STM/STS measurements of two-dimensional electronic states trapped around surface defects in magnetic fields

The local density of states (LDOS) near point defects on a surface of highly oriented pyrolytic graphite (HOPG) was studied at very low temperatures in magnetic fields up to 6 T. We observed localized electronic states over a distance of the magnetic length around the defects in differential tunnel conductance images at the valley energies of the Landau levels (LLs) as well as relatively extended states at the peak ones of LLs. These states appear mainly at energies above the Fermi energy corresponding to the electron LL bands. The data suggest that the quantum Hall state is realized in the quasi two dimensional electron system in HOPG. At the peak energy associated with the n=0 (electron) and -1 (hole) LLs characteristic of the graphite structure, a reduced LDOS around the defects is observed. The spatial distribution is almost field independent, which indicates that it represents the potential shape produced by the defects.     

扫描隧道显微术中的微分谱学及其应用

文章介绍了扫描隧道显微术中微分谱学的原理及其在实验中的诸多应用。微分谱（dI／dV谱）和dI／dV成像可用来研究电子局域态密度在能量和空间的分布，即微分谱固定空间一点，反映电子态密度以能量为变量的分布；而dI／dV图像则反映某给定能量的电子局域态密度以空间为变量的分布，二次微分谱（d^2I／dV^2谱）和二次微分成像可以用来反映分子的非弹性隧穿过程，从而研究分子的振动态。     

Partial ordered homogeneous magnetic moments in the Hubbard-model

In this contribution, we study the behaviour of magnetically disordered electron systems. In a model with localized magnetic fields at the atomic sites, a CPA-like method, which has regard for the vector character of the fields, is used to examine the case where the localized fields, which correspond to atomic magnetic moments, are distributed statistically. In an example for a non-isotropic distribution of the fields, we construct a system state with partial homogeneous order of the localized fields (or moments). The ordering behaviour of the system and the comparison of the new magnetic state with pure magnetic and non-magnetic band states and with the non-magnetic state of (isotropic) stochastic distribution of the localized fields is discussed. With this paper we are able to introduce typical properties of localized models into a band model.Work supported in part by the Deutsche Forschungsgemeinschaft     

Quasiparticle states and quantum interference induced by magnetic impurities on a two-dimensional topological superconductor

We theoretically study the effect of localized magnetic impurities on two-dimensional topological superconductor (TSC). We show that the local density of states (LDOS) can be tuned by the effective exchange field m, the chemical potential μ of TSC, and the distance Δr as well as the relative spin angle α between two impurities. The changes in Δr between two impurities alter the interference and result in significant modifications to the bonding and antibonding states. Furthermore, the bound-state spin LDOS induced by single and double magnetic impurity scattering, the quantum corrals and the quantum mirages are also discussed. Finally, we briefly compare the impurities in TSC with those in topological insulators.     

Local density of states around a magnetic impurity in high- T(c) superconductors based on the t-J model

The local density of states (LDOS) around a magnetic impurity in high- T(c) superconductors is studied using the two-dimensional t-J model with a realistic band structure. The order parameters are determined in a self-consistent way within the Gutzwiller approximation and the Bogoliubov-de Gennes theory. In sharp contrast with the nonmagnetic impurity case, the LDOS near the magnetic impurity shows two resonance peaks reflecting the presence of spin-dependent resonance states. It is also shown that these resonance states are approximately localized around the impurity. The present results have an immediate connection with the scanning tunneling spectroscopy observation of Bi2Sr2Ca(Cu1-xNi[Zn](x))(2)O(8+delta).     

Effects of the spin–orbit coupling on magnetic and superconducting properties in iron-based superconductors

We analyze the magnetic properties through two-orbital Hubbard model with the spin–orbit coupling (SOC) interaction in the iron-based superconductors. With the help of the Ising approximation for the Hund’s coupling between the itinerant electrons and the localized spins, we give a self-consistent account of the various magnetic orders observed in pnictides and the pairing symmetry. We also calculate the local density of states (LDOS) of the vortex state when a magnetic field is applied. The LDOS without SOC shows no resonant peak at the vortex core center in the superconducting state, while it shows an obvious resonant peak when SOC is applied.     

Imaging of Friedel oscillation patterns of two-dimensionally accumulated electrons at epitaxially grown InAs(111) A surfaces

The local density of states (LDOS) at the epitaxially grown InAs surface on a GaAs(111) A substrate were characterized using low-temperature scanning tunneling microscopy. Using dI/dV signal mapping, LDOS standing waves were clearly imaged at point defects and within nanostructures. Measurement of the wavelength as a function of bias voltage showed a nonparabolic dispersion relation for the conduction band. The observed wave features originate from the Friedel oscillations of the two-dimensional electron gas in the semiconductor surface accumulation layer.     

