Reentrant Integer Quantum Hall States Research Articles

Finite-thickness effect and spin polarization of the even-denominator fractional quantum Hall states

The spin-polarized even-denominator fractional quantum Hall (FQH) states in the second Landau level (LL), i.e. 5/2 and 7/2, may possess novel quasi-particle excitations obeying non-Abelian statistics. However, the spin polarization of the 7/2 FQH state has not been investigated experimentally and the spin polarization of the 5/2 FQH state from tilted field experiments remains controversial. Using a piezo-driven sample rotator with the lowest electron temperature down to 25 mK, we studied the energy gap of the even-denominator FQH states in the second LL by precise control of the tilted angles with a resolution less than 0.1{\deg}. We observed two different energy gap dependences on the in-plane magnetic field for 5/2, 7/2, other FQH states (7/3 and 8/3) in the second LL and reentrant integer quantum Hall (RIQH) states in the third LL. Though the transition fields vary from states, their corresponding in-plane magnetic lengths are comparable to the quantum well thickness of the sample, which may result from the influence of the finite-thickness effect. At low in-plane magnetic fields, before the conjectured finite-thickness effect starts to dominate, the energy gaps of both 5/2 and 7/2 states show a non-decreasing behavior, supporting spin-polarized ground states. Our results also suggest that the 7/3, 8/3 FQH states, and the RIQH states in the third LL are spin-polarized or partially spin-polarized.

Superfluidity of indirect excitons vs quantum Hall correlation in double Hall systems: Different types of physical mechanisms of correlation organization in Hall bilayers

Bilayer Hall systems can be divided into two groups—with and without tunneling of carriers across the barrier between layers. We demonstrate that these both classes differ in topology sense which leads to the distinct quantum Hall hierarchy. In the case of forbidden interlayer carrier tunneling we developed the Metropolis Monte Carlo simulation for an energy competition of the reentrant integer quantum Hall state against the superfluid Bose Einstein condensate of indirect excitons in double-layer 2D Hall systems, GaAs/GaAlAs/GaAs and b-graphene/hBN/b-graphene, with complementary layer filling, νbot+νtop=1. The resulted phase diagrams for both systems have been determined in consistence with the experimental data.

Phase diagrams for superfluidity of indirect excitons in double Hall systems GaAs/GaAlAs/GaAs and bilayer-graphene/hBN/bilayer-graphene

The energy competition of the reentrant integer quantum Hall state and the superfluid Bose Einstein condensate of indirect excitons in twin 2D Hall systems separated by an insulating barrier and with complementary layer fillings, , has been analysed and compared with experimental observations in GaAs/GaAlAs/GaAs and bilayer-graphene/hBN/bilayer-graphene in the so-called counterflow and drag configurations. The related phase diagrams for varying fillings of layers and barrier thickness have been determined. A modification of the phase transition diagrams due to a change of the drag to the counterflow configuration is illustrated in agreement with the observations. The presented model appears to be consistent with the experimental observations.

Impact of Heterostructure Design on Transport Properties in the Second Landau Level ofIn SituBack-Gated Two-Dimensional Electron Gases

We report on transport in the second Landau level in \emph{in-situ} back-gated two-dimensional electron gases in GaAs/Al$_x$Ga$_{1-x}$As quantum wells. Minimization of gate leakage is the primary heterostructure design consideration. Leakage currents resulting in dissipation as small as $\sim$ 10 pW can cause noticeable heating of the electrons at 10 mK, limiting the formation of novel correlated states. We show that when the heterostructure design is properly optimized, gate voltages as large as 4V can be applied with negligible gate leakage, allowing the density to be tuned over a large range from depletion to over 4 $\times$ 10$^{11}$ cm$^{-2}$. As a result, the strength of the $\nu = 5/2$ state can be continuously tuned from onset at n $\sim 1.2 \times 10^{11}$ cm$^{-2}$ to a maximum $\Delta_{5/2} = 625$ mK at n = $3.35 \times 10^{11}$ cm$^{-2}$. An unusual evolution of the reentrant integer quantum Hall states as a function of density is also reported. These devices can be expected to be useful in experiments aimed at proving the existence of non-Abelian phases useful for topological quantum computation.

Depinning transition of bubble phases in a high Landau level

While in the lowest Landau level the electron-electron interaction leads to the formation of the Wigner crystal, in higher Landau levels a solid phase with multiple electrons in a lattice site of crystal was predicted, which was called the bubble phase. Reentrant integer quantum Hall states are believed to be the insulating bubble phase pinned by disorder. We carry out nonlinear transport measurements on the reentrant states and study the de-pinning of the bubble phase, which is complementary to previous microwave measurements and provides unique information. In this study, conductivity is directly measured with Corbino geometry. Based on the threshold electric field of de-pinning, a phase diagram of the reentrant state is mapped. We discuss an interaction-driven topological phase transition between the integer quantum Hall state and the reentrant integer quantum Hall state.

Contrasting energy scales of reentrant integer quantum Hall states

We report drastically different onset temperatures of the reentrant integer quantum Hall states in the second and third Landau level. This finding is in quantitative disagreement with the Hartree-Fock theory of the bubble phases which is thought to describe these reentrant states. Our results indicate that the number of electrons per bubble in either the second or the third Landau level is likely different than predicted.

