Influence of excited Landau levels on a two-dimensional electron-hole system in a strong perpendicular magnetic field

The study of the quantum states of a two-dimensional electron-hole system in a strong perpendicular magnetic field is carried out with special attention to the influence of virtual quantum transitions of interacting particles between the Landau levels. These virtual quantum transitions from the lowest Landau levels to excited Landau levels with arbitrary quantum numbers n and m and their reversion to the lowest Landau levels in second order perturbation theory result in an indirect attraction between the particles. The influence of the indirect interaction on the magnetoexciton ground state, on the chemical potential of the Bose-Einstein condensed magnetoexcitons, and on the ground state energy of the metallic-type electron-hole liquid is investigated in the Hartree-Fock approximation. The coexistence of different phases is suggested.     

Electronic properties of a Penrose tiling lattice in a magnetic field

The one-electron energy spectrum of a two-dimensional Penrose tiling lattice in a uniform magnetic field is calculated as a function of magnetic fields with a tight-binding Hamiltonian. The calculated results show the following remarkable features characteristic of the Penrose lattice. (1) The density of states in a magnetic field has a central peak with zero width at the zero energy. It is shown that the zero-energy states correspond to the ring states in which the wavefunction has a non-vanishing amplitudes only at the sites on a ring-like region around the origin. (2) The energy levels coalesce into Landau type levels and the boundary states due to the finite size effects based on a fixed boundary condition appear in the gap region between Landau levels. (3) The magnetic field dependence of the energy spectrum has a repeated pattern of self-similarity with the golden mean ratio of two successive periods.     

Quantum Hall effect in twisted bilayer graphene

We address the quantum Hall behavior in twisted bilayer graphene transferred from the C face of SiC. The measured Hall conductivity exhibits the same plateau values as for a commensurate Bernal bilayer. This implies that the eightfold degeneracy of the zero energy mode is topologically protected despite rotational disorder as recently predicted. In addition, an anomaly appears. The densities at which these plateaus occur show a magnetic field dependent offset. It suggests the existence of a pool of localized states at low energy, which do not count towards the degeneracy of the lowest band Landau levels. These states originate from an inhomogeneous spatial variation of the interlayer coupling.     

外场调控下硼磷烯量子点的电子结构和光学性质研究

采用紧束缚近似方法对锯齿状六边形硼磷烯量子点在平面电场和垂直磁场调控下的电子结构和光学性质进行了研究. 研究表明,硼磷烯量子点作为直接带隙半导体,在无外加电场和磁场作用时,能隙不随尺寸的改变而变化. 在平面电场调控下,能隙随电场强度的增加逐渐减小直至消失,平面电场方向几乎不会对硼磷烯量子点体系产生影响, 且随量子点尺寸的增大,能隙消失所需电场强度逐渐减小. 在垂直磁场调控下,表现为体态的能级在磁场作用下形成朗道能级,而能隙边缘处的朗道能级近似为一个平带,不随磁通量的改变而变化,态密度主要分布于朗道能级处. 另外,垂直磁场作用下的光吸收主要是由朗道能级之间的跃迁引起的.     

Strong effect of resonant impurities on Landau-level quantization

We investigate experimentally the effect of a random distribution of nitrogen (N) impurities on the Landau-level spectrum of a GaAs quantum well. Our magnetotunneling study reveals complex and nonequally spaced Landau levels and a quenching of the Landau states at a well-defined bias and electron energy which is resonant with that of the N atoms. Analysis of the magnetic field dependence of the tunnel current into the Landau levels of the well also provides quantitative information about the nonresonant component of the N-related scattering potential.     

Unexpected features in the magnetoresistance of a quantum well at room temperature

Well-resolved oscillations are reported in the resistivity of an InGaAs quantum well as a function of applied magnetic field below 1 Tesla. The oscillations are observed at room temperature and their magnetic field position depends on the component of the magnetic field in the plane of the well. Because of these unusual properties, the results cannot be due to bound states within the well but it is suggested that they can be explained by quantised states lying above the well in energy. The condition for the formation of the states is satisfied at lower magnetic fields than for normal Landau levels and the states are separated by larger energy intervals.     

