Table of contents

This volume contains invited and contributed papers from the 19th International Conference on the Application of High Magnetic Fields in Semiconductor Physics and Nanotechnology (HMF-19) held in Fukuoka, Japan, from 1–6 August 2010. This conference was mainly sponsored by the Tokyo University-'Horiba International fund', which was donated by Dr Masao Horiba, the founder of Horiba Ltd. The scientific program of HMF-19 consisted of 37 invited talks, 24 contributed talks, and 83 posters, which is available from the conference homepage http://www.hmf19.iis.u-tokyo.ac.jp/index.html. Each manuscript submitted for publication in this volume has been independently reviewed. The Editor is very grateful to all the reviewers for their quick responses and helpful reports and to all the authors for their submissions and patience for the delay in the editorial process. Finally, the Editor would like to express his sincere gratitude to all the individuals involved in the conference organization and all the attendees, who made this conference so successful.

Koji Muraki

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

We review the tight-binding model of ABA-stacked trilayer graphene. The presence of mirror reflection symmetry of the crystal structure leads to a decomposition of the band structure into separate monolayerlike and bilayerlike parts. Owing to a lack of spatial inversion symmetry, next-nearest layer coupling induces gaps in the monolayerlike and the bilayerlike parts of the spectrum, and also shifts the monolayerlike and bilayerlike bands with respect to each other. We calculate the Landau level spectrum of ABA-stacked trilayer graphene taking into account terms within the single-particle picture that break level degeneracy including next-nearest layer coupling and spin-orbit coupling.

Chirally stacked neutral N-layer graphene systems with N ≥ 2 exhibit spontaneous inversion symmetry breaking and interaction induced charge gaps due to interlayer exchange interactions. A variety of distinct broken symmetry states are distinguished by their charge, spin, and valley Hall conductivities, by their orbital magnetizations, and by their edge state properties. In the spinless case, quantum anomalous and valley Hall states are favored by a weak magnetic field and by an electric field between the graphene layers, respectively. At interfaces between different phases one dimensional gapless modes exhibit novel Luttinger liquid behaviors.

The ground state and low-energy excitations of graphene and its bilayer are investigated by the density matrix renormalization group (DMRG) method. We analyze the effect of Coulomb interaction between the electrons including valley degrees of freedoms. The obtained results show finite charge excitation gap at various fractional fillings ν_n = 1/3, 2/5, 2/3 in the n = 0 and 1 Landau levels of single-layer graphene (SLG) and n = 2 Landau level of bilayer graphene (BLG). The lowest charge excitations at ν = 1/3, and 1 in SLG are valley skyrmions.

Topological aspects of graphene are reviewed focusing on the massless Dirac fermions with/without magnetic field. Doubled Dirac cones of graphene are topologically protected by the chiral symmetry. The quantum Hall effect of the graphene is described by the Berry connection of a manybody state by the filled Landau levels which naturally possesses non-Abelian gauge structures. A generic principle of the topologically non trivial states as the bulk-edge correspondence is applied for graphene with/without magnetic field and explain some of the characteristic boundary phenomena of graphene.

Orbital magnetic susceptibility is calculated for massive Dirac systems, such as graphene with a band gap, and bismuth. Gap opening allows us to relate the singular orbital magnetism of massless Dirac system to the usual magnetism of conventional metal. In gapped graphene, we show that the valley degree of freedom produces Zeeman splitting as a real spin does, and causes Pauli paramagnetism which dominates over Landau diamagnetism. Singular susceptibility of intrinsic graphene can be understood as divergence of those contributions in zero-mass limit. A similar analysis is applied to three-dimensional Dirac systems to explain the strong diamagnetism of bismuth.

Tilt induced anisotropic transport is observed in a series of three wide GaAs quantum wells. In the absence of tilt the transport is isotropic and well developed quantum Hall states are observed. For large values of tilt (θ>60°) the quantum Hall states at ν = 5 and 7 are replaced by strongly anisotropic states in the two widest wells, occurring at slightly lower values of θ for the widest well. A similar transition is also seen at ν = 9 in the widest quantum well. This transition is not observed in the narrowest quantum well up to the largest tilt angle measured.

Low temperature transport properties of high mobility two-dimensional electron systems placed in a weak perpendicular magnetic field can be modified dramatically by microwave or dc electric fields. This paper surveys recent experimental developments which include zero-differential resistance states, Hall field-induced resistance oscillations in tilted magnetic fields, nonlinear response of the Shubnikov-de Haas Oscillations, and a novel microwave photoconductivity peak near the second harmonic of the cyclotron resonance.

