Anomalous quantum Hall effect induced by nearby quantum dots

Transport measurements in high magnetic fields have been performed on two-dimensional electron system (2DES) separated by a thin barrier layer from a layer of InAs self-assembled quantum dots (QDs). Clear feature of quantum Hall effect was observed in spite of presence of QDs nearby 2DES. However, both magnetoresistance, ρ_xx, and Hall resistance, ρ_xy, are suppressed significantly only in the magnetic field range of filling factor in 2DES ν<1 and voltage applied on a front gate . The results indicate that the electron state in QDs induces spin-flip process in 2DES.     

Thermodynamic properties of a quantum Hall anti-dot interferometer

We study quantum Hall interferometers in which the interference loop encircles a quantum anti-dot. We base our study on thermodynamic considerations, which we believe reflect the essential aspects of interference transport phenomena. We find that similar to the more conventional Fabry–Perot quantum Hall interferometers, in which the interference loop forms a quantum dot, the anti-dot interferometer is affected by the electro-static Coulomb interaction between the edge modes defining the loop. We show that in the Aharonov–Bohm regime, in which effects of fractional statistics should be visible, is easier to access in interferometers based on anti-dots than in those based on dots. We discuss the relevance of our results to recent measurements on anti-dots interferometers.     

A new network model for the integer quantum Hall effect

A Landauer–Büttiker-type formulation of backscattering between pairs of opposite directed channels is used to describe the coupling at the nodes of a network. Physically, these nodes correspond to saddle points of a slowly varying lateral potential modulation in a 2D electron system in the high magnetic field regime. We show that the network can be solved without needing a transfer matrix as used by Chalker and Coddington. We use an exponential dependence of the coupling on the filling factor of the associated Landau level. We demonstrate that our network representation allows a quantitative modeling of almost every realistic sample geometry in the quantum Hall regime, including the effect of gate electrodes across a Hall bar.     

Bulk and edge properties of the Chern-Simons Ginzburg-Landau theory for the fractional quantum Hall effect

The Chern-Simons Ginzburg-Landau theory for the fractional quantum Hall effect is studied in the presence of a confining potential We review the bulk properties of the model and discuss how the plateau formation emerges without any impurity potential. The effect is related to changes, by accumulation of charge, at the edge when the chemical potential is changed. Fluctuations about the ground state are examined and an expression is found for the velocity of the massless edge mode in terms of the confining potential. The effect of including spin is examined for the case when the system is fully polarized in the bulk. In general a spin texture may appear at the edge, and we examine this effect in the case of a small spin-down component. The low-frequency edge modes are examined and a third-order equation is found for velocities which indicates the presence of three different modes. The discussions are illustrated by numerical studies of the ground states, both for the one- and two-component cases.     

Ballistic transport under quantum Hall effect conditions

The paper addresses details of the single-particle electron spectrum ?_l(p)${?}_l(p)$ in narrow Coulomb channels (l is the transverse spectrum part discrete index and p   is the continuous longitudinal electron momentum). The channel is said to be narrow if differences between transverse spectrum branches ?_l(p)${?}_l(p)$ are larger than temperature. Considered are two extreme cases with respect to magnetic field. For the first case where ?_F≥?ω_c${?}_F\ge \mathit{?}{\omega }_c$, the spectrum ?_l(p)${?}_l(p)$ first calculated by Stern et al. numerically is obtained with approximate analytical analysis (here ?_F${?}_F$ is the Fermi energy of the 2D electron system ?ω_c$\mathit{?}{\omega }_c$ is the cyclotron frequency). In the second case the proposed formalism is extended to high magnetic fields satisfying the inequality ?_F≤?ω_c${?}_F\le \mathit{?}{\omega }_c$. Calculated results are compared with available experimental data.     

Integer quantum Hall effect in a PbTe quantum well

Transport measurements have been carried out on a 10 nm n-type PbTe/Pb_0.9Eu_0.1Te quantum well at millikelvin temperatures. The Hall and longitudinal resistances are measured in a Van der Pauw geometry under high magnetic fields up to 23 T. A robust signature of the integer quantum Hall effect is observed without any sign of parasitic parallel conduction. The unconventional sequence of filling factors associated with the integer quantum Hall effect is discussed in terms of the occupancy of multiple valleys.     