Density of states of random Schrödinger operators with a uniform magnetic field

We consider the density of states of Schrödinger operators with a uniform magnetic field and a random potential with a Gaussian distribution. We show that the restriction to the states of the first Landau level is equivalent to a scaling limit where one looks at the density of states near to the energy of the first Landau level and simultaneously lets the strength of the coupling to the random potential go to zero. We also consider a different limit where we look at the suitably normalised density of states near to the energy of the first Landau level when the intensity of the magnetic field goes to infinity.     

Impurity states of electrons in quantum dots in external magnetic fields

The influence of isolated impurity atoms on the electron energy spectrum in a parabolic quantum dot in quantizing magnetic field is studied. The impurity potential is approximated by a Gaussian separable operator which allows one to obtain the exact solution of the problem. We demonstrate that in the electron energy spectrum there is a set of local levels which are split from the Landau zone boundaries in the upward or downward direction depending on the impurity type. We have calculated the local level positions, the wave functions of electrons in bound states, and the residues of the electron scattering amplitudes by impurity atoms at the poles.     

Homogeneous-inhomogeneous transitions in a Landau level with spin splitting

The homogeneous-inhomogeneous transitions of a two-dimensional electron gas in a strong perpendicular magnetic field are studied in the particular case when half of the states in a spin splitted Landau level are occupied. To this end the dielectric susceptibility in the homogeneous states as well as the free energy in the modulated states are calculated. Unless theg factor dos not exceed a certain value the charge-density waves are stable in an interval of finite temperatures.     

Novel optical probe for quantum Hall system

Surface photovoltage (SPV) spectroscopy has been used for the first time to explore Landau levels of a two-dimensional electron gas (2DEG) in modulation doped InP/InGaAs/InP QW in the quantum Hall regime. The technique gives spectroscopically distinct signals from the bulk Landau levels and the edge states. Evolution of the bulk Landau levels and the edge electronic states is investigated at 2.0 K for magnetic field up to 8 T using SPV spectroscopy.     

Relativistic Landau quantization in the spiral dislocation spacetime

We analyse the interaction of a relativistic electron with a uniform magnetic field in the spiral dislocation spacetime.We show that analytical solutions to the Dirac equation can be obtained,where the spectrum of energy corresponds to the relativistic Landau levels.We also analyse the influence of the spiral dislocation on the relativistic Landau levels by showing that there exists an analogue of the Aharonov–Bohm effect for bound states.     

Bound and continuum states of a vortex line in a pure type-II superconductor

The Bogoliubov equations for the quasi-particle excitations of an isolated vortex line in a pure type-II superconductor are solved by means of a method due to Bardeenet al. The low lying energy levels of the bound states are found to have the form of Landau levels where the effective field is determined by the pair potential and the magnetic field in the core region of the vortex. From the solutions of the continuum states of high energy simple expressions for the phase shifts are derived. The contributions of the continuum states to the pair potential and the current density are calculated. The pair potential is shown to tend to the BCS gap parameter, and thus to be serf-consistent, at large distances from the vortex axis.     

Forward scattering approximation and bosonization in integer quantum Hall systems

In this work, we present a model and a method to study integer quantum Hall (IQH) systems. Making use of the Landau levels structure we divide these two-dimensional systems into a set of interacting one-dimensional gases, one for each guiding center. We show that the so-called strong field approximation, used by Kallin and Halperin and by MacDonald, is equivalent, in first order, to a forward scattering approximation and analyze the IQH systems within this approximation. Using an appropriate variation of the Landau level bosonization method we obtain the dispersion relations for the collective excitations and the single-particle spectral functions. For the bulk states, these results evidence a behavior typical of non-normal strongly correlated systems, including the spin-charge splitting of the single-particle spectral function. We discuss the origin of this behavior in the light of the Tomonaga-Luttinger model and the bosonization of two-dimensional electron gases.     