By using scanning tunnelling spectroscopy, we study the influence of potential disorder on an adsorbate-induced two-dimensional electron system in the integer quantum Hall regime. The real-space imaged local density of states exhibits transition from localized drift states encircling the potential minima to another type of localized drift states encircling the potential maxima. While the former states show regular round shapes, the latter have irregular-shaped patterns. This difference is induced by different sources for the potential minima and maxima, i.e., substrate donors and an inhomogeneous distribution of the adsorbates, respectively.

Electric dipole spin resonance of two individual electrons and the influence of hyperfine coupling on the spin resonance are studied for a double quantum dot equipped with a micro-magnet. The spin resonance occurs by oscillating the electron in each dot at microwave (MW) frequencies in the presence of a micro-magnet induced stray field. The observed continuous wave (CW) and time-resolved spin resonances are consistent with calculations in which the MW induced AC electric field and micro-magnet induced stray field are taken into account. The influence of hyperfine coupling causes an increase and broadening of the respective CW spin resonance peaks through dynamical nuclear polarization when sweeping up the magnetic field. This behaviour appears stronger for the larger of the two spin resonance peaks and in general becomes more pronounced as the MW power increases, both reflecting that the electron-nuclei interaction is more efficient for the stronger spin resonance. In addition the hyperfine coupling effect only becomes pronounced when the MW induced AC magnetic field exceeds the fluctuating nuclear field.

We create electrostatically induced quantum dots by thermal diffusion of interstitial Mn out of a p-type (GaMn)As layer into the vicinity of a GaAs quantum well. This leads to the formation of deep, approximately circular and strongly confined dot-like potential minima in a large mesa diode structure. The minima are formed without need for advanced lithography or electrostatic gating. Using fields of up to 30 T, magnetotunnelling spectroscopy of an individual dot reveals the symmetry of the electronic eigenfunctions and, for the approximately circular dots, a rich spectrum of Fock-Darwin-like states with an orbital angular momentum component |l_z| ranging from 0 up to 11. We find that a small fraction of the dots has elongated potential minima, giving rise to quenching of the orbital angular momentum of the electronic eigenstates. By developing a model to describe the diffusion of the Mn interstitial ions, we determine the electrostatic potential landscape in the quantum well and hence the distribution of dot shapes and sizes. This is in a good agreement with our experimental data.

We report on magneto-optical studies of strongly coupled quantum dot – micropillar cavity systems. Large In_0.3Ga_0.7As quantum dots (QDs) in the active layer of the micropillar facilitate the observation of strong coupling. In addition, they exhibit a particular large diamagnetic response which is exploited to demonstrate magneto-optical resonance tuning in the strong coupling regime. The magnetic field employed in Faraday configuration induces a transition from strong coupling towards the critical coupling regime which is explained in terms of a magnetic field dependent oscillator strength of the In_0.3Ga_0.7As QDs. We further study the coherent interaction between spin resolved states of the QDs and microcavity photon modes. A detailed oscillator model is used to extract the associated coupling parameters of the individual spin and cavity modes and reveals an effective coupling between photon modes that is mediated by the exciton spin states.

We present detailed data on the unusual angular-dependent magnetoresistance oscillation phenomenon recentiy discovered in a topological insulator Bi_0.91Sb_0.09. Direct comparison of the data taken before and after etching the sample surface gives compelling evidence that this phenomenon is essentially originating from a surface state. The symmetry of the oscillations suggests that it probably comes from the (111) plane, and obviously a new mechanism, such as a coupling between the surface and the bulk states, is responsible for this intriguing phenomenon in topological insulators.

Topological insulators have gapless edge/surface states with novel transport properties. Among these, there are two classes of perfectly conducting channels which are free from backscattering: the edge states of two-dimensional topological insulators and the one-dimensional states localized on dislocations of certain three-dimensional topological insulators. We show how these novel states affect thermoelectric properties of the systems and discuss possibilities to improve the thermoelectric figure of merit using these materials with perfectly conducting channels.

We experimentally demonstrate the existence of microwave-induced zero-resistance states (ZRS) in bilayer electron systems created in wide quantum wells. In contrast to single-layer two-dimensional electron systems, ZRS are developed from the strongest magneto-intersubband oscillation peaks inverted by microwave radiation. Our experimental work is discussed within the theories of microscopic mechanisms of photoresistance, and the calculations reveal that the condition for absolute negative resistivity correlates with the appearance of ZRS.

A theory of nonequilibrium magnetotransport in high Landau levels of inhomogeneous quantum Hall systems is presented. A nonlinear current is calculated in response to given local gradients of the chemical and electrostatic potential in the presence of moderately strong microwave radiation. In the regime of high temperature, theory generalizes previously obtained results describing microwave- and Hall-induced oscillations of magnetoresistivity for the case of spatially non-uniform systems. Additionally, the regime of low temperatures is studied, where strong modification of Shubnikov-de Haas oscillations by the ac and dc fields is demonstrated.

