The spin reversal energies obtained from the spectra illustrate the significant residual interactions of composite fermions. At ν=1/3 energies of spin reversal modes are larger but relatively close to spin conserving excitations that are linked to activated transport. Predictions of composite fermion theory are in good quantitative agreement with experimental results.     

Quantum magneto-transport in two-dimensional GaAs electron gases and SiGe hole gases

We have measured the low-temperature transport properties of two-dimensional (2D) GaAs electron gases and 2D SiGe hole gases. Our experimental results fall into three categories. (i) Collapse of spin-splitting and an enhanced Landé g-factor at Landau level filling factors both ν=3 and ν=1 in a 2D GaAs electron gas are observed. Our experimental results show direct evidence that the effective disorder is stronger at ν=1 than that at ν=3 over approximately the same perpendicular magnetic field range. (ii) We present evidence for spin-polarisation of a dilute 2D GaAs electron gas. The Lande g-factor of the system is estimated to be 1.66. This enhanced g value is ascribed to electron–electron interactions at ultra low carrier density limit. (iii) In a high-quality SiGe hole gas, there is a temperature-independent point in the magnetoresistivity ρ_xx and ρ_xy which is ascribed to experimental evidence for a quantum phase transition between ν=3 and ν=5. We also present a study on the temperature(T)-driven flow lines in our system.     

Multicomponent dense electron gas as a model of Si MOSFET

We solve a 2D model of N-component dense electron gas in the limit N→∞ and in the range of the Coulomb interaction parameter N ^?3/2?r _s ?1. The quasiparticle interaction on the Fermi circle vanishes as ?²/Nm. The ground-state energy and the effective mass are found as series in powers of r _s ^2/3 . In the quantum Hall state on the lowest Landau level at integer filling 1?ν<N, the charge-activation-energy gap and the exchange constant are Δ=log(r _s N^3/2)?ω_H/ν and J=0.66?ω_H/ν.     

Landau levels in deformed bilayer graphene at low magnetic fields

We review the effect of uniaxial strain on the low-energy electronic dispersion and Landau level structure of bilayer graphene. Based on the tight-binding approach, we derive a strain-induced term in the low-energy Hamiltonian and show how strain affects the low-energy electronic band structure. Depending on the magnitude and direction of applied strain, we identify three regimes of qualitatively different electronic dispersions. We also show that in a weak magnetic field, sufficient strain results in the filling factor ν=±4 being the most stable in the quantum Hall effect measurement, instead of ν=±8 in unperturbed bilayer at a weak magnetic field. To mention, in one of the strain regimes, the activation gap at ν=±4 is, down to very low fields, weakly dependent on the strength of the magnetic field.     

Is the chiral Luttinger liquid exponent universal?

We present experimental evidence from electron tunneling measurements that the chiral Luttinger liquid power-law exponent, α, for tunneling into the fractional quantum Hall edge deviates substantially from the universal behavior predicted by theory. Our results suggest that the existing standard analyses based on effective Chern–Simon field theories deserve careful reexamination when applied to the dynamics at the Hall fluid edge. To cite this article: A.M. Chang, C. R. Physique 3 (2002) 677–684.     

Electron fluid and quasiparticles in the quantum Hall effect

To explain fractional quantum Hall effect, it is necessary to take into account both the interaction between electrons and their interaction with impurities. We propose a simple model, where the Coulomb repulsion is replaced by a short range potential. For this model we are able to find many-body wave functions of the electron system interacting with impurities and calculate the Hall conductivityσ _xy. A simple physical picture, arising in the framework of this model, provides the understanding of a general reason for both fractional and integral quantum Hall effect. In the model, electrons forming a two-dimensional system, is supposed to occupy the first Landau level. The interaction of electrons is regarded as being small compared with the distance between the Landau levels. The radius of interaction is much less than the magnetic length. The following statements have been proved (Pokrovsky and Talapov 1985a,b; Trugman and Kivelson 1985). For the fillingν=1/m of the first Landau level the ground state is nondegenerate and has the wave functionΩ _w, proposed by Laughlin (1983). Forν, which is slightly less than 1/m the ground state is highly degenerate in the absence of impurities. It can be described as a system of noninteracting quasiholes as proposed by Laughlin (1983). These quasiholes float in the uniform incompressible fluid. Each quasihole has the charge |e|/m. The total number of quasiholes isq=S?mN, whereS is a number of states on the Landau level,N is the number of electrons. The impurities capture quasiholes. If the number of quasiholesq is less than the number of impuritiesN _i, then the ground state becomes nondegenerate. This fact permits us to calculateσ _xy (Pokrovsky and Talapov 1985b). Let there be a small electric fieldE in the system. In the absence of impurities the electron fluid is at rest in the frame of reference, moving with velocityν=cE/H. In this frame of reference the impurities move with the velocity ?v, carrying captured quasiholes. Therefore, the quasihole currents isj _q=(?ν)(| e|/m)q. Hence, in the initial frame of reference the total current isj=Nev+j _q=Sev/m. This means thatσ _xy=(1/m)e ²/2π?).     

Resonant enhancement of inelastic light scattering in the fractional quantum Hall regime at ν=1/3

Strong resonant enhancements of inelastic light scattering from the long wavelength inter-Landau level magnetoplasmon and the intra-Landau level spin wave excitations are seen for the fractional quantum Hall state at ν=1/3. The energies of the sharp peaks (FWHM 0.2 meV) in the profiles of resonant enhancement of inelastic light scattering intensities coincide with the energies of photoluminescence bands assigned to negatively charged exciton recombination. To interpret the observed enhancement profiles, we propose three-step light scattering mechanisms in which the intermediate resonant transitions are to states with charged excitonic excitations.     

