Quantum Hall Effect States Research Articles

Giant Spatial Redistribution of Electrons in a Wide Quantum Well Induced by Quantizing Magnetic Field

In samples of field-effect transistors based on GaAs/AlGaAs heterostructures with an electron system in a single 50-nm-wide GaAs quantum well, a transition stimulated by a quantizing magnetic field has been detected from a bilayer state of the system in zero magnetic field to a single-layer state when only the lowest Landau level is filled. In contrast to the results for the 60-nm-wide quantum well obtained in [S. I. Dorozhkin, A. A. Kapustin, I. V. Fedorov, V. Umansky, and J. H. Smet, Phys. Rev. V 102, 235307 (2020)], the single-layer state is observed not only in incompressible quantum Hall effect states of the electron system at filling factors of 1 and 2, but also in compressible states between these filling factors. The spatial location of the single-layer system in the quantum well has been established; it appears to be independent of the electron distribution over the layers in a low magnetic field. A possible qualitative explanation for this observation has been proposed. The detected transition is supposedly due to the negative compressibility of two-dimensional electron systems caused by exchange-correlation contributions to the electron−electron interaction.

Birotons and ‘dark hierarchies’ in fractional quantum Hall effect

A computational scheme has been developed to determine the energies of neutral excitations in fractional states of the quantum Hall effect. The fractional states are brought into a general hierarchical system (Farey-number hierarchy structure). It is shown that in addition to the well-known hierarchy of fractional states (Laughlin–Jane), there are other ‘dark hierarchies’ of fractional quantum Hall effect that are not observed experimentally in the most highly mobile samples but can have a significant impact on the thermodynamics and spectral characteristics of fractional quantum Hall effect states. The connection of the ‘dark hierarchies’ of fractional quantum Hall effect with the existing experimental data is considered.

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.

Quantum Hall effect systems of electrons with anisotropic patterns

An almost ideal two-dimensional system of electrons can now be easily created in semiconductor heterojunctions. The quantum Hall effect state of the electrons is induced via the application of a strong perpendicular magnetic under specific quantum conditions. The most robust integer and/or fractional quantum Hall states already observed show the expected characteristic magnetoresistance for such systems. However, anisotropic patterns and features in transport properties have been seen for a few other peculiar cases. The origin of such anisotropic patterns may have various mechanisms or may also be due the specific details of the system and material such as the isotropic or anisotropic nature of the effective mass of electrons, the nature of the host substrate parameters, the nature of the interaction potentials, as well as other subtler effects. The interplay between all these factors can lead to many outcomes. In this work we consider small quantum Hall states of electrons at filling factor 1/6 and study the appearance of such anisotropic patterns as a result of some form of innate interaction anisotropy in the system.

Shot noise does not always provide the quasiparticle charge

The fractional charge of quasiparticles is a fundamental feature of quantum Hall effect (QHE) States. The charge has long been measured via shot-noise at moderate temperatures ($T$>30mK), with the Fano factor $F=e^*/e$ revealing the charge $e^*$ of the quasiparticles. However, at sufficiently low temperatures ($T\approx$10mK), we consistently find $F$ being equal to the bulk filling factor, $\nu_b$. Surprisingly, noise with $F=\nu_b$ is also observed on intermediate conductance plateaus in the transmission of the quantum point contact (QPC), where shot noise is not expected. We attribute the unexpected Fano factor to upstream neutral modes, which proliferate at the lowest spinless Landau level. The universality of the Fano factor is also confirmed when the edge modes do not conform to the bulk. For this, the ubiquitous edge modes at the periphery of the sample are replaced by artificially constructed 'interface modes', propagating at the interface between two adjoined QHE states: the tested state and a different state. We present a new theoretical paradigm based on an interplay between charge and neutral modes, explaining the origin of the universal Fano factor.

Birotons and “Dark” Quantum Hall Hierarchies

A computational scheme is suggested to estimate neutral excitation energies in the fractional quantum Hall effect (FQHE) states. The FQHE states are systematized according to the Farey-number hierarchy structure. We show that besides the widely known Laughlin–Jain hierarchy of fractional states, there exist other “dark” hierarchies. Although hardly observed in the highest mobility samples, they can significantly affect the thermodynamics and spectral characteristics of the FQHE states. The known problems in the interpretation of the FQHE’s experimental results are explained in terms of the coexistence of two fundamentally different transformations of the electron system, one of which is a neutral excitation in the FQHE state, whereas the other is a transition between two FQHE ground states, one of which represents the Laughlin–Jain FQHE hierarchy and the other a state of “dark” hierarchies.

Majorana Anyon Composites in Magneto-Photoluminescence Spectra of Natural Quantum Hall Puddles.