Zero resistance differential states have been observed in two-dimensional electron gases (2DEG) subject to a magnetic field and a strong dc current. In a recent work we presented a model to describe the nonlinear transport regime of this phenomenon. From the analysis of the differential resistivity and the longitudinal voltage we predicted the formation of negative differential resistivity states, although these states are known to be unstable. Based on our model, we derive an analytical approximated expression for the Voltage-Current characteristics, that captures the main elements of the problem. The result allow us to construct an energy functional for the system. In the zero temperature limit, the system presents a quantum phase transition, with the control parameter given by the magnetic field. It is noted that above a threshold value (B > B_th), the symmetry is spontaneously broken. At sufficiently high magnetic field and low temperature the model predicts a phase with a non-vanishing permanent current; this is a novel phase that has not been observed so far.

In this work, we test the feasibility of a resistance standard based on a serial array of ten lithographically interconnected quantum Hall bars based on an Al(Ga)As heterostructure. Our investigation involves a novel multiple layer process for the fabrication of our samples which allows to realize a thin SiO₂ insulations by means of a lift-off process. Additionally, we have performed preliminary precision measurements of the i = 2 Hall plateau in order to characterize the metrological properties of our samples.

We present observations of potential fluctuation distributions in two-dimensional systems of a GaAs/AlGaAs interface and of a graphene surface. We have exploited scanning electrometers based on gate effects for the sensor via capacitive coupling with a sample. The experimental data for the GaAs/AlGaAs sample show that the temporal potential fluctuation (noise voltage) largely occurs in the transition region between two adjacent quantum-Hall plateaus and that it is concentrated on a sample boundary. This fluctuation can be understood as arising from unstable electron relaxation in the non-equilibrium edge state. For the graphene sample, a Hall potential profile was imaged and a potential fluctuation with the period of 50-100nm was observed.

The distribution of the Hall voltage induced by low-frequency AC current is studied theoretically in the incoherent linear transport of quantum Hall systems with slowly-varying confining potential. It is shown that in the low-frequency limit the Hall potential has a steeper slope where the diagonal conductivity is smaller, while at higher frequencies it exhibits a peak or a dip where the Hall conductivity has a slope.

We developed a non-equilibrium network model for magneto transport in 2D electronic systems in the quantum Hall effect regime, which is able to capture the real sample geometry, including contacts, leads and in-homogeneities like introduced by gate electrodes. In this paper we investigate non-local effects in magneto transport for a number of contact configurations of a quantum Hall system, including the effect of having unused metallic contacts between the active region of classical current flow and the remote region where the non-local signals are obtained.

Spin polarization measurement is important for the study of a variety of spin states in quantum Hall system. Kerr rotation is proportional to spin polarization, so we developed a high sensitive measurement of Kerr rotation by using homodyne detection and a variety of modulation techniques. Furthermore, we developed Kerr rotation spectra measurement system base on the multi-channel homodyne detection, which enables the assignment of the optical transitions and semi-quantitative estimation of spin polarization by integrating the spectra over the specific optical transition. The spin polarization presents a rapid spin depolarization on both sides of ν = 1 due to Skyrmionic excitation. However the top of spin polarization presents a narrow flat region. Furthermore the spin polarization around ν = 3 also shows a rapid spin depolarization which suggest the existence of Skyrmion at higher odd filling factor.

In the photoluminescence spectra of a two-dimensional electron gas in the fractional quantum Hall regime we observe the states at filling factors ν = 4/5, 5/7, 4/11 and 3/8 as clear minima in the intensity or area emission peak. The first three states are described as interacting composite fermions in fractional quantum Hall regime. The minimum in the intensity at ν = 3/8, which is not explained within this picture, can be an evidence of a suppression of the screening of the Coulomb interaction among the effective quasi-particles involved in this intriguing state. The magnetic field energy dispersion at very low temperatures is also discussed. At low field the emission follows a Landau dispersion with a screened magneto-Coulomb contribution. At intermediate fields the hidden symmetry manifests. At high field above ν = 1/3 the electrons correlate into an insulating phase, and the optical emission behaviour at the liquid-insulator transition is coherent with a charge ordering driven by Coulomb correlations.

We have experimentally examined the state of a two-dimensional electron gas subjected to unidirectional periodic potential modulation in the vicinity of the filling ν = 5/3 (equivalent to ν = 1/3 by the particle-hole symmetry). In addition to a peak in the longitudinal resistivity ρ_xx, we find small amplitude oscillations roughly periodic in the magnetic field B in the Hall resistivity ρ_yx. The oscillations appear in a narrow range of the electron density n_e, and the period ΔB of the oscillations increases with the slight increase in n_e. The oscillations are interpreted as resulting from the commensurability between the high harmonics of the modulation potential and the stripe state, which is predicted by the density matrix renormalization group calculations to be the ground state in our system.