磁场下含结构缺陷多组分超晶格中的局域电子态和电子输运

在有效质量近似理论下，利用转移矩阵和有效垒高方法研究了有限磁场下含结构缺陷的多组分超晶格中局域电子态的性质.在考虑各组分层有效质量的失配时，外加磁场会导致磁耦合效应的出现.磁耦合效应不仅引起局域电子能级的量子化，并且随着朗道指数或磁场强弱的变化，局域能级及其局域程度都会发生显著移动，特别是对高能区域的局域电子态影响更大.此外，还计算了电子输运系数，讨论了含结构缺陷的三组分超晶格中局域电子能级与输运谱透射禁区中的共振透射峰的关系，发现两者之间有着很好的对应关系，为相应的实验研究提供了依据. 关键词： 超晶格 局域电子态 磁场     

Dyadic Green's functions and electromagnetic local density of states

A formal proof to relate the concept of electromagnetic local density of states (LDOS) to the electric and magnetic dyadic Green's functions (DGF) is provided. The expression for LDOS is obtained by relating the electromagnetic energy density at any location in a medium at uniform temperature T to the electric and magnetic DGFs. The appropriate boundary conditions governing the DGFs are obtained and it is seen that the two types of DGFs are electromagnetic duals of each other. With this the concept of LDOS is also extended to material media. The LDOS is split into two terms—one that originates from the energy density in an infinite, homogeneous medium and the other that takes into account scattering from inhomogeneities. The second part can always be defined unambiguously, even in lossy materials. For lossy materials, the first part is finite only if spatial dispersion is taken into account.     

Spatial imaging of two-dimensional electronic states in semiconductor quantum wells

We measure the spatial distribution of the local density of states (LDOS) at cleaved surfaces of InAs/GaSb isolated quantum wells and double quantum wells (DQWs) by low-temperature scanning tunneling spectroscopy. Distinct standing wave patterns of LDOS corresponding to subbands are observed. These LDOS patterns and subband energies agree remarkably well with simple calculations with tip-induced band bending. Furthermore, for the DQWs, coupling of electronic states between the quantum wells is also clearly observed.     

Ab initio electronic structure of the Ge(111)-(2 × 1) surface in the presence of surface vacancy. Application to STM data analysis

We present the results of ab initio modeling of Ge(111)-(2 × 1) surface in the presence of atomic vacancy in surface bilayer. We showed that simple crystal structure defect affects surface electronic structure to the extent comparable with the influence of doping atom. We demonstrated the strong difference of surface LDOS structure above surface defects of different kind. We have proved that spatial oscillations of LDOS exist around individual surface vacancy in the same tunneling bias range as in case of donor doping atom on Ge(111)-(2 × 1) surface.     

Spatial encoding and the single-scan acquisition of high definition MR images in inhomogeneous fields

We have recently proposed a protocol for retrieving multidimensional magnetic resonance spectra and images within a single scan, based on a spatial encoding of the spin interactions. The spatial selectivity of this encoding process also opens up new possibilities for compensating magnetic field inhomogeneities; not by demanding extreme uniformities from the B(0) fields, but by compensating for their effects at an excitation and/or refocusing level. This potential is hereby discussed and demonstrated in connection with the single-scan acquisition of high-definition multidimensional images. It is shown that in combination with time-dependent gradient and radiofrequency manipulations, the new compensation approach can be used to counteract substantial field inhomogenities at either global or local levels over relatively long periods of time. The new compensation scheme could find uses in areas where heterogeneities in magnetic fields present serious obstacles, including rapid studies in regions near tissue/air interfaces. The principles of the B(0) compensation method are reviewed for one- and higher-dimensional cases, and experimentally demonstrated on a series of 1D and 2D single-scan MRI experiments on simple phantoms.     

Particle size effect on magnetotransport properties of nanocrystalline Nd<Subscript>0.7</Subscript>Sr<Subscript>0.3</Subscript>MnO<Subscript>3</Subscript>

Nanocrystalline samples with an average particle size of 40 and 52 nm have been synthesized by citrate-complex auto-ignition method. Magnetic properties of the samples show para- to ferromagnetic transition at around 135 K. The electron magnetic resonance (EMR) study on these samples indicates the presence of coexistence of two magnetic phases below 290 K. Electrical resistivity follows variable range hopping (VRH) mechanism in the paramagnetic regime. The magnetoresistance (MR) data has been analysed by spin dependent hopping between the localized spin clusters together with the phase-separation phenomenon. These clusters are assumed to be formed by distribution of canted spins and defects all over the nanoparticle. In addition, the hopping barrier depends on the magnetic moment orientation of the clusters. The magnetic moments of the clusters are narrowly oriented in ferro- and are randomly oriented in paramagnetic phase. The ferromagnetic phase contributes to the total MR at low applied magnetic fields whereas the paramagnetic phase contributes at relatively high fields in both the samples. The average cluster size in ferromagnetic phase is bigger than that in paramagnetic phase. It is also observed that the cluster size, in ferromagnetic phase, in 52 nm sample is bigger than that in the 40 nm sample. However, the average cluster size in paramagnetic phase is almost same in both the samples.     