Localization length at the conductivity minima of the quantum Hall effect

The quantum localization is known to be responsible for the deep conductivity minima of the quantum Hall effect. In this paper we calculate the localization length as a function of magnetic field at such minima for several models of disorder (“white-noise”, short-range, and long-range random potentials). We find that with the exponent between one and , depending on the model. In particular, for the “white-noise” random potential roughly coincides with the classical cyclotron radius. Our results are in agreement with available experimental data.     

Anyons and the quantum Hall effect—A pedagogical review

The dichotomy between fermions and bosons is at the root of many physical phenomena, from metallic conduction of electricity to super-fluidity, and from the periodic table to coherent propagation of light. The dichotomy originates from the symmetry of the quantum mechanical wave function to the interchange of two identical particles. In systems that are confined to two spatial dimensions particles that are neither fermions nor bosons, coined “anyons”, may exist. The fractional quantum Hall effect offers an experimental system where this possibility is realized. In this paper we present the concept of anyons, we explain why the observation of the fractional quantum Hall effect almost forces the notion of anyons upon us, and we review several possible ways for a direct observation of the physics of anyons. Furthermore, we devote a large part of the paper to non-abelian anyons, motivating their existence from the point of view of trial wave functions, giving a simple exposition of their relation to conformal field theories, and reviewing several proposals for their direct observation.     

Inelastic light scattering by collective excitations in the fractional quantum Hall regime

We report an inelastic light scattering study of long wavelength collective gap excitations of fractional quantum Hall (FQH) states at ν=p/(2p+1) for . The ν-dependence of the gap energy suggests a collapse of the collective excitation gap near . In a range of filling factors close to , where the FQH gap is believed to collapse, we observe a collective excitation mode that exists only at temperatures below 150 mK.     

Effect of incoherent scattering on three-terminal quantum Hall thermoelectrics

A three-terminal conductor presents peculiar thermoelectric and thermal properties in the quantum Hall regime: it can behave as a symmetric rectifier and as an ideal thermal diode. These properties rely on the coherent propagation along chiral edge channels. We investigate the effect of breaking the coherent propagation by the introduction of a probe terminal. It is shown that chiral effects not only survive the presence of incoherence but they can even improve the thermoelectric performance in the totally incoherent regime.     

Transverse electric field-induced quantum valley Hall effects in zigzag-edge graphene nanoribbons

We have investigated gapless edge states in zigzag-edge graphene nanoribbons under a transverse electric field across the opposite edges by using a tight-binding model and the density functional theory calculations. The tight-binding model predicted that a quantum valley Hall effect occurs at the vacuum-nanoribbon interface under a transverse electric field and, in the presence of edge potentials with opposite signs on opposite edges, an additional quantum valley Hall effect occurs under a much lower field. Dangling bonds inevitable at the edges of real nanoribbons, functional groups terminating the edge dangling bonds, and spin polarizations at the edges result in the edge potentials. The density functional theory calculations confirmed that asymmetric edge terminations, such as one having hydrogen at an edge and fluorine at the other edge, lead to the quantum valley Hall effect even in the absence of a transverse electric field. The electric field-induced half-metallicity in the antiferromagnetic phase, which has been intensively investigated in the last decade, was revealed to originate from a half-metallic quantum valley Hall effect.     

Detection of hidden localized states by the quantum Hall effect in graphene

We fabricated a monolayer graphene transistor device in the shape of the Hall-bar structure, which produced an exactly symmetric signal following the sample geometry. During electrical characterization, the device showed the standard integer quantum Hall effect of monolayer graphene except for a broader range of several quantum Hall plateaus corresponding to small filling factors in the electron region. We investigated this anomaly on the basis of localized states owing to the presence of possible electron traps, whose energy levels were estimated to be near the Dirac point. In particular, the inequality between the filling of electrons and holes was ascribed to the requirement of excess electrons to fill the trap levels. The relations between the quantum Hall plateau, Landau level, and filling factor were carefully analyzed to reveal the details of the localized states in this graphene device.     

Wave function multifractality and dephasing at metal–insulator and quantum Hall transitions

We analyze the critical behavior of the dephasing rate induced by short-range electron–electron interaction near an Anderson transition of metal–insulator or quantum Hall type. The corresponding exponent characterizes the scaling of the transition width with temperature. Assuming no spin degeneracy, the critical behavior can be studied by performing the scaling analysis in the vicinity of the non-interacting fixed point, since the latter is stable with respect to the interaction. We combine an analytical treatment (that includes the identification of operators responsible for dephasing in the formalism of the non-linear sigma-model and the corresponding renormalization-group analysis in 2 + ? dimensions) with numerical simulations on the Chalker–Coddington network model of the quantum Hall transition. Finally, we discuss the current understanding of the Coulomb interaction case and the available experimental data.     