Integer and fractional quantum Hall effect in a strip of stripes

We study anisotropic stripe models of interacting electrons in the presence of magnetic fields in the quantum Hall regime with integer and fractional filling factors. The model consists of an infinite strip of finite width that contains periodically arranged stripes (forming supercells) to which the electrons are confined and between which they can hop with associated magnetic phases. The interacting electron system within the one-dimensional stripes are described by Luttinger liquids and shown to give rise to charge and spin density waves that lead to periodic structures within the stripe with a reciprocal wavevector 8k _F in a mean field approximation. This wavevector gives rise to Umklapp scattering and resonant scattering that results in gaps and chiral edge states at all known integer and fractional filling factors ν. The integer and odd denominator filling factors arise for a uniform distribution of stripes, whereas the even denominator filling factors arise for a non-uniform stripe distribution. We focus on the ground state of the system, and identify the quantum Hall regime via the quantized Hall conductance. For this we calculate the Hall conductance via the Streda formula and show that it is given by σ _H = νe ²/h for all filling factors. In addition, we show that the composite fermion picture follows directly from the condition of the resonant Umklapp scattering.     

On the study of high-resolution rovibrational spectrum of H2S in the region of 7300-7900 cm

High-resolution Fourier transform infrared spectrum of H₂S was recorded and analyzed in the region of the v=v₁+v₂/2+v₃=3 poliad. Experimental transitions were assigned to the 3ν₁, 2ν₁+ν₃, ν₁+2ν₃, 3ν₃, 2ν₁+2ν₂, and ν₁+2ν₂+ν₃ bands with the maximum value of quantum number J equal to 11, 14, 10, 11, 8, and 11, respectively. The theoretical analysis was fulfilled with the Hamiltonian model which takes into account numerous resonance interactions between all the mentioned vibrational states. The rms deviation of the reproduction of 510 upper energy levels (derived from more than 1550 transitions) with 75 parameters was 0.0022 cm⁻¹.     

Quantum transitions in bilayer states

The possible phase transitions when two layers at filling factor ν_t=1 are gradually separated are studied in this article. In the bosonic case the system should undergo a pairing transition from a Fermi liquid to an incompressible state. In the Fermionic case, the state evolves from an incompressible (1,1,1) state to a Fermi liquid. It is speculated that there is an intermediate phase involving charge two quasiparticles. To cite this article: V. Pasquier, C. R. Physique 3 (2002) 709–715.     

Interferometry of non-Abelian anyons

We develop the general quantum measurement theory of non-Abelian anyons through interference experiments. The paper starts with a terse introduction to the theory of anyon models, focusing on the basic formalism necessary to apply standard quantum measurement theory to such systems. This is then applied to give a detailed analysis of anyonic charge measurements using a Mach-Zehnder interferometer for arbitrary anyon models. We find that, as anyonic probes are sent through the legs of the interferometer, superpositions of the total anyonic charge located in the target region collapse when they are distinguishable via monodromy with the probe anyons, which also determines the rate of collapse. We give estimates on the number of probes needed to obtain a desired confidence level for the measurement outcome distinguishing between charges, and explicitly work out a number of examples for some significant anyon models. We apply the same techniques to describe interferometry measurements in a double point-contact interferometer realized in fractional quantum Hall systems. To lowest order in tunneling, these results essentially match those from the Mach-Zehnder interferometer, but we also provide the corrections due to processes involving multiple tunnelings. Finally, we give explicit predictions describing state measurements for experiments in the Abelian hierarchy states, the non-Abelian Moore-Read state at ν=5/2 and Read-Rezayi state at ν=12/5.     

Magnetic field influence on the low temperature heat capacity of the spin-Peierls compound CuGeO3

We have investigated the effect of magnetic field on the low-temperature heat capacity C_p of the undoped spin-Peierls inorganic compound CuGeO₃ in the dimerized phase. Below 1 K, C_p is dominated by a Schottky anomaly, which is removed above 1 K for field B higher than 3 T. This anomaly is well accounted for by a molar concentration x=0.75×10⁻³ of intrinsic defects, which occur predominantly on the Cu chains. This amount is confirmed by magnetization measurements. A second contribution, varying as T^−ν with ν=1 or 2, rises up with the field for B>1 T in the lower temperature range (from 70 mK to 0.3 K). At high field this contribution becomes very sensitive to the experimental dynamics.     

Disorder effect on the quantum Hall effect in thin films of three-dimensional topological insulators

We numerically study the quantum Hall effect (QHE) in three-dimensional topological insulator (3DTI) thin film in the presence of the finite Zeeman energy g and the hybridization gap Δ under a strong magnetic field and disorder. For Δ = 0 but g ≠ 0, the Hall conductivity remains to be odd-integer quanti-zed σ _xy = ν(e ²/h) , where ν = 2? + 1 with ? being an integer. In the presence of disorder, the Hall plateaus can be destroyed through the float-up of extended levels toward the band center and the higher plateaus disappear first. The two central plateaus with ν = ± 1 around the band center are strongest against disorder scattering. With the increasing of the disorder strength, Hall plateaus are destroyed faster for the system with a weaker magnetic field. If g = 0 but Δ ≠ 0, there is a splitting of the central (n = 0) Landau level, yielding a new plateau with ν = 0, in addition to the original odd-integer plateaus. In the strong-disorder regime, the QHE plateaus can be destroyed due to the float-up of extended levels toward the band center. The ν = 0 plateau around the band center is strongest against disorder scattering, which eventually disappears. For both g ≠ 0 and Δ ≠ 0, the simultaneous presence of nonzero g and Δ causes the splitting of the degenerating Landau levels, so that all integer Hall plateaus ν = ? appear. The ν = 0,1 plateaus are the most stable ones. In the strong-disorder regime, all QHE states are destroyed by disorder, and the system transits into an insulating phase.