Photoemission electron microscopy of neodymium-iron-boron (Nd<Subscript>2</Subscript>Fe<Subscript>14</Subscript>B)

The magnetic domain structure of a neodymium-iron-boron single crystal (Nd₂Fe₁₄B) was investigated in a photoemission electron microscope equipped with an aperture for partial restriction of the electron beam. As a result of the influence of magnetic microfields, electron trajectories are deflected in such a way that some of them are stopped by the aperture in the electron optical path. As a result, the contrast caused by the stray fields of the magnetic domains is significantly enhanced. The distribution of the local magnetic fields at the surface is reconstructed from the image by means of the proposed theory on the contrast mechanism. The size of the stray field close to the sample surface under study was 0.5–0.7 T. PACS 68.37.Xy; 75.50.Bb; 75.70-i; 75.70.Kw     

3D calculation of hysteresis loops,magnetic orientations and reversal processes for exchange-spring bilayers with perpendicular anisotropy

Hysteresis loops and magnetic reversal processes have been determined by a three dimensional (3D) micromagnetic model for exchange-coupled Nd₂Fe₁₄B/α-Fe bilayers and carefully compared with a popular one-dimensional (1D) micromagnetic model. It is found that the calculated hysteresis loops, the critical fields and the magnetic phase diagrams agree well with the results given by the 1D model. However, the calculated nucleation mode is a quasi-curling one where the magnetic moment exhibits a curling in the film plane and varies in the thickness direction, in contrast with the reported quasi-coherent mode. The calculated spatial distribution of the magnetization orientation in the thickness direction at various applied fields signifies a three-step magnetic reversal process, which includes nucleation, growth and displacement of the domain wall as well as the rotation and the reversal of magnetization in the hard phase. The magnetic reversal of the hard phase is much slower than that given by the 1D model, leading to a more slant hysteresis loop near the coercivity point.     

Filling factor dependence of the fractional quantum Hall effect gap

We directly measure the chemical potential jump in the low-temperature limit when the filling factor traverses the nu=1/3 and nu=2/5 fractional gaps in two-dimensional (2D) electron system in GaAs/AlGaAs single heterojunctions. In high magnetic fields B, both gaps are linear functions of B with slopes proportional to the inverse fraction denominator, 1/q. The fractional gaps close partially when the Fermi level lies outside. An empirical analysis indicates that the chemical potential jump for an ideal 2D electron system, in the highest accessible magnetic fields, is proportional to q(-1) B(1/2).     

New applications of the magnetic X-ray circular dichroism method for surface-magnetism investigations in a photoemission electron microscope

It is shown that magnetic X-ray circular dichroism (MXCD) can be exploited in photoemission electron microscopy not only to visualize the domain structure of ferromagnets, but also to perform quantitative measurements of the stray magnetic fields at the domain boundaries. In the general situation, two MXCD images obtained at different extractor voltages are required. In specific cases, however, it suffices to consider a single image, if it is deformed by the stray magnetic fields compared to a known object geometry. The object geometry means its real shape, scratches or other defects. It is also possible to deposit a paramagnetic film structured in the form of stripes or a grid as a reference on the ferromagnetic sample being investigated. Received: 2 August 2001 / Accepted: 6 September 2001 / Published online: 20 December 2001     

Arrays of microscopic magnetic traps for cold atoms and their applications in atom optics

A single microscopic magnetic trap for neutral atoms using planar current-carrying wires was proposed and studied theoretically by Weinstein et al.In this paper,we propose three structures of composite current-carrying wires to provide 1D,2D and 3D arrays of microscopic magnetic traps for cold alkali atoms.The spatial distributions of magnetic fields generated by these structures are calculated and the field gradient and curvature in each single microtrap are analysed.Our study shows that arrays of microscopic magnetic traps can be used to provide 1D,2D or 3D atomic magnetic lattices,and even to realize 1D,2D and 3D arrays of magneto-optical traps,and so on.     

Scattering Matrix Method for Modeling Defect Modes in 2-D Photonic Crystals

A novel and numerically efficient treatment of electromagnetic modes localized at defects in two-dimension (2D) photonic crystals is presented in this paper. The method represents the fields in terms of scattered fields by each column of the photonic crystals. With the method, the field distributions in two photonic crystal structures are calculated with satisfying results.     

Direct comparison between potential landscape and local density of states in a disordered two-dimensional electron system

The local density of states (LDOS) of the adsorbate-induced two-dimensional electron system (2DES) on n-InAs(110) is studied by scanning tunneling spectroscopy. In contrast to a similar 3DES, the 2DES LDOS exhibits 20 times stronger corrugations and rather irregular structures. Both results are interpreted as consequences of weak localization. Fourier transforms of the LDOS reveal that the k values of the unperturbed 2DES still dominate the 2DES, but additional lower k values contribute. To clarify the origin of the LDOS patterns, we measure the potential landscape of the 2DES area. We use it to calculate the expected LDOS and find reasonable agreement between calculation and experiment.