In magneto-photoluminescence (magneto-PL) spectra of quasi two-dimensional islands (quantum dots) having seven electrons and Wigner–Seitz radius rs~1.5, we revealed a suppression of magnetic field (B) dispersion, paramagnetic shifts, and jumps of the energy of the emission components for filling factors ν > 1 (B < 10 T). Additionally, we observed B-hysteresis of the jumps and a dependence of all these anomalous features on rs. Using a theoretical description of the magneto-PL spectra and an analysis of the electronic structure of these dots based on the single-particle Fock–Darwin spectrum and many-particle configuration-interaction calculations, we show that these observations can be described by the rs-dependent formation of the anyon (magneto-electron) composites (ACs) involving single-particle states having non-zero angular momentum and that the anyon states observed involve Majorana modes (MMs), including zero-B modes having an equal number of vortexes and anti-vortexes, which can be considered as Majorana anyons. We show that the paramagnetic shift corresponds to a destruction of the equilibrium self-formed ν~5/2 AC by the external magnetic field and that the jumps and their hysteresis can be described in terms of Majorana qubit states controlled by B and rs. Our results show a critical role of quantum confinement in the formation of magneto-electrons and implies the liquid-crystal nature of fractional quantum Hall effect states, the Majorana anyon origin of the states having even ν, i.e., composite fermions, which provide new opportunities for topological quantum computing.

Possible fractional quantum Hall effect and Wigner crystal states in two-dimensional Coulomb gases as a result of anyon correlations

Recently, we have derived an approximate analytic formula for the ground state energy of (2D) charged anyon gas. This result allows us in the present paper to estimate the exchangecorrelation energy, which is as it is well known from a literature the difference of the ground state energy and the Hartree-Fock energy, for fermions with the anyon parameter ν=1, and to formulate the anyon correlation energy for other ν&lt;1. The minima of the last one for all fixed values of ν as well as the minima of the ground state energy at the same ν are only the ν dependent, which means they are only the anyon statistics dependent with no effect of the Coulomb interaction. From this, we conclude that there should appear the localized real space macroscopic structure for any fixed ν from ν&lt;1. For instance, since the Landau level fillingfactor (LLFF) of the fractional quantum Hall effect (FQHE) quasi-particles is equal to the anyon parameter then these quasi-particles should condense in the some real space structure at this LLFF, forming the FQHE plateau and showing that the FQHE is a result of anyoncorrelations. On the other hand, expressing the above mentioned minima function of ν through the density parameter rs of the Coulomb gas, we obtain the values of rs, for which the 2D Wigner crystal (WC) can be observed. It is interesting that the simultaneous observation of the FQHE and WC states in accord with our consideration.

Magnetocatalysis: The Interplay between the Magnetic Field and Electrocatalysis

Magnetocatalysis: The Interplay between the Magnetic Field and Electrocatalysis

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.

Energy Relaxation in Edge Modes in the Quantum Hall Effect.

Studies of energy flow in quantum systems complement the information provided by common conductance measurements. The quantum limit of heat flow in one-dimensional ballistic modes was predicted, and experimentally demonstrated, to have a universal value for bosons, fermions, and fractionally charged anyons. A fraction of this value is expected in non-Abelian states; harboring counterpropagating edge modes. In such exotic states, thermal-energy relaxation along the edge is expected, and can shed light on their topological nature. Here, we introduce a novel experimental setup that enables a direct observation of thermal-energy relaxation in chiral 1D edge modes in the quantum Hall effect. Edge modes, emanating from a heated reservoir, are partitioned by a quantum point contact (QPC) constriction, which is located at some distance along their path. The resulting low frequency noise, measured downstream, allows determination of the "effective temperature" of the edge mode at the location of the QPC. An expected, prominent energy relaxation was found in hole-conjugate states. However, relaxation was also observed in particlelike states, where heat is expected to be conserved. We developed a model, consisting of distance-dependent energy loss, which agrees with the observations; however, we cannot exclude energy redistribution mechanisms, which are not accompanied with energy loss.

Resonant Photoluminescence of a Two-Dimensional Electron System upon the Formation of a Bulk 1/3 State of the Fractional Hall Effect

Resonant and nonresonant photoluminescence spectra of a two-dimensional electron system have been studied under the conditions of the formation of the 1/3 fractional quantum Hall effect state. It has been shown that resonant photoluminescence, in contrast to nonresonant photoluminescence, is a universal marker of the formation of the 1/3 state in the bulk of the two-dimensional system. It has been found that the probabilities of optical transitions from the zeroth Landau level of electrons in the 1/3 state vary so strongly that these variations cannot be explained within the existence theoretical concepts.

Alternative Interpretation and Prediction of Quantum Hall Effect via Electron Pairing Picture

As a two-body system, hydrogen atom with quantum exact solution played an important role for explaining shell structure of multi-electron atoms. Inspired by this, we suggest an alternative interpretation of the integer and fractional quantum Hall effect (QHE) by establishing a direct connection between the exact solutions of a two-dimensional (2D) magnetically trapped electron-pair and the “fundamental” (non-fine) Hall hierarchies of a multi-electron system. We analyze the topology of the exact pair states and report the filling factors of the lowest Landau level based on the exact solutions, which fit the previously and recently reported spectrum of experimental data on the QHE states well and predict some new Hall plateaus for the plateau positions and the eigenenergies reflecting stability and plateau widths. The theoretical prediction associated with the relatively lower minima of the diagonal resistivity is in accurate agreement with the experimental datum spectrum of the fundamental QHE hierarchies.