Bound states of Dirac electrons in a graphene-based magnetic quantum dot

We investigate the magnetically confined states of the massless Dirac fermions in a graphene quantum dot formed by the inhomogeneous distributions of the magnetic fields inside and outside the dot. The calculated energy spectrum exhibits quite different features with and without the magnetic field inside the dot. It is found that the degeneracy of the relativistic Landau level with negative angular momenta can be lifted, and this degeneracy breaking can be modulated by the magnetic field inside the dot. Moreover, such a system can form the strongly localized states within the dot and along its boundary, especially with the magnetic field inside the dot.     

Electron on a cylinder with topological defects in a homogeneous magnetic field

In this work we study the effects of the geometry and topology of a cylinder on the energy levels of an electron moving in a homogeneous magnetic field. We consider the existence of topological defects as a screw dislocation and a disclination. When we take the region of movement as the full cylindrical surface, we find that, by increasing the strength of the screw dislocation, the dispersion on the electronic energy levels is affected and monotonically increasing. For an electron moving in an almost flat region we show that the dispersion on the Landau levels decrease monotonically as we increase the strength of the screw dislocation. The lowest Landau level can reach a zero value, leaving the energy of the system solely given by the geometry of the cylinder, which does not depend on the magnetic field. In both situations, as we change the deficit angle of the disclination, we observe that the energy levels are shifted and the magnitude of such shift depends on the magnetic field. The Landau levels for a flat sample are recovered in the limit of an infinite cylinder radius.     

Effect of a transverse electric field on the Landau bands in a Weyl semimetal

The Landau bands in crossed magnetic and electric fields are studied for the case of a Weyl semimetal. The expression for the energy spectrum of such a system is obtained using an approach based on the Lorentz shift. It is shown that the electric field leads to a substantial transformation of the Landau bands. At the electric field equal to v_F H/c, the collapse of the Landau levels occurs and the motion becomes completely linear. Under this condition, the wavefunction is nonzero only for the states with p _z = 0. This significantly affects the phenomena related to the unusual surface states, which are characteristic of such materials.     

Fisher Information of Free-Electron Landau States

An electron in a constant magnetic field has energy levels, known as the Landau levels. One can obtain the corresponding radial wavefunction of free-electron Landau states in cylindrical polar coordinates. However, this system has not been explored so far in terms of an information-theoretical viewpoint. Here, we focus on Fisher information associated with these Landau states specified by the two quantum numbers. Fisher information provides a useful measure of the electronic structure in quantum systems, such as hydrogen-like atoms and under some potentials. By numerically evaluating the generalized Laguerre polynomials in the radial densities, we report that Fisher information increases linearly with the principal quantum number that specifies energy levels, but decreases monotonically with the azimuthal quantum number m. We also present relative Fisher information of the Landau states against the reference density with m=0, which is proportional to the principal quantum number. We compare it with the case when the lowest Landau level state is set as the reference.     

Lifshitz-like argument for low-lying states in a strong magnetic field

Localization of an electron moving in two dimensions, submitted to a strong magnetic field and scattered by randomly distributed zero-range impurities is investigated. Considering the explicit expression for the density of states obtained by Brézin, Gross and Itzykson, the Lifshitz argument is adapted in order to analyze the unusual power-law behavior of the low energy spectrum. When the impurity density is smaller than the Landau degeneracy, typical configurations of disorder responsible for low energy states are identified as cluster of impurities of well defined form. This allows for an interpretation of low-lying states, localized around these clusters, whose size diverges logarithmically as the energy goes to zero. Received 5 January 2000     

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.     

Localization and the integer-quantized Hall effect: Diffusion constant for high Landau levels and white noise potential

The diffusion constant and the diagonal conductivity for non-interacting electrons in a two-dimensional, disordered system are studied. A homogeneous magnetic field perpendicular to the electron system is assumed. For weak short-range random potentials and high fields the Landau quantum numbern can be used as expansion parameter. In the limit of high Landau levels the system shows metallic behaviour. Corrections for finiten decrease the conductivity and indicate localized states in the whole energy band. A breakdown of the expansion and stronger localization are observed only for the lowest Landau levels if the typical experimental length scale of the quantized Hall effect is used.