Extension of the Barut-Girardello Coherent State and Path Integral II

We have constructed the coherent state of $U(N,1)$, which is an extension of the Barut-Girardello (BG) coherent state of $SU(1,1)$, in our previous paper. However there is a restriction that the eigenvalue of the Casimir operator is natural number. In this paper we construct the coherent state in the analytic representation to overcome this restriction. Next we show that the measure of the BG coherent state is not the symplectic induced measure.Comment: latex, no figure, 14 page

Coherent states, Path integral, and Semiclassical approximation

Using the generalized coherent states we argue that the path integral formulae for $SU(2)$ and $SU(1,1)$ (in the discrete series) are WKB exact,if the starting point is expressed as the trace of $e^{-iT\hat H}$ with $\hat H$ being given by a linear combination of generators. In our case,WKB approximation is achieved by taking a large ``spin'' limit: $J,K\rightarrow \infty$. The result is obtained directly by knowing that the each coefficient vanishes under the $J^{-1}$($K^{-1}$) expansion and is examined by another method to be legitimated. We also point out that the discretized form of path integral is indispensable, in other words, the continuum path integral expression leads us to a wrong result. Therefore a great care must be taken when some geometrical action would be adopted, even if it is so beautiful, as the starting ingredient of path integral.Comment: latex 33 pages and 2 figures(uuencoded postscript file), KYUSHU-HET-19 We have corrected the proof of the WKB-exactness in the section

Intergrowth and thermoelectric properties in the Bi-Ca-Co-O system

Single crystals of the Bi-Ca-Co-O system have been grown using the flux method with cooling from 900\celsius and 950\celsius, respectively. The single crystals are characterized by transmission electron microscopy and X-ray diffraction. The misfit cobaltite [Ca$_2$Bi$_{1.4}$Co$_{0.6}$O$_4$]$^{RS}$[CoO$_2$]$_{1.69}$ single crystals with quadruple ($n$=4) rocksalt (RS) layer are achieved with cooling from 900\celsius. Such crystal exhibits room-temperature thermoelectric power (TEP) of 180$\mu$V/K, much larger than that in Sr-based misfit cobaltites with quadruple RS layer. However, intergrowth of single crystals of quadruple ($n$=4) and triple ($n$=3) RS-type layer-based misfit cobaltites is observed with cooling from 950\celsius. Both of TEP and resistivity were obviously enhanced by the intergrowth compared to [Ca$_2$Bi$_{1.4}$Co$_{0.6}$O$_4$]$^{RS}$[CoO$_2$]$_{1.69}$ single crystal, while the power factor at room temperature remains unchanged.Comment: 8 pages, 7 figures. To be published in Journal of Crystal Growt

Multi-Periodic Coherent States and the WKB-Exactness II ``Non-compact Case and Classical theories Revisited''

We show that the WKB approximation gives the exact result in the trace formula of ``$CQ^N$'', which is the non-compact counterpart of $CP^N$, in terms of the ``multi-periodic'' coherent state. We revisit the symplectic 2-forms on $CP^N$ and $CQ^N$ and, especially, construct that on $CQ^N$ with the unitary form. We also revisit the exact calculation of the classical patition functions of them.Comment: LaTeX, 29 page

Multi-Periodic Coherent States and the WKB-Exactness

We construct the path integral formula in terms of ``multi-periodic'' coherent state as an extension of the Nielsen-Rohrlich formula for spin. We make an exact calculation of the formula and show that, when a parameter corresponding to the magnitude of spin becomes large, the leading order term of the expansion coincides with the exact result. We also give an explicit correspondence between the trace formula in the multi-periodic coherent state and the one in the ``generalized'' coherent state.Comment: 28 pages, late

Enhanced Photovoltaic Performances of Graphene/Si Solar Cells by Insertion of an MoS2 Thin Film

Atomically thin layered materials such as graphene and transition-metal dichalcogenides exhibit great potential as active materials in optoelectronic devices because of their high carrier-transporting properties and strong light-matter interactions. Here, we demonstrated that the photovoltaic performances of graphene/Si Schottky junction solar cells were significantly improved by inserting a chemical vapor deposition (CVD)-grown, large MoS2 thin-film layer. This layer functions as an effective passivation and electron-blocking/hole-transporting layer. We also demonstrated that the photovoltaic properties are enhanced with increasing number of graphene layers and decreasing thickness of the MoS2 layer. A high photovoltaic conversion efficiency of 11.1% was achieved with the optimized trilayer-graphene/MoS2/n-Si solar cell.Comment: Main text: 24 pages, 5 figures; Supporting Information: 8 pages, 5 figures, 1 tabl