Transport and tunneling is studied in the regime of the excitonic condensate at total filling factor one using the counterflow geometry. At small currents the coupling between the layers is large making the two layers virtually electrically inseparable. Above a critical current the tunneling becomes negligible. An onset of dissipation in the longitudinal transport is observed in the same current range.

We investigate the evolution of the total Landau level filling factor ν_T = 1 bilayer quantum Hall (QH) state versus density imbalance at full spin polarization under a tilted magnetic field. When the system is well below the compressible-incompressible transition point at the balanced density, the ν_T = 1 QH state extends widely versus density imbalance, continuously merging into the single-layer ν = 1 QH state. In the vicinity of the transition point, the ν_T = 1 QH state is only weakly developed at small imbalance but increases in strength toward ν_T = 1/3 + 2/3, where it is clearly separated from the single-layer ν = 1 QH state. These results suggest that the system at the imbalance of Δν = 1/3 undergoes a transition from the correlated ν_T = 1 QH state to single-layer fractional QH states with increasing density.

This work reports on the experimental observation of the even-denominator state ν = 3/2 in a trilayer electron system in tilted magnetic fields. The ν = 3/2 state demonstrates a strong minimum in longitudinal resistance and is accompanied by a plateau in Hall resistance in a narrow range of tilt angles.

We study the hysteresis of magnetoresistance in the bilayer ν = 4/3 and monolayer ν = 2/3 quantum Hall states (QHSs), where ν is the Landau level filling factor, in order to understand the mechanism of dynamic nuclear polarizations (DNPs) that affects transport properties of GaAs/AlAs two-dimensional electron gas system. Basically hysteresis around the bilayer ν = 4/3 is resulted in the monolayer ν = 2/3 in each layer. However, we also find hysteresis that appears around the bilayer ν = 1 QHS region caused by the strong effects of DNPs as a consequence of the sweep over ν = 2/3 QHS in one layer. These findings suggest the effects of nuclear spin polarizations in the bilayer QHSs over a wide range of filling factors.

Dynamic polarization of nuclear spins has been studied in the breakdown regime of fractional quantum Hall effect using a Corbino-disk device. We find that nuclear spins are polarized in the Corbino disk in the breakdown regime of fractional quantum Hall effect. Since edge channel is completely absent in the Corbino disk, the demonstration of dynamic nuclear polarization in the Corbino disk shows that nuclear spins are polarized and detected in the bulk channel of the quantum Hall conductor.

We present a DC measurement of resistively detected NMR (RDNMR) in a single InSb/AlInSb quantum well. Dynamic nuclear polarization has been demonstrated around the resistance spike, which is the signature of the pseudospin quantum Hall ferromagnet at the filling factor of two. The RDNMR signals with dispersive lineshape occur on each side of the spike, but show the shape inversion. The dispersionlike lineshape is found to be independent of measurement conditions (current intensity, temperature, and RF power), provided the polarized nuclei are in equilibrium.

As found from quantum magnetotransport under tilted magnetic fields in a (013)-oriented n-Cd_0.7Hg_0.3Te/HgTe/Cd_0.7Hg_0.3Te quantum well of ~20nm width, the positions of magnetic level coincidences agree quite well with a traditional description of the coincidence effect like in a simple Γ₆ band in spite of the Γ₈ character of the conduction band in HgTe. The coincidence angles yield the effective g-factor g* = 33 while g* = 50÷60 is obtained with different magnetotransport techniques under fields oriented perpendicular to the layers. The difference is settled when assuming the g-factor anisotropy of g_⊥/g_||≈ 2. Level anticrossings are revealed at high values of perpendicular magnetic fields, corresponding to the quantum Hall regime. They manifest themselves in a splitting of the coincidence magnetoresistivity peaks and in a shift of the split-off peaks from the integer filling factors ν to the neighbouring half-integer filling factors. The anticrossing at ν = 3 is found to be significantly stronger than the neighbouring ones at ν = 2 and ν = 4 that is tentatively explained in terms of formation of easy-axis quantum Hall ferromagnetic states in the vicinity of the expected crossings.

We investigate the equilibrium and non-equilibrium electron transport in a quantum wire (QW) in the quantum Hall regime. While the equilibrium conductance of the QW is quantized reflecting the dissipation-less quantum Hall edge transport, the quantization collapses when the QW is voltage-biased with the voltages larger than the critical ones. This phenomenon is accompanied by the dynamic nuclear polarization which causes the temporal variation of the QW conductance of the order of minutes.

