Microscopic calculation of the magnetic field of neutron stars

Based on the Dirac equation describing an electron moving in a uniform and cylindrically symmetric magnetic field which may be the result of the self-consistent mean field of the electrons themselves in a neutron star, we have obtained the eigen solutions and the orbital magnetic moments of electrons in which each eigen orbital can be calculated. From the eigen energy spectrum we find that the lowest energy level is the highly degenerate orbitals with the quantum numbers pZ=0, n=0, and m≥0. At the ground state, the electrons fill the lowest eigen states to form many Landau magnetic cells and each cell is a circular disk with the radius λfree and the thickness λe, where λfree is the electron mean free path determined by Coulomb cross section and electron density and λe is the electron Compton wavelength. The magnetic moment of each cell and the number of cells in the neutron star are calculated, from which the total magnetic moment and magnetic field of the neutron star can be calculated. The results are compared with the observational data and the agreement is reasonable.     

Quantum Hall states near the charge-neutral Dirac point in graphene

We investigate the quantum Hall (QH) states near the charge-neutral Dirac point of a high mobility graphene sample in high magnetic fields. We find that the QH states at filling factors nu=+/-1 depend only on the perpendicular component of the field with respect to the graphene plane, indicating that they are not spin related. A nonlinear magnetic field dependence of the activation energy gap at filling factor nu=1 suggests a many-body origin. We therefore propose that the nu=0 and +/-1 states arise from the lifting of the spin and sublattice degeneracy of the n=0 Landau level, respectively.     

Quenching of the quantum Hall effect in multilayered epitaxial graphene: the role of undoped planes

We propose a mechanism for the quenching of the Shubnikov-de Haas oscillations and the quantum Hall effect observed in epitaxial graphene. Experimental data show that the scattering time of the conduction electron is magnetic field dependent and of the order of the cyclotron orbit period, i.e., it can be much smaller than the zero field scattering time. Our scenario involves the extraordinary graphene n=0 Landau level of the uncharged layers which is pinned at the Fermi level. We find that the coupling between this n=0 Landau level and the conducting states of the doped plane leads to a scattering mechanism having the right magnitude to explain the experimental data.     

Landau-level splitting in graphene in high magnetic fields

The quantum Hall (QH) effect in two-dimensional electrons and holes in high quality graphene samples is studied in strong magnetic fields up to 45 T. QH plateaus at filling factors nu = 0, +/-1, +/-4 are discovered at magnetic fields B > 20 T, indicating the lifting of the fourfold degeneracy of the previously observed QH states at nu = +/-4(absolute value(n) + 1/2), where n is the Landau-level index. In particular, the presence of the nu = 0, +/-1 QH plateaus indicates that the Landau level at the charge neutral Dirac point splits into four sublevels, lifting sublattice and spin degeneracy. The QH effect at nu = +/-4 is investigated in a tilted magnetic field and can be attributed to lifting of the spin degeneracy of the n = 1 Landau level.     

Fractional quantum Hall effect at high fillings in a two-subband electron system

Magnetotransport measurements in a clean two-dimensional electron system confined to a wide GaAs quantum well reveal that, when the electrons occupy two electric subbands, the sequences of fractional quantum Hall states observed at high fillings (ν>2) are distinctly different from those of a single-subband system. Notably, when the Fermi energy lies in the ground state Landau level of either of the subbands, no quantum Hall states are seen at the even-denominator ν=5/2 and 7/2 fillings; instead, the observed states are at ν=[i+p/(2p±1)], where i=2, 3, 4 and p=1, 2, 3, and include several new states at ν=13/5, 17/5, 18/5, 25/7, and 14/3.     

Observation of collapse of pseudospin order in bilayer quantum Hall ferromagnets

The Hartree-Fock paradigm of bilayer quantum Hall states with finite tunneling at filling factor nu=1 has full pseudospin ferromagnetic order with all the electrons in the lowest symmetric Landau level. Inelastic light scattering measurements of low energy spin excitations reveal major departures from the paradigm at relatively large tunneling gaps. The results indicate the emergence of a novel correlated quantum Hall state at nu=1 characterized by reduced pseudospin order. Marked anomalies occur in spin excitations when pseudospin polarization collapses by application of in-plane magnetic fields.     

Evidence for skyrmion crystallization from NMR relaxation experiments

A resistively detected NMR technique was used to probe the two-dimensional electron gas in a GaAs/AlGaAs quantum well. The spin-lattice relaxation rate (1/T(1)) was extracted at near complete filling of the first Landau level by electrons. The nuclear spin of (75)As is found to relax much more efficiently with T --> 0 and when a well developed quantum Hall state with R(xx) approximately 0 occurs. The data show a remarkable correlation between the nuclear spin relaxation and localization. This suggests that the magnetic ground state near complete filling of the first Landau level may contain a lattice of topological spin texture, i.e., a Skyrmion crystal.     

