Integer Fillings Research Articles

On the phase diagram of a two‐dimensional electron gas near integer fillings and fractions such as 1/5 and 1/7

AbstractThe phase diagram of the 2DEG at high magnetic fields is discussed in the light of recent experiments showing the presence of crystalline phases around integer as well as certain fractional fillings. We suggest that a Hall crystal is a proper competing phase compatible with the odd denominator rule that characterizes the fractional quantum Hall effect, and that near integer filling a pinned crystal coexists with an incompressible fluid with no longitudinal resistance. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Microwave resonance of the 2D Wigner crystal around integer Landau fillings.

We have observed a resonance in the real part of the finite frequency diagonal conductivity using microwave absorption measurements in high quality 2D electron systems near integer fillings. The resonance exists in some neighborhood of filling factor around corresponding integers and is qualitatively similar to previously observed resonance of weakly pinned Wigner crystal in high B and very small filling factor regime. Data measured around both nu=1 and nu=2 are presented. We interpret the resonance as the signature of the Wigner crystal state around integer Landau levels.

Excitations in quantum hall ferromagnet with strong Coulomb interaction

The limit of the large Coulomb energy compare the cyclotron energy is considered. It is possible to relate the electron density with the analytical properties of one electron Green function and show that one electron gap exists at integer fillings of Landau level. The energy of collective excitations of plasmon type is calculated at small momenta. It is shown that the activation energy of Skyrmion-antiskyrmion pairs and the energy of spin waves is proportional to the cyclotron energy in this limit.

Excitations in a quantum Hall ferromagnet with strong Coulomb interaction

The limit of the large Coulomb energy compare the cyclotron energy is considered. It is possible to relate the electron density with the analytical properties of one electron Green function and show that one electron gap exists at integer fillings of Landau level. The energy of collective excitations of plasmon type is calculated at small momenta. It is shown that the activation energy of Skyrmion-antiskyrmion pairs and the energy of spin waves is proportional to the cyclotron energy in this limit.

Metal–insulator transitions in systems with electron–phonon and Coulomb interactions

We consider a model which includes the electron–phonon coupling to A g or Jahn–Teller H g phonons, the Coulomb interaction U and an exchange integral K. We study the metal–insulator transition for the integer fillings n=3 and 4. We find that the coupling to A g phonons increases the critical value U c where the transition takes place, while the coupling to H g phonons decreases U c. Without electron–phonon coupling the Hund's rule coupling also decreases U c. There is, however, an interesting competition between the Hund's rule coupling and the Jahn–Teller effect. Thus the reduction of U c due to the H g phonons becomes smaller when the Hund's rule coupling is turned on. The implications of this is discussed in the context of A n C 60.

Hopf invariant for long-wavelength skyrmions in quantum Hall systems for integer and fractional fillings

We show that a Hopf term exists in the effective action of long-wavelength skyrmions in quantum Hall systems for both odd integer and fractional filling factors $\ensuremath{\nu}=1/(2s+1),$ where s is an integer. We evaluate the prefactor of the Hopf term using the Green function method in the limit of strong external magnetic field using a model of local interaction. The prefactor (N) of the Hopf term is found to be equal to $\ensuremath{\nu}.$ The spin and charge densities and hence the total spin and charge of the skyrmion are computed from the effective action. The total spin is found to have a dominant contribution from the Berry term in the effective action and to increase with the size of the skyrmion. The charge and the statistics of the skyrmion, on the other hand, are completely determined by the prefactor of the Hopf term. Consequently, the skyrmions have charge $\ensuremath{\nu}e$ and are Fermions (anyons) for odd integer (fractional) fillings. We also obtain the effective action of the skyrmions at finite temperature. It is shown that at finite temperature, the value of the prefactor of the Hopf term depends on the order in which the zero-momentum and zero-frequency limits are taken.