We investigate edge channel properties in integer quantum Hall regime through time-of-flight measurements of edge magnetoplasmons (EMPs). EMPs are injected by applying a voltage pulse to on Ohmic contact and detected by applying another voltage pulse to a quantum point contact. By controlling the time interval between the injection and detection pulses, the velocity of EMPs is determined. The width of edge channels calculated from the velocity of EMPs oscillates with filling factor: as the filling factor is decreased to an integer, the width increases almost by one order of magnitude from ~ 0.3 to ~ 3μm. Furthermore, we find that the width at a fixed filling factor increases with decreasing electron density in the bulk two-dimensional system.

We study theoretically dynamic response of a mesoscopic capacitor, which consists of a quantum dot connected to an electron reservoir via a point contact and capacitively coupled to a gate voltage. A quantum Hall edge state with a filling factor ν is realized in a strong magnetic field applied perpendicular to the two-dimensional electron gas. We discuss a noise-driven quantum phase transition of the transport property of the edge state by taking into account an ohmic bath connected to the gate voltage. Without the noise, the charge relaxation resitance for ν > 1/2 is universally quantized at R_q = h/(2e²ν), while for ν < 1/2, the system undergoes the Kosterlitz-Thouless transition, which drastically changes the nature of the dynamical resistance. The phase transition is facilitated by the noisy gate voltage, and we see that it can occur even for an integer quantum Hall edge at ν = 1. When the dissipation by the noise is sufficiently small, the quantized value of R_q is shifted by the bath impedance.

In this study we analyze the density distributions of the two dimensional electron system for an experimental geometry which is topologically equivalent of an Aharonov-Bohm interferometer in three dimensions in the quantum Hall regime and obtain the spatial distribution of the edge states. We employ the Thomas-Fermi approximation in our analysis and solve the Poisson equation in three dimensional using a multi grid technique. Also we obtain the distribution of incompressible strips for a wide range of magnetic fields strengths and comment on their relation with experimental results in literature.

We present recent low-temperature magnetotransport experiments on single-layer and bilayer graphene in high magnetic field up to 33 T. In single layer graphene the fourfold degeneracy of the zero-energy Landau level is lifted by a gap opening at filling factor ν = 0. In bilayer graphene, we observe a partial lifting of the degeneracy of the eightfold degenerate zero-energy Landau level.

We have investigated the magneto-transport around filling factor ν = 0 in monolayer graphene sheet. Zero Hall plateau of Hall conductivity and minimum of longitudinal conductivity have been clearly observed despite the highly fluctuated behaviour of magneto-resistance above 10 T. These phenomena can be understood by the transport of counter-propagating electron and hole edge states at the charge neutrality point. We tried to explain the origin of remarkable fluctuations in magneto-resistance by the energy relaxations among the counter-propagating edge channels.

We report on the magnetotransport measurements of mono- and bi-layer graphene in pulsed high magnetic fields up to B = 53 T. In a mono-layer graphene, the Hall resistance R_H is quantized to R_H = (h/e²)ν⁻¹ with ν = 2, 6, and 10 for either hole or electron doping. In a bi-layer graphene, R_H is quantized to R_H = (h/e²)ν⁻¹ with ν = 4, 8, and 12. These results indicate that the precise magnetotransport measurements of the graphene can be conducted in the environment of pulse magnetic fields.

Magnetotransport across monolayer-bilayer boundary on a graphene piece has been studied in the quantum Hall state. The edge channel transport in monolayer-bilayer junctions has been discussed based on the Landauer-Buttiker picture following p-n bipolar junctions of monolayer graphene. We considered two extreme cases of transmission from input edge channels to output channels at the junction, the maximum transmission model and the full-mixing model. They give different two-terminal conductance as a function of carrier filling. We measured the two-terminal conductance in monolayer-bilayer junction devices, and the measured conductance agreed better with the full-mixing model. This result suggests that edge channels of monolayer and bilayer regions are almost fully mixed up at the monolayer-bilayer boundary.

The magnetoresistance of a monolayer graphene in a random magnetic field(RMF) with zero mean has been investigated. The RMF was produced by applying a magnetic field parallel to the graphene plane utilizing ripples. The magnetoresistance has shown the same magnetic field dependence and, unexpectedly, the same carrier density dependence as the conventional two-dimensional electron systems in random magnetic fields. The relation between the characteristic length of ripples and the magnitude of the magnetoresistance is discussed.