Lattice relaxation of graphene under high magnetic field

We investigate the n = 0 Landau level (LL) in monolayer graphene with high magnetic field. We find that the energy gap is opened in the n = 0 LL by the magnetic-field-dependent lattice relaxation originating from the interactions between the electrons (holes) and longitudinal-deformation-acoustic phonon. Both the linear and square-foot dependence of the energy gap on the magnetic field are obtained depending on the choice of the Debye cut-off wave number for the acoustic phonon. The relations of the Huang-Rhys parameter (lattice relaxation strength) and the transition linewidths with the magnetic field are also discussed. Our results agree with the current experiments on graphene in high magnetic field, and provide an alternative explanation for the experimental measurements.     

Nonconventional odd-denominator fractional quantum Hall states in the second Landau level

We report the observation of a new fractional quantum Hall state in the second Landau level of a two-dimensional electron gas at the Landau level filling factor ν=2+6/13. We find that the model of noninteracting composite fermions can explain the magnitude of gaps of the prominent 2+1/3 and 2+2/3 states. The same model fails, however, to account for the gaps of the 2+2/5 and the newly observed 2+6/13 states suggesting that these two states are of exotic origin.     

Unconventional integer quantum Hall effect in graphene

Monolayer graphite films, or graphene, have quasiparticle excitations that can be described by (2+1)-dimensional Dirac theory. We demonstrate that this produces an unconventional form of the quantized Hall conductivity sigma(xy) = -(2e2/h)(2n+1) with n = 0, 1, ..., which notably distinguishes graphene from other materials where the integer quantum Hall effect was observed. This unconventional quantization is caused by the quantum anomaly of the n=0 Landau level and was discovered in recent experiments on ultrathin graphite films.     

NaBn(n=1—9)团簇的几何结构和电子性质

应用密度泛函理论(DFT)中B3LYP方法在6-311+G(d)水平上计算并分析了 NaB_n(n=1—9)团簇的几何结构及电子性质. 同时, 讨论了团簇的平均结合能、能级间隙、二阶能量差分和极化率.研究表明:NaB_n(n=1—9) 团簇基态绝大多数为平面构型. 能级间隙和二阶能量差分结果表明NaB₃与NaB₅是幻数团簇. 另外, 对平均线性极化率和极化率的各向异性不变量研究表明基态NaB_n团簇的电子结构随B原子的增加虽然趋于紧凑, 但尚未形成特定的堆积方式.     

The Hubbard model extended by nearest‐neighbor Coulomb and exchange interaction on a cubic cluster – rigorous and exact results

The Hubbard model on a cube was revisited and extended by both nearest‐neighbor Coulomb correlation W and nearest‐neighbor Heisenberg exchange J. The complete eigensystem was computed exactly for all electron occupancies and all model parameters ranging from minus infinity to plus infinity. For two electrons on the cluster the eigensystem is given in analytical form. For six electrons and infinite on‐site correlation U we determinded the groundstate and the groundstate energy of the pure Hubbard model analytically. For fixed electron numbers we found a multitude of ground state level crossings depending on the various model parameters. Furthermore the groundstates of the pure Hubbard model in dependence on a magnetic field h coupled to the spins are shown for the complete U‐h plane. The critical magnetic field, where the zero spin groundstate breaks down is given for four and six electrons. Suprisingly we found parameter regions, where the ground state spin does not depend monotonously on J in the extended model. For the cubic cluster gas, i.e. an ensemble of clusters coupled to an electron bath, we calculated the density n (μ, T, h) and the thermodynamical density of states from the grand potential. The ground states and the various spin‐spin correlation functions are studied for both attractive and repulsive values of the three interaction constants. We determined the various anomalous degeneration lines, where n (μ, T = 0, h = 0) shows steps higher than one, since in this parameter regions exotic phenomena as phase separation are to expect in extended models. For the cases where these lines end in triple points, i.e. groundstates of three different occupation numbers are degenerated, we give the related parameter values. Regarding the influence of the nn‐exchange and the nn‐Coulomb correlation onto the anomalous degeneration we find both lifting and inducing of degeneracies depending on the parameter values.     

Li2Bn(n=1—10)团簇的几何结构和电子性质

应用密度泛函理论(DFT)B3LYP方法在6-311+G(d)水平上计算并分析了Li2Bn(n=1-10)团簇的几何结构及电子性质.同时,讨论了团簇的平均结合能、能级间隙、二阶能量差分和极化率.研究表明: Li2Bn(n=1-10)团簇基态大多为立体构型. 能级间隙和二阶能量差分结果表明Li2B8是幻数团簇.对平均线性极化率和极化率的各向异性不变量研究表明,基态Li2Bn团簇的电子结构随B原子的增加虽然趋于紧凑,但尚未形成特定的堆积方式.     