Filling dependence of the Mott transition in the degenerate Hubbard model

Describing the doped Fullerenes using a generalized Hubbard model, we study the Mott transition for different integer fillings of the ${t}_{1u}$ band. We use the opening of the energy-gap ${E}_{g}$ as a criterion for the transition. ${E}_{g}$ is calculated as a function of the on-site Coulomb interaction U using fixed-node diffusion Monte Carlo. We find that for systems with doping away from half filling the Mott transitions occurs at smaller U than for the half-filled system. We give a simple model for the doping dependence of the Mott transition.

Metal-insulator transition in a degenerate Hubbard model

We have studied the metal-insulator transition at integer fillings in a triply degenerate Hubbard model using the Lanczos method. The critical Coulomb interaction strength U-c, is found to depend strongly on the band filling, with U-c similar to root 3 W (W is the bandwidth) at half filling for this case with threefold degeneracy. We discuss the implications of our results on metal-insulator transitions in strongly correlated systems in general, and on the unusual electronic ground state of the alkali-metal-doped fullerenes, in particular. [S0163-1829(99)11003-8].

Magnetic-field-induced hybridization of electron subbands in a coupled double quantum well

We employ a magnetocapacitance technique to study the spectrum of the soft two-subband (or double-layer) electron system in a parabolic quantum well with a narrow tunnel barrier in the centre. In this system unbalanced by gate depletion, at temperatures $T\agt 30$ mK we observe two sets of quantum oscillations: one originates from the upper electron subband in the closer-to-the-gate part of the well and the other indicates the existence of common gaps in the spectrum at integer fillings. For the lowest filling factors $\nu=1$ and $\nu=2$, both the common gap presence down to the point of one- to two-subband transition and their non-trivial magnetic field dependences point to magnetic-field-induced hybridization of electron subbands.

The Metal-Insulator Transition in the Doubly Degenerate Hubbard Model

A systematic study has been made on the metal-insulator (MI) transition of the doubly degenerate Hubbard model (DHM) in the paramagnetic ground state, by using the slave-boson mean-field theory which is equivalent to the Gutzwiller approximation (GA). For the case of infinite electron-electron interactions, we obtain the analytic solution, which becomes exact in the limit of infinite spatial dimension. On the contrary, the finite-interaction case is investigated by numerical methods using the simple-cubic model with the nearest-neighbor hopping. The mass-enhancement factor, Z , is shown to increase divergently as one approaches the integer fillings ( N = 1, 2, 3), at which the MI transition takes place, N being the total number of electrons. The calculated N dependence of Z is compared with the observed specific-heat coefficient, γ, of Sr 1- x La x TiO 3 which is reported to significantly increase as x approaches unity.

Degenerate Hubbard model in infinite dimensions

Numerically exact solutions of the degenerate Hubbard model in the limit of large dimensions are obtained. We find successive Mott-Hubbard metal insulator transitions at integer fillings for intermediate values of the interaction and low enough temperature in the paramagnetic phase.

Incompressible, metallic and insulating states of two-dimensional systems: Recent experiments

This paper provides a brief summary of some recent experimental results regarding the states of two-dimensional electron systems at high magnetic fields. The states include the incompressible, quantum Hall liquid at integer and fractional Landau-level fillings, the metallic-like state of the flux-particle composite Fermions at half-filling and the insulating phase at low fillings. Some unifying features of these states and their interrelation are also discussed.

Integer-filling metal-insulator transitions in the degenerate Hubbard model

We obtain exact numerical solutions of the degenerate Hubbard model in the limit of large dimensions (or large lattice connectivity). Successive Mott-Hubbard metal insulator transitions at integer fillings occur at intermediate values of the interaction and low enough temperature in the paramagnetic phase. The results are relevant for transition metal oxides with partially filled narrow degenerate bands.

Breakdown phenomena of integer and fractional quantum Hall effects under pulsed magnetic fields

Current-driven breakdown of integer and fractional quantum Hall effects are studied in a wide range of magnetic fields up to 43 T using a pulsed magnet and a 3He refrigerator. An abrupt increase of magnetoresistance above a critical current was found at fractional filling, in a similar manner to the breakdown phenomena at integer fillings. Magnetic-field dependence of the critical electric fields of the breakdown is discussed in terms of the composite fermion picture. The electron heating model of the breakdown is discussed in comparison with the breakdown of integer quantum Hall effect.