Randomly networked nanographene sheets have been studied by electron spin resonance (ESR) technique at 20 GHz (K-band) and 35 GHz (Q-band). Nanographene has spin-polarized non-bonding π-electron states (edge-state spins) localized in the zigzag edge region. We have investigated the temperature dependence of an ESR signal of activated carbon fibers at two different microwave powers for each frequency. The signal intensity smoothly increases with decreasing temperature at any microwave power. The line width of ESR signal with a Lorentzian line shape decreases linearly upon cooling, and then increases steeply after taking a minimum at about 20 K irrespective of microwave power. The former is interpreted as the Korringa relation in the localized edge spins and conduction π carriers. The latter may be caused by inhomogeneous line broadening of the ESR signal from randomly distributed nanographene sheets with different sizes due to the suppression of electron hopping between nanographene sheets, i.e. electron localization. The discontinuous line broadening and the signal intensity drop at around 20 K reported in the previous X-band ESR at 1 μW were not observed, probably because of either higher microwave power than 1 μW or some amount of oxygen adsorption in our sample in the present study.

We have fabricated parallel-coupled quantum dots on single-layer graphene. The tunnel coupling between the quantum dots can be tuned by a graphene in-plane gate. Owing to the tunnel coupling, the Coulomb blockade oscillation peaks exhibit periodic shifts as the number of electron in the non-conducting side-coupled QD is changed. The result suggests the observation of the single electron switching effect, which is a prerequisite for a single photon detection scheme using parallel-coupled quantum dots.

The electronic structure of periodic lattice under uniform magnetic field was studied numerically for multi-band tight-binding models with non-orthogonal basis sets. When magnetic translational symmetry is fully taken into account, computational time can be greatly reduced. Quantized Hall conductance was evaluated by robust multi-band formulation of Chern number. We found that calculated quantized Hall conductance coincides with the semi-classical results. Discontinuous jumps of Hall conductance occur at van-Hove singularities and correspond to mod q ambiguity of the Diophantine equation of Chern number.

While usual edge states in the quantum Hall effect (QHE) reside between adjacent Landau levels, QHE in graphene has a peculiar edge mode at E = 0 that resides right within the n = 0 Landau level as protected by the chiral symmetry. In real graphene, disorder always exists, and here we study how the edge states appear in disordered graphene QHE. We have to discriminate bond disorder and potential disorder, since the former respects the chiral symmetry in the bipartite lattice while the latter does not. We have found that, for a bond disorder, the charge accumulation along zigzag edges persists to occur, while a potential disorder destroys them. The charge accumulation along zigzag edges should be measured with an STM imaging in magnetic fields.

The quantum Hall effect in graphene is regarded to be involving half-integer topological numbers associated with the massless Dirac particle, this is usually not apparent due to the doubling of the Dirac cones. Here we theoretically consider two classes of lattice models in which we manipulate the Dirac cones with either (a) two Dirac points that have mutually different energies, or (b) multiple Dirac cones having different Fermi velocities. We have shown, with an explicit calculation of the topological (Chern) number for case (a) and with an adiabatic argument for case (b) that the results are consistent with the picture that a single Dirac fermion contributes the half-odd integer series (... -3/2, -1/2, 1/2, 3/2, ...) to the Hall conductivity when the Fermi energy traverses the Landau levels.

Dynamical scaling of the optical Hall conductivity σ_xy(ε_F, ω) at the n = 0 Landau level in graphene is analyzed for the 2D effective Dirac fermion and honeycomb lattice models with various types of disorder. In the Dirac fermion model with potential disorder, σ_xy(ε_F, ω) obeys a well-defined dynamical scaling, characterized by the localization exponent ν and the dynamical critical exponent z. In sharp distinction, scaling behavior of σ_xy(ε_F, ω) in the honeycomb lattice model with bond disorder (preserving chiral symmetry), becomes anomalous.

We report our recent study of cyclotron resonance in graphene, with focus on the many-body effect on the resonance energies. The genuine many-body corrections turn out to derive from vacuum polarization, specific to graphene, which diverges at short wavelengths and which requires renormalization of velocity and, for bilayer graphene, interlayer coupling as well. As a result, the renormalized velocity and interlayer coupling strength run with the magnetic field, and many-body corrections are uniquely determined from one resonance to another. Theory is compared with the experimental data for both monolayer and bilayer graphene.

We study the tight-binding model on the generalized honeycomb lattice, where nearest-neighbor and next-nearest-neighbor transfer integrals and the on-site potentials are taken as parameters. We obtain the condition for the untilted Dirac cone. We discuss the effects of the uniaxial strain on the opening of the gap and the tilting of the Dirac cone.

We have employed large scale exact numerical diagonalization in Haldane spherical geometry in a comparative analysis of the correlated many-electron states in the half-filled low Landau levels of graphene and such conventional semiconductors as GaAs, including both spin and valley (i.e., pseudospin) degrees of freedom. We present evidence that the polarized Fermi sea of essentially non-interacting composite fermions remains stable against a pairing transition in both lowest Landau levels of graphene. However, it undergoes spontaneous depolarization, which in (ideal) graphene is unprotected for the lack of a single-particle pseudospin splitting. These results point to the absence of the non-Abelian Pfaffian phase in graphene.

