Integer Quantum Hall Effect States Research Articles

Unconventional Fractional Quantum Hall States in a Wide Quantum Well

A bilayer electron system that is formed in a 60-nm-wide GaAs quantum well and has a large difference of the electron densities in the layers has been studied. It has been found that, when a magnetic field is tilted from the normal to the plane of the system, integer quantum Hall effect states at the filling factors of Landau levels of 1 and 2 disappear; instead, fractional quantum Hall effect states in the interval between these filling factors appear at the filling factors νF = 4/3, 10/7, and 6/5 with odd denominators and at the filling factor νF = 5/4. Several different states can be observed under the variation of the magnetic field. The detected fractional quantum Hall effect states are interpreted as combined states with the same filling factor 1 in the layer with the higher density and with the filling factors νF – 1 in the layer with the lower density. These states are formed because of the redistribution of electrons between the layers, which occurs under the variation of the magnetic field. The appearance of the state with the filling factor νF = 5/4 with the even denominator is presumably attributed to the dominance of the interlayer electron–electron interaction over the intralayer one for electrons in the layer with the lower density.

Integer quantum Hall effect with an anisotropic Coulomb interaction potential

We consider the properties of an integer quantum Hall effect state at filling factor one of the lowest Landau level in presence of an anisotropic Coulomb interaction potential. We adopt a disk geometry and calculate analytically the energy per particle corresponding to a system in the thermodynamic limit. It is found that the main effect of this particular anisotropic Coulomb interaction potential is an overall increase of the energy. The energy of the state at filling factor one in presence of this anisotropic Coulomb interaction potential can be scaled to that of the isotropic Coulomb counterpart by a scaling function tuned by the interaction anisotropy parameter.

Pairing states of composite fermions in double-layer graphene

Pairing interaction between fermionic particles leads to composite Bosons that condense at low temperature. Such condensate gives rise to long range order and phase coherence in superconductivity, superfluidity, and other exotic states of matter in the quantum limit. In graphene double-layers separated by an ultra-thin insulator, strong interlayer Coulomb interaction introduces electron-hole pairing across the two layers, resulting in a unique superfluid phase of interlayer excitons. In this work, we report a series of emergent fractional quantum Hall ground states in a graphene double-layer structure, which is compared to an expanded composite fermion model with two-component correlation. The ground state hierarchy from bulk conductance measurement and Hall resistance plateau from Coulomb drag measurement provide strong experimental evidence for a sequence of effective integer quantum Hall effect states for the novel two-component composite fermions (CFs), where CFs fill integer number of effective LLs (Lambda-level). Most remarkably, a sequence of incompressible states with interlayer correlation are observed at half-filled Lambda-levels, which represents a new type of order involving pairing states of CFs that is unique to graphene double-layer structure and beyond the conventional CF model.

Topological BF field theory description of topological insulators

Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau–Ginzburg field theories. We propose that topological insulators in two and three dimensions are described by a version of abelian BF theory. For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern–Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states. The BF description can be motivated from the local excitations produced when a π flux is threaded through this state. For the three-dimensional topological insulator, the BF description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when time-reversal-symmetry is preserved and yields “axion electrodynamics”, i.e., an electromagnetic E · B term, when time-reversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D Chern–Simons theory allows one to obtain fractional quantum Hall states starting from integer states, BF theory could also describe (at a macroscopic level) fractional 3D topological insulators with fractional statistics of point-like and line-like objects.

On the phase boundaries of the integer quantum hall effect

It has been pointed out that, according to the two-parameter scaling theory, the magnetic-field position of the phases of the integer quantum Hall effect (IQHE) at ωcτ ≲ 1 is not determined by the filling factor ν = nh/eB. The position of the IQHE phases is given by the bare Hall conductivity σxy0. In this regard, it has been shown that the diagonal resistivity in the magnetic field measured by Sakr et al. [Phys. Rev. B 64, 161308 (2001)] does not exhibit transitions between the σxy = 3, 4 and 6 IQHE states on the one hand and the dielectric state on the other hand in contrast to the assertion by Sakr et al.

Odd-Integer Quantum Hall Effect in Graphene: Interaction and Disorder Effects

We study the competition between the long-range Coulomb interaction, disorder scattering, and lattice effects in the integer quantum Hall effect (IQHE) in graphene. By direct transport calculations, both nu=1 and nu=3 IQHE states are revealed in the lowest two Dirac Landau levels. However, the critical disorder strength above which the nu=3 IQHE is destroyed is much smaller than that for the nu=1 IQHE, which may explain the absence of a nu=3 plateau in recent experiments. While the excitation spectrum in the IQHE phase is gapless within numerical finite-size analysis, we do find and determine a mobility gap, which characterizes the energy scale of the stability of the IQHE. Furthermore, we demonstrate that the nu=1 IQHE state is a Dirac valley and sublattice polarized Ising pseudospin ferromagnet, while the nu=3 state is an xy plane polarized pseudospin ferromagnet.