Observation of Reentrant Integer Quantum Hall States in the Lowest Landau Level

Measurements on very low disorder two-dimensional electrons confined to relatively wide GaAs quantum well samples with tunable density reveal a close competition between the electron liquid and solid phases near the Landau level filling factor ν=1. As the density is raised, the fractional quantum Hall liquid at ν=4/5 suddenly disappears at a well-width dependent critical density, and then reappears at higher densities with insulating phases on its flanks. These insulating phases exhibit reentrant ν=1 integer quantum Hall effects and signal the formation of electron Wigner crystal states. Qualitatively similar phenomena are seen near ν=6/5.

Collective Nature of the Reentrant Integer Quantum Hall States in the Second Landau Level

We report an unexpected sharp peak in the temperature dependence of the magnetoresistance of the reentrant integer quantum Hall states in the second Landau level. This peak defines the onset temperature of these states. We find that in different spin branches the onset temperatures of the reentrant states scale with the Coulomb energy. This scaling provides direct evidence that Coulomb interactions play an important role in the formation of these reentrant states evincing their collective nature.

Density dependence of theν=52energy gap: Experiment and theory

A density-tunable GaAs-AlGaAs heterostructure is used to study the density dependence of the filling factor $\ensuremath{\nu}=\frac{5}{2}$ and other fractional and reentrant integer quantum-Hall states in the second Landau level. The activation energy at $\ensuremath{\nu}=\frac{5}{2}$ can be determined for densities between 1.3 and $2.7\ifmmode\times\else\texttimes\fi{}{10}^{11}/{\text{cm}}^{2}$ and reaches up to 310 mK. The 5/2 energy gap is calculated numerically, including finite width and Landau-level-mixing corrections, both as a function of electron density. The discrepancy between theory and experiment increases moderately with density and reaches about 1.5 K at the highest density. We argue that the activation energy is strongly influenced by disorder from ionized donors and attribute this to the surprisingly large size of the 5/2 quasiparticles. We find that the quasiparticles have a diameter of at least 12 times the magnetic length or 150 nm at a magnetic field of 4 T. Implications for heterostructure design are discussed.

Astability and Negative Differential Resistance of the Wigner Solid

We report spontaneous narrow band oscillations in the high field Wigner solid. These oscillations are similar to the recently seen and yet unexplained oscillations in the reentrant integer quantum Hall states. The current-voltage characteristic has a region of negative differential resistance in the current biased setup and it is hysteretic in the voltage biased setup. As a consequence of the unusual breakdown, the oscillations in the Wigner solid are of the relaxation type.

Observation of narrow-band noise accompanying the breakdown of insulating states in high Landau levels.

Recent magnetotransport experiments on high mobility two-dimensional electron systems have revealed many-body electron states unique to high Landau levels. Among these are reentrant integer quantum Hall states which undergo sharp transitions to conduction above some threshold field. Here we report that these transitions are often accompanied by narrow- and broad-band noise with frequencies which are strongly dependent on the magnitude of the applied dc current.

DMRG study of the ground state at higher Landau levels—stripes, bubbles and the Wigner crystal

Hartree–Fock theory predicted stripe or bubble phase in the third and higher Landau levels for two-dimensional electrons, and experimental evidence has been accumulated. In this paper theoretical confirmation of the stripe phase and bubble phase in higher Landau level is given by means of the density matrix renormalization group (DMRG) method, which can give essentially exact ground state for electron systems with up to 18 electrons. From the study of the pair correlation function, the stripe phase, bubble phase, and the Wigner crystal phase are identified, and a phase diagram is obtained. The reentrant integer quantum Hall state is identified as the bubble state. The phase diagram of the fourth Landau level shows more diversity than the third level.

Two-dimensional electrons in excited Landau levels: evidence for new collective states

Recent magneto-transport experiments on high mobility two-dimensional electron systems have provided strong evidence that a new class of collective electronic states exists at high Landau level occupancy. Among the phenomena observed are strongly anisotropic resistances near half-filling and curious re-entrant integer quantum Hall states in the flanks of high Landau levels. These results have been widely interpreted as evidence for the existence of an unusual class of charge density wave states. This paper emphasizes the underlying arguments for the existence of new phases and reviews the charge density wave interpretation.

Possible composite-fermion liquid as a crossover from Wigner crystal to bubble phase in higher Landau levels

The ground state cohesive energies per electron of the composite fermion (CF) Fermi sea, the Laughlin state and the charge density wave (CDW) at higher Landau levels (LLs) are computed. It is shown that whereas for $n\geq 2$ LL, the CDW state is generally more energetically preferable than those of the CF liquid and the Laughlin liquid, the $\nu =4+1/6$ CF liquid state unexpectedly has lower ground state energy than that of the CDW state. We suggest this CF liquid between the Wigner crystal and the bubble phase may lead to the crossover from the normal integer quantum Hall liquid to the novel re-entrant integer quantum Hall state observed in the recent magneto-transport experiments.

New physics in high Landau levels

Recent magneto-transport experiments on ultra-high mobility 2D electron systems in GaAs/AlGaAs heterostructures have revealed the existence of whole new classes of correlated many-electron states in highly excited Landau levels. These new states, which appear only at extremely low temperatures, are distinctly different from the familiar fractional quantum Hall liquids of the lowest Landau level. Prominent among the recent findings are the discoveries of giant anisotropies in the resistivity near half-filling of the third and higher Landau levels and the observation of re-entrant integer quantum Hall states in the flanks of these same levels. This contribution will survey the present status of this emerging field.