Current breakdown of the integer and fractional quantum Hall effects detected by torque magnetometry

We have developed a novel technique that enables measurements of the breakdown of both the integer and fractional quantum Hall effects in a two-dimensional electron system without the need to contact the sample. The critical Hall electric fields that we measure are significantly higher than those reported by other workers, and support the quasi-elastic inter-Landau-level tunnelling model of breakdown. Comparison of the fractional quantum Hall effect results with those obtained on the integer quantum Hall effect allows the fractional quantum Hall effect energy gap to be determined and provides a test of the composite-fermion theory. The temperature dependence of the critical current gives an insight into the mechanism by which momentum may be conserved during the breakdown process.     

Experimental probes of emergent symmetries in the quantum Hall system

Experiments studying renormalization group flows in the quantum Hall system provide significant evidence for the existence of an emergent holomorphic modular symmetry Γ₀(2)${\Gamma }_0(2)$. We briefly review this evidence and show that, for the lowest temperatures, the experimental determination of the position of the quantum critical points agrees to the parts per mille   level with the prediction from Γ₀(2)${\Gamma }_0(2)$. We present evidence that experiments giving results that deviate substantially from the symmetry predictions are not cold enough to be in the quantum critical domain. We show how the modular symmetry extended by a non-holomorphic particle–hole duality leads to an extensive web of dualities related to those in plateau–insulator transitions, and we derive a formula relating dual pairs (B,Bd)$(B,B_d)$ of magnetic field strengths across any transition. The experimental data obtained for the transition studied so far is in excellent agreement with the duality relations following from this emergent symmetry, and rule out the duality rule derived from the “law of corresponding states”. Comparing these generalized duality predictions with future experiments on other transitions should provide stringent tests of modular duality deep in the non-linear domain far from the quantum critical points.     

Electrostatic theory for imaging experiments on local charges in quantum Hall systems

We use a simple electrostatic treatment to model recent experiments on quantum Hall systems, in which charging of localised states by addition of integer or fractionally charged quasiparticles is observed. Treating the localised state as a compressible quantum dot or antidot embedded in an incompressible background, we calculate the electrostatic potential in its vicinity as a function of its charge, and the chemical potential values at which its charge changes. The results offer a quantitative framework for analysis of the observations.     

Electron–hole states in the fractional quantum Hall regime probed by photoluminescence

The electron–hole states in the fractional quantum Hall regime is investigated with a back-gated undoped quantum well by photoluminesccence in magnetic fields. The evolution of the photoluminescence spectra is discussed depending on the electron density. We find anomalies of the photoluminescence at the integer as well as the fractional filling factors.     

Nuclear-spin-lattice relaxation in a bilayer quantum Hall system

We examined the electron spin degree of freedom around the total Landau-level filling factor ν=1 in a bilayer system via nuclear spins. In a balanced bilayer system, nuclear-spin-lattice relaxation rate 1/T₁, which probes low-energy electron spin fluctuations, increases gradually as the system is driven from the quantum Hall (QH) state through a phase transition to the compressible state. This result demonstrates that the electron spin degree of freedom is not frozen either in the QH or compressible states. Furthermore, as the density difference between the two layers is increased from balanced bilayer to monolayer configurations, 1/T₁ around ν=1 shows a rapid yet smooth increase. This suggests that pseudospin textures around the bilayer ν=1 system evolves continuously into the spin texture for the monolayer system.     

THz imaging of cyclotron emission in quantum Hall conductors

Recent studies of cyclotron emission microscopy on quantum Hall related states are reported. The topics include non-equilibrium between edge and bulk states, current-induced breakdown of the quantum Hall effect, and the emission threshold at hot spots. Experimental method of scanning-type terahertz microscopes developed towards photon-counting level sensitivity is also described.     

Spectral measurement of weak THz waves with quantum Hall detectors

A terahertz (THz) microspectroscope is developed, in which the frequency of extremely weak THz radiation is resolved by scanning the magnetic field for a quantum Hall detector. The electron density of the detectors is controlled by the back-gate biasing, so that the detector sensitivity is calibrated over a spectral range studied. Reliable spectral measurements with a spectral resolution of 1.2 cm⁻¹ has been made with a sensitivity better than 10 femtowatt level over 1 s integration time.