Float-up picture of extended levels in the integer quantum Hall effect: A numerical study

The fate of the integer quantum Hall effect (IQHE) at weak magnetic field is studied numerically in the presence of correlated disorders. We find a systematic float-up and merging picture for extended levels on the low-energy side which results in direct transitions from higher-plateau IQHE states to the insulator. Such direct transitions are controlled by a quantum critical point with a universal scaling form of conductance. The phase diagram is in good agreement with recent experiments.

Heat instability of quantum Hall conductors

Breakdown of the integer quantum Hall effect (IQHE) is discussed based on the consideration of heat stability of a two-dimensional electron gas (2DEG). First, the 2DEG system in the IQHE state is suggested to become thermally unstable when the Hall electric field ${E}_{y}$ reaches a threshold value ${E}_{b}.$ Above ${E}_{b},$ a small number of excited electrons in the higher Landau level, which are initially present in the conductor as fluctuation, are accelerated by ${E}_{y},$ and the 2DEG thereby undergoes a transition to a warm dissipative state. This abrupt transition is referred to as the bootstrap-type electron heating (BSEH). Second, the critical field, ${E}_{b},$ for BSEH is theoretically derived and compared with the experimental values of the IQHE breakdown reported earlier by different groups. The agreement is satisfactory, suggesting that BSEH is the basic mechanism behind the IQHE breakdown. Third, dynamical aspects of BSEH are discussed. It is argued that the BSEH is a process of the avalanche-type electron-hole pair multiplication, in which a small number of nonequilibrium carriers gains kinetic energy within a Landau level and excites other electron-hole pairs via the inter-Landau-level impact ionization. Electrons travel a macroscopic distance during the process of electron-hole multiplication. This feature is confirmed by experiments. Experiments indicate that ${E}_{y}$ does not locally influence the longitudinal conductivity when the IQHE breaks down, providing definite proof of BSEH. Finally, a variety of characteristics of the IQHE, reported in earlier works, is reviewed and suggested to be consistent with the BSEH model.

New Universality of the Metal-Insulator Transition in an Integer Quantum Hall Effect System

A new universality of metal-insulator transition in integer quantum Hall effect (IQHE) system is studied based on a lattice model, where the IQHE states only exist within a finite range of Fermi energy in the presence of disorders. A two-parameter scaling law is found at the high-energy boundary where direct transitions from high IQHE states to insulator occur. We find $\rho_{xx}= \rho_{xy}$ at the critical point whose value can continuously vary as a single function of the Landau-level filling number $n_{\nu}$. Such a new universality well explains recent experiment by Song et al. (Phys. Rev. Lett. 78, 2200 (1997)).

Back gating of a two-dimensional hole gas in a SiGe quantum well

A device comprising a low-resistivity, n-type, Si substrate as a back gate to a p-type (boron), remote-doped, SiGe quantum well has been fabricated and characterized. Reverse and forward voltage biasing of the gate with respect to the two-dimensional hole gas in the quantum well allows the density of holes to be varied from 8×1011 cm−2 down to a measurement-limited value of 4×1011 cm−2. This device is used to demonstrate the evolution with decreasing carrier density of a re-entrant insulator state between the integer quantum Hall effect states with filling factors 1 and 3.

Collapse of the quantum Hall state by floating-up of extended-state bands with increasing disorder

We measured the diagonal and Hall conductivities across the transition between the integer quantum Hall effect state and the insulating state in a two-dimensional electron system formed in Si-MOSFETs. Sample dependence of the transition indicates that the insulating state is caused by Anderson localization due to disorder, not by a formation of an electron solid.

Transport properties of a 2D electron solid in Si-MOSFETs

Recently we reported the observation of magnetic field induced transitions between insulator and integer quantum Hall effect states in very high mobility Si-MOSFETs at temperatures below 0.5 K and dilute electron concentrations n s below 10 11 cm −2. We present results of activation energy, current-voltage characteristics and threshold field measurements which are attributed to sliding transport in a pinned electron solid (ES) forming near half filled Landau levels at low magnetic fields in Si-MOSFETs.