Planar Dirac electrons in magnetic quantum dots

In this paper, we explore the size- and mass-dependent energy spectra and the electronic correlation of two- and three-electron graphene magnetic quantum dots. It is found that only the magnetic dots with large size can well confine the electrons. For large graphene magnetic dots with massless (ultra-relativity) electrons, the energy level structures of two Dirac electrons and even the ground state spin and angular momentum of three electrons are quite different from those of the usual semiconductor quantum dots. Also we reveal that such differences are not due to the magnetic confinement but originate from the character of the Coulomb interaction of two-component electronic wavefunctions in graphene. We reveal that the increase of the mass leads to both the crossover of the energy spectrum structures from the ultra-relativity to non-relativity ones and the increasing of the crystallization. The results are helpful for the understanding of the mass and size effects and may be useful in controlling the few-electron states in graphene-based nanodevices.     

Transport through graphene on SrTiO3

We report transport measurements through graphene on SrTiO(3) substrates as a function of magnetic field B, carrier density n, and temperature T. The large dielectric constant of SrTiO(3) very effectively screens long-range electron-electron interactions and potential fluctuations, making Dirac electrons in graphene virtually noninteracting. The absence of interactions results in an unexpected behavior of the longitudinal resistance in the N=0 Landau level and in a large suppression of the transport gap in nanoribbons. The "bulk" transport properties of graphene at B=0 T, on the contrary, are completely unaffected by the substrate dielectric constant.     

Edge physics of graphene in the quantum Hall regime

We study the electronic edge states of graphene in the quantum Hall regime. For non-interacting electrons, graphene supports both electron-like and hole-like edge states. We find there are half as many edge states of each type in the lowest Landau level compared to higher Landau levels, leading to a quantization of the Hall conductance that is shifted relative to standard two dimensional electron gases. We also consider the effect of quantum Hall ferromagnetism on this edge structure, and find an unusual Luttinger liquid at the edge in undoped graphene. This arises due to a domain wall that forms near the edge between partially spin-polarized and valley-polarized regions. The domain wall has a U(1) degree of freedom which generates both collective and charged gapless excitations, whose consequences for tunneling experiments are discussed.     

Tunable electron interactions and fractional quantum Hall States in graphene

The recent discovery of fractional quantum Hall (FQH) states in graphene raises the question of whether the physics of graphene offers any advantages over GaAs-based materials in exploring strongly correlated states of two-dimensional electrons. Here we propose a method to continuously tune the effective electron interactions in graphene and its bilayer by the dielectric environment of the sample. Using this method, the charge gaps of prominent FQH states, including ν=1/3 or ν=5/2 states, can be increased several times, or reduced to zero. The tunability of the interactions can be used to realize and stabilize various strongly correlated phases and explore the transitions between them.     

Spontaneously gapped ground state in suspended bilayer graphene

Bilayer graphene bears an eightfold degeneracy due to spin, valley, and layer symmetry, allowing for a wealth of broken symmetry states induced by magnetic or electric fields, by strain, or even spontaneously by interaction. We study the electrical transport in clean current annealed suspended bilayer graphene. We find two kinds of devices. In bilayers of type B1 the eightfold zero-energy Landau level is partially lifted above a threshold field revealing an insulating ν=0 quantum-Hall state at the charge neutrality point. In bilayers of type B2 the Landau level lifting is full and a gap appears in the differential conductance even at zero magnetic field, suggesting an insulating spontaneously broken symmetry state. Unlike B1, the minimum conductance in B2 is not exponentially suppressed, but remains finite with a value G is < or approximately equall to e(2)/h even in a large magnetic field. We suggest that this phase of B2 is insulating in the bulk and bound by compressible edge states.     

Local compressibility measurements of correlated states in suspended bilayer graphene

Bilayer graphene has attracted considerable interest due to the important role played by many-body effects, particularly at low energies. Here we report local compressibility measurements of a suspended graphene bilayer. We find that the energy gaps at filling factors ν= ± 4 do not vanish at low fields, but instead merge into an incompressible region near the charge neutrality point at zero electric and magnetic field. These results indicate the existence of a zero-field ordered state and are consistent with the formation of either an anomalous quantum Hall state or a nematic phase with broken rotational symmetry. At higher fields, we measure the intrinsic energy gaps of broken-symmetry states at ν=0, ± 1, and ± 2, and find that they scale linearly with magnetic field, yet another manifestation of the strong Coulomb interactions in bilayer graphene.