We theoretically study the generic behavior of the penetration depth of the edge states in two-dimensional quantum spin Hall systems. We found that the momentum-space width of the edge-state dispersion scales with the inverse of the penetration depth. As an example of well-localized edge states, we take the Bi(111) ultrathin film. Its edge states are found to extend almost over the whole Brillouin zone. Correspondingly, the bismuth (111) 1-bilayer system is proposed to have well-localized edge states in contrast to the HgTe quantum well. 72.25.Dc, 73.20.At, Introduction-The quantum spin Hall (QSH) phase [1, 2] is a new state of matter predicted theoretically, and has received a lot of attention recently. This phase is a nonmagnetic insulator in the bulk or film, and has gapless surface or edge states. The edge states consist of counterpropagating states with opposite spins. The notable feature of these edge states is that they are topologically protected; they remain gapless even in the presence of nonmagnetic impurities and interaction [3,4]. We still know few systems in which the QSH phase is realized. The first theoretical proposal for the QSH system on the Bi ultrathin film by one of the authors [5]. In addition, HgTe quantum well has been theoretically proposed [6], and experimentally shown to be in the 2D QSH state [7,8].

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synopsisGelation of poly(ethy1ene terephthalate) by heating at 263°-3000C was investigated. Under nitrogen flow, crosslinks were scarcely formed. However in air, degradation and crosslinking were common, and these were accelerated by purging gaseous and sublimable degradation products out of the system with a stream of air. The main component of the sublimate was terephthalic acid. Infusible and insoluble gel was treated with methanol at 26OoC, and then the methanolysis products were separated into two parts. The methanol-insoluble part exhibited a polyene structure with ester groups, and the methanol-soluble part contained dimethyl terephthalate, ethylene glycol, and some 1,2,4-butanetriol. To clarify the relation between the crosslinking and the formation of vinyl ester groups, the degradation of vinyl methyl terephthalate was studied. Thermooxidative degradation of linear polyesters other than poly(ethy1ene terephthalate) was also studied. Poly(ethy1ene isophthalate) and poly(ethy1ene sebacate) were easily gelated. However, poly(trimethy1ene terephthalate) and poly(neopenty1 terephthalate) were scarcely gelated. The primary reaction leading to crosslinking is assumed as follows. At fist, the random scission of polyester chain may take place forming carboxylic acids, vinyl esters, aldehydes, etc. After accumulation of vinyl esters to some extent, vinyl polymerization of the esters takes place and network structures are formed.

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