Magnetotransport has been considered in multilayer massless Dirac fermion systems, in which two-dimensional (2D) layers with a pair of Dirac-cone dispersion stack with weak interlayer coupling. The Fermi level is assumed to be fixed at the Dirac point resulting in the zero-gap conductor. At the high-field quantum limit, where only the n = 0 Landau level at the Dirac point is partially occupied, all elements of conductivity tensor have been evaluated by the lowest order contribution of interlayer coupling. We have deduced saturation of in-plane resistance, local maxima of in-plane Hall resistance, negative interlayer magnetoresistance, and cotθ-type unusual angle-dependence of interlayer Hall resistance. These results propose good explanations for mysterious transport features observed in organic zero-gap conductors, α-(BEDT-TTF)₂I₃ and its related compounds.

We have investigated polarisation resolved magneto-photoluminescence from 22 nm wide asymmetric GaAs quantum well. In contrast to previous studies we observed abrupt decrease of photoluminescence intensity of the neutral exciton line with increasing temperatures whereas photoluminescence intensity of the positively charged exciton remains unchanged. The effect is a clear evidence of different mechanisms of neutral and charged exciton recombination. We have also detected a coupling of two different radiative states: an acceptor-bound and an essentially free trions.

The Ajiki-Ando (A-A) splitting of single-walled carbon nanotubes was observed by the magneto-absorption measurements conducted up to a very high magnetic field, 78 T for PFO-samples. The well-resolved absorption spectra from the E₁₁ transitions in the PFO-samples showed a clear A-A splitting. The electro-magnetic flux compression method was used for generation of the field up to 360 T, where the absorption spectra of the E₂₂ transition of the HiPco samples were measured by the streak spectroscopy. Parameters for the A-A splitting were determined for different chiralty of each case.

Singlet excitonic states at the first subband-edge in single-walled carbon nanotubes (SWCNTs) have been studied through near-infrared magneto-absorption spectroscopy under magnetic fields to 105.9 T. Well-resolved absorption spectra of stretch-aligned SWCNT(CoMoCAT)-gelatin films were obtained above 100 T. By the application of magnetic fields in parallel to the alignment of SWCNTs, peak shift toward the lower energy was observed for (8, 4) and (7, 6) tubes and the opposite behavior was observed for (7, 5) and (6, 5) tubes. Above 28.8 T, new peaks emerged at the higher energy side of the peak for the (8, 4) and (7, 6) tubes, and at the lower energy side of the peaks for the (7, 5) and (6, 5) tubes. The magnetic splitting between the existing peak and the new peak was symmetric for every tube, which is in line with the energy splitting due to the Aharonov-Bohm effect. Judging from the energetic positions where the new peaks emerged, the singlet dark excitonic state locates at the lower energy than the singlet bright one in the (7, 5) and (6, 5) tubes while it is suggested strongly that the bright one locates at the lower energy in the (8, 4) and (7, 6) tubes.

CdS/ZnSe multiple quantum wells (MQWs) shows very strong photoluminescence at low temperatures. The strong photoluminescence (PL) arises from the interface localization of the type-II excitons. A systematic study was attempted on the exciton density dependence of magneto-PL behavior up to 53 T by using a pulse magnet. We obtained a strong excitation density dependence of the type-II exciton Bohr radius trapped in interface roughness potentials.

We have detected a cyclotron resonance signal of the electrons induced by an external photoexcitation in an undoped ZnSe/BeTe type-II quantum well. The experimental spectra have also been well reproduced by the dielectric function (Drude) model. The photo-induced electron density is estimated at 1 × 10¹² cm⁻².

We have studied propagating spin-flip waves excited in a two dimensional electron gas by angle resolved magneto-Raman spectroscopy. The damping rate of these excitations follows a quadratic law, as a function of q, and the group velocity is linearly dependent with q. Consequently the propagation length presents a maximum for a given q. We have estimated and analyzed the maximum propagation length showing that the spin waves are drastically attenuated in a microscopic distance, even in the intrinsic regime.

We report cyclotron resonance measurements on ferromagnetic InMnAs and InMnSb films at high magnetic fields in the megagauss range (B > 100 T). The cyclotron resonance transitions between the Landau levels with small indices (N = 0, 1, 2,..) are clearly observed. The effective masses deduced from the resonance fields at 117 meV are 0.037m₀ and 0.051m₀ in InMnAs and InMnSb, respectively. They are considerably smaller than the classical band edge effective masses of heavy holes in the host semiconductors (0.35m₀ in InAs and 0.32m₀ in InSb) due to the quantum effect in high-magnetic fields. The Landau levels calculated by the 8-band model, semi-quantitatively can explain the cyclotron resonance positions, indicating the itinerant holes in InMnAs and InMnSb are p-like holes in the valence band of the host semiconductors.