Current-driven breakdown of integer and fractional quantum hall effects in [formula omitted] heterostructures in pulsed high magnetic fields

Current-driven breakdown of integer and fractional quantum Hall effects are studied in a wide range of magnetic fields up to 43T using a He 3 refrigerator. Abrupt increase of magnetoresistance above a critical current was found at fractional filling in a similar manner to the breakdown phenomena at integer fillings. Magnetic field dependence of the critical electric fields of the breakdown is discussed in terms of the composite Fermion picture.

Experiments in pulsed magnetic fields at AT&T Bell Laboratories

We review a pair of experiments performed in the pulsed magnets at AT&T Bell Laboratories. Resonant tunneling experiments directly measure the two-dimensional (2-D) density of states of a quantum well, including a series of energy level anti-crossings due to magnetopolaron formation. These experiments also study the degenerate 2-D emitter, directly measuring chemical potential jumps at both integer and fractional Landau level fillings. Pulsed field studies of the Kondo insulator Ce 3Bi 4Pt 3 establish that a correlated insulating ground state forms at low temperatures. Magnetic fields of ∼50 T suppress the Kondo interaction and the associated collective energy gap.

Cooper-pair tunneling into a quantum Hall fluid.

Transport through a tunnel junction connecting a superconductor to a spin-aligned quantum Hall fluid at filling $\nu$ is studied theoretically. The dominant transport channel at low temperatures is the tunnelling of Cooper pairs into edge states of the quantum Hall fluid. This process, which is greatly suppressed at low energies due to both Coulomb and Pauli exclusion effects, leads to a tunnelling conductance which vanishes with temperature as $T^{4/\nu -2}$, for $\nu^{-1}$ an odd integer. For integer fillings with $\nu >1$ the "Pauli blockade" is circumvented and a non-vanishing conductance is predicted.

Correlations and Local Field Corrections for a Two-Dimensional Electronic System in an External Magnetic Field

It is shown that the correlation effects on a two-dimensional electron gas in a uniform perpendicular magnetic field are significantly affected by a strong magnetic field. A dielectric function approach is used to go beyond the RPA by improving the effective potential. This is done by including the local field correction Gq to the mean Hartree field. Following Singwi et al. we replace the two-particle distribution function ƒ2(r, p; r′, p′; t) by a product of two equilibrium one-particle distribution functions ƒ(r, p; t)ƒ(r′, p′; t) g(r − r′), where g(r) is the static equilibrium pair correlation function. We have shown that the form of the effective potential is not altered by a uniform magnetic field. Both Gq and the pair correlation function oscillate as functions of the magnetic field. The local field correction has maxima at half-odd integer fillings and minima at integer filling factors. As a result, the effective inter-particle potential has enhanced oscillations. The effect due to correlations on the plasma excitations is also discussed.

Superconductor-Mott-insulator transition in Bose systems with finite-range interactions.

We study the superconductor-insulator transition of Bose-Hubbard models with finite-range interactions. Commensurability of the charge distribution with the underlying lattice leads to a richly structured phase diagram. In addition to the lobes of insulating phase characterized by integer fillings, we find--for finite-range interactions--lobes with rational filling factors. At low temperatures we can investigate the phase transition by mapping the model onto a XXZ spin-1/2 Heisenberg model.

A new method for measuring the effective diffusion constant of two-dimensional electrons in the presence of magnetic fields

The transient charge response Q( t) of a two-dimensional electron gas (2DEG) in GaAs/Al x Ga 1− x As heterostructures to a small pulse of the gate voltage, applied between the top gate and source electrodes in a Corbino structure, was employed to directly measure the effective diffusion constant of a 2DEG in the quantum Hall regime. The measured diffusion constant D showed a drastic change as the magnetic field was swept through the integer fillings of the Landau levels.