Quantum Effects in the Capacitance of Field-Effect Transistors with a Double Quantum Well

The compressibility of electrons in a bilayer electron system implemented in a GaAs double quantum well is investigated. Manifestations of the negative compressibility of a low-density two-dimensional electron system in zero and quantizing magnetic fields are observed. It is found that the magnetic field ranges where incompressible phases at the spin-resolved Landau level filling factors of 2 and 1 exist in the layer with the higher electron density are broadened considerably upon the filling of the other layer. The effect is explained by the stabilization of the quantum Hall effect states owing to the transfer of electrons from the layer with the lower density. The magnitude of jumps in the chemical potential for the corresponding quantum Hall effect states is estimated.

Explanation of an unexpected occurrence of fractional quantum Hall effect states in monolayer graphene

Recent experiment reveals the appearance of incompressible fractional quantum Hall effect states in monolayer graphene at and , substituting the compressible Hall metal states at these fillings in the lowest Landau level in a narrow magnetic field window depending on the sample parameters. Simultaneously, none such behavior has been observed either for or , . We propose an explanation of these observations in terms of homotopy of monolayer graphene in consistence with a general theory of correlated states in planar Hall systems.

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.

High-Quality Magnetotransport in Graphene Using the Edge-Free Corbino Geometry.

We report fabrication of graphene devices in a Corbino geometry consisting of concentric circular electrodes with no physical edge connecting the inner and outer electrodes. High device mobility is realized using boron nitride encapsulation together with a dual-graphite gate structure. Bulk conductance measurement in the quantum Hall effect (QHE) regime outperforms previously reported Hall bar measurements, with improved resolution observed for both the integer and fractional QHE states. We identify apparent phase transitions in the fractional sequence in both the lowest and first excited Landau levels (LLs) and observe features consistent with electron solid phases in higher LLs.

Nuclear spin dynamics in [001] AlAs quantum well in the regime of integer and fractional quantum Hall effect

Relaxation of nuclear spins located in the vicinity of 2D electron system confined in a 16 nm [001] AlAs/AlGaAs quantum well was studied with the aid of electron spin resonance (ESR) in the regime of integer and fractional quantum Hall effect. Nuclear spin-lattice relaxation time τ was measured from the time decay of the Overhauser shift near different filling factors of the electron system. The resultant dependence of τ on filling factor turned out to be nontrivial. At the temperature 1.5 K τ reached its maximal value at the exact filling ν = 1 and decreased when ν was altered, yet this maximum vanished when the system was cooled down to 0.5 K. The fractional quantum Hall effect state at the filling of 2∕3 was formed at the temperature of 0.5 K, and the development of this state was accompanied by the slowing of the nuclear spin relaxation. This observation suggests the enhancement of energy gap in the spin excitation spectrum of two-dimensional electrons at 2/3 state.

Edge reconstruction in fractional quantum Hall states

Questions on the nature of edge reconstruction and "where does the current flow" in the quantum Hall effect (QHE) have been debated for years. Moreover, the recent observation of proliferation of "upstream" neutral modes in the fractional QHE raised doubts about the present models of edge channels. In this article we focus on hole-conjugate states, nu=2/3 and nu=3/5, and present a new picture of their edge reconstruction. For example, while the present model for nu=2/3 consists of a single downstream charge channel with conductance 2/3 e^2/h and an upstream neutral mode, we show that the current is carried by two separate downstream edge channels, each with conductance 1/3 e^2/h, accompanied by upstream neutral mode(s). We find that if the two downstream channels are not equilibrated, inter-mode equilibration (via particle exchange) takes place over a distance of microns, with the two channels effectively behaving as a single channel. Moreover, the inter-channel equilibration is accompanied by an excitation of upstream neutral modes. In turn, the counter-propagating neutral modes, moving in close proximity to the charge modes, fragment into propagating charges, inducing thus downstream current fluctuations with zero net current - a novel mechanism for non-equilibrium noise. This unexpected edge reconstruction underlines the need for better understanding of edge reconstruction and energy transport in all fractional QHE states.

Microwave spectroscopic observation of a Wigner solid within the ν=1/2 fractional quantum Hall effect

The fractional quantum Hall effect (FQHE) states at half integer Landau fillings ($\nu$) have long been of great interest, since they have correlations that differ from those of the fundamental Laughlin states found at odd denominators. At $\nu=1/2$ the FQHE has been observed in wide or double quantum wells, and is ascribed to the two-component Halperin-Laughlin $\Psi_{331}$ state. $\Psi_{331}$ excitations carry charge $\pm e/4$, like the carriers of $\nu=5/2$ states which are of interest in quantum computation. Further, such an excitation (quasiparticle or -hole) of $\Psi_{331}$ has unequal, opposite charge in the top and bottom layers, and hence an up or down dipole moment. Here we report evidence for a Wigner solid (WS) of such dipolar quasiholes from a quantitative study of the microwave spectra of a wide quantum well (WQW) at $\nu$ close to 1/2.