We have performed cyclotron resonance measurements on two-dimensional electrons near the metal-insulator transition. Both the cyclotron scattering time τ_CR and the transport scattering time τ_t decrease with the electron density. The values of τ_t/τ_CR are close to unity, indicating that the scattering mechanism does not depend on scattering angle in the metallic phase. Short-range potential fluctuations seem to play an important role in the appearance of the metallic behavior.

We have developed high-field ESR system using commercially available SQUID magnetometer equipped with the superconducting magnet up to 5 T. This is a longitudinal magnetization detection type ESR. The minimum detectable spin number is evaluated as 2×10¹³ spins/G for 105 GHz. The most advantageous points as compared with other high-field ESR are that high-field ESR can be done very easily and both microscopic and macroscopic magnetic properties can be obtained at once. Moreover, the transmission technique without using cavity enables us to make multi-frequency ESR measurement in the wide frequency region. We have succeeded in observing ESR from 70 to 315 GHz.

It is shown that a population inversion can be achieved in the system of Landau levels in cascade quantum well structures in a magnetic field under a condition of sequential resonant tunneling. This mechanism allows a wide range tuning of the emitted terahertz frequency by the magnetic field strength variation.

We propose an all optical way to measure the recently proposed "photovoltaic Hall effect", i.e., a Hall effect induced by a circularly polarized light in the absence of static magnetic fields. This is done in a pump-probe experiment with the Faraday rotation angle being the probe. The Floquet extended Kubo formula for photo-induced optical response is formulated and the ac-Hall conductivity is calculated. We also point out the possibility of observing the effect in two layered graphene, three-dimensional graphite, and more generally in multi-band systems such as materials described by the dp-model.

We observed an anti-crossing behavior for the magnetic field dependence of the cyclotron resonance in a InGaAs/InAlAs two-dimensional Rashba system. Two resonances can be observed at a narrow millimeter frequency region, and this is due to the resonant coupling between different two spin levels because of the large zero-field spin splitting by the Rashba effect. The electron effective mass is obtained as m* = 0.04m₀, which is in good agreement with the previous result at a terahertz region.

Spin transport affected by competition between Zeeman effect and spin-orbit interaction (SOI) is investigated in order to check a proposed method to deduce the Rashba SOI α and Dresselhaus SOI β ratio. The experimentally obtained ratio α/β of the present sample is about 4 from angle dependence of magnetoconductance under in-plane magnetic field. The proposed method to detect the ratio by transport measurement is promising although further improvement of sample fabrication and measurement is required.

High-field magneto-resistance (MR) properties including Shubnikov de-Haas (SdH) oscillation and integer quantum Hall effect are observed and analyzed in high In-content InGaAs/InAlAs two-dimensional electron gas (2DEG) with strong Rashba effect. From the results, conventional longitudinal resistance oscillations with Zeeman splittng as well as quantum Hall plateaus are confirmed and a transition from zero-field spin-splitting to high-field Zeeman splitting is discussed. The two-kind spin splittings are seem to be connected via the sign changing process at finite (~3 Tesla) magnetic field, the value of which is about two times larger than that in high In-content InGaSb/InAlSb system.

We investigate theoretically magnetic properties of tunable lateral double quantum dots (DQDs) containing few electrons, subjected to spin-orbit interaction (SOI) and vertical magnetic field, using exact diagonalization (ED) method. To circumvent the cumbersome construction of matrix elements of the Hamiltonian, we adopt the modified Gaussian functions to describe atomic-like orbital states of single quantum dots. The numerical artifacts in the single-electron energy spectrum are avoided by separating the full Hilbert space into two sub-spaces. The interplay of SOI and interdot tunnel coupling leads to an oscillatory behaviour in the magnetization at low temperature. Sweeping interdot barrier voltage and adjusting interdot distance produce not only magnetic phase transition but also switches between atomic and molecular orbitals.

The dynamical Green's function and energy spectrum of a 2D symmetric quantum double-dot system on a planar host in a normal magnetic field are analyzed here, representing the two dots by Dirac delta function potentials. The proliferation of energy levels due to Landau quantization is examined in detail.

In this study, we present the spatial distributions of the edge channels for each layer in bilayer quantum Hall bar geometry for a wide range of applied magnetic fields. For this purpose, we employ a self-consistent Thomas-Fermi-Poisson approach to obtain the electron density distributions and related screened potential distributions. In order to have a more realistic description of the system we solve three dimensional Poisson equation numerically in each iteration step to obtain self consistency in the Thomas-Fermi-Poisson approach instead of employing a 'frozen gate' approximation.