We present anyonic vortex solutions made of real electrons which could be interpreted as nontopological solitons of the (2 + 1)-dimensional Chern-Simons electrodynamics. The n-soliton solutions, which we obtain by imposing an effective axial symmetry on the (3+ 1)-dimensional quantum electrodynamics, have 4n real parameters which represent the position, size, and phase of each soliton.PACS number(s): 11.15. -q, 03.50.Kk, 12.20.Ds, 74.65. +n The axially symmetric vortex solutions which exist in ( 3 + 1 )-dimensional gauge theories have played a very important role in physics. They describe the quantized magnetic flux lines in superconductivity [I], the string model in hadrodynamics [2], and the large-scale cosmic strings in cosmology [3]. Similar vortex solutions also exist in the ( 2 + 1 )-dimensional Chern-Simons gauge theory[4]. In all these solutions, however, the presence of scalar fields has played a crucial role in providing the source of the vortices. So far no vortex solution made of a fermionic source has been constructed, although the fermionic bound states coupled to an arbitrary external magnetic vortex have been discussed by many authors [5]. The purpose of this paper is to show the existence of axially symmetric vortex solutions in which a fermion field provides the source of the vortices, and to discuss the physical implication of the solutions.The system we discuss is the one derived from the (3+ 1)-dimensional quantum electrodynamics which has an effective axial symmetry described in the following. With the symmetry one can reduce the theory to the ( 2 + 1 )-dimensional Maxwell electrodynamics which has two interacting fermionic sources: the right-handed and the left-handed fermions. Furthermore, when the effective axial symmetry is chosen in such a way to violate parity, one may add the Chern-Simons interaction to the theory. This is because the Chern-Simons interaction could be induced by the higher-order quantum correction of the fermions when a parity-violating interaction is present [ 6 ] . In this case the theory becomes Maxwell-Chern-Simons electrodynamics, but again with two fermionic sources. This means that, in the longdistance limit in which the Chern-Simons term dominates the Maxwell term, the theory can be approximated to an effective Chern-Simons electrodynamics. In this limit we show that the theory admits vortex solutions made offermions.Let us start with ( 3 + 1 )-dimensional quantum electrodynamics. In the chiral representation in which y 5 becomes diagonal one can describe the Dirac spinor \V with two two-components spinors where \V+ and \V-are the right-handed and the lefthanded Weyl spinors. Now we impose the effective axial symmetry 2nd assume that the Weyl spinors \ V, are periodic in the z coordinate (with different periodicities), but the gauge potential is independent of the z coordinate. With this effective axial symmetry one can easily reduce the theory to ( 2 + 1 )-dimensional electrodynamics.After the dimensional reduction by integrating out the z dependence, we o...

By combining PS-PMMA self-assembled diblock copolymer (BC) and lift off process, gold nanodot array was fabricated. For surface neutralization, a novel method using conventional self assembled monolayer (SAM), MPTS (3-(pmethoxyphenyl)propyltrichlro-silane) was used. Surface treatment with SAM was analyzed by contact angle measurement and XPS. Upon the fabricated cylindrical nanohole array, gold was evaporated and 10 nm size gold nanoparticle array was fabricated by lift-off process.Keywords-components; diblock copolymer, self-assembled monolayer, nanodot Ⅰ. INTRODUCTION Metal nanodots have been used for various applications in nanotechnology, including nanocrystal memory (1) and plasmonics (2) etc. Many methods such as electrodeposition, evaporation, and solution based techniques have been employed for nanodot formaiton. However, the lack of fabrication method of nanodot array on Si surface with good long range order hinders its practical use in industry. Self assembly of nanomaterials is greatly interesting for solving this problem. Block copolymer (BC) attracts great interest since it spontaneously organizes into a various nanostructures including dense lamellar, cylindrical, or spherical nanodomains easily by controlling molecular weight ratio with nanometer scale. Especially, the possibility of converging already well developed semiconductor fabrication methods with BC makes it strong candidate for practical fabrication method. (3) In this study, we fabricated gold nanodot array on Si substrate using cylindrical nanohole array template from BC and lift off process. For making cylindrical nanohole array, neutralization of surface is required, which has been usually done by random copolymer. (4) However, self assembled monolayer (SAM), also controls the interaction between BC and substrate (5) . Thus, we have used MPTS to neutralize the surface and cylindrical nanohole array template was successfully fabricated. Using this nanotemplate, simple lift off process was utilized to fabricate 10 nm gold nanodot array with good local hexagonal ordering. The fabricated gold nanodots were analyzed by high resolution transmission electron microscopy (HR-TEM) Ⅱ. EXPERIMENTS Si substrate with native oxide was cleaned with a H 2 SO 4 /H 2 O 2 at 100℃ for 30min. SAM coating was carried out by dipping the substrate in MPTS solution. PS-PMMA BC film was spin cast onto the substrate. The thickness of the film was controlled by solution concentration and spinning speed. BC thin films were annealed at 180℃ in vacuum oven. Next, the PMMA was removed by exposure to ultraviolet (UV) light for 90min. To make nanodot array, gold was thermally evaporated in high vacuum chamber. After deposition, lift off was carried out in NMP (1-methyl-2-pyrrolidone) solution at 202°C. Finally, further cleaning of the remaining PS was performed by oxygen plasma ashing. Ⅲ. EXPERIMENTAL RESULT The rate of SAM formation is influenced by many factors, such as temperature, time, solvent, and concentration. We have used contact angle measurement to study the...

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