Effect of Hexagonal Boron Nitride on Energy Band Gap of Graphene Antidot Structures

The zero band gap (Eg) graphene becomes narrow Eg semiconductor when graphene is patterned with periodic array of hexagonal shaped antidots, the resultant is the hexagonal Graphene Antidot Lattice (hGAL). Based on the number of atomic chains between antidots, hGALs can be even and odd. The even hGALs (ehGAL) are narrow Eg semiconductors and odd hGALs (ohGAL) are semi-metals. The Eg opening up by hGALs is not sufficient to operate a realistic switching transistor. Also hGAL transistors realized on Si/SiO2 substrate are suffering with low carrier mobility and ON-OFF current ratio. In order to achieve a sizable Eg with good mobility, AB Bernal stacked hGALs on hexagonal Boron Nitride (hBN), ABA Bernal stacked hBN / hGAL / hBN sandwiched structures and AB misaligned hGAL /hBN structures are reported here for the first time. Using the first principles method the electronic structure calculations are performed. A sizable Eg of about 1.04 eV (940+100 meV) is opened when smallest neck width medium radius ehGAL supported on hBN and about 1.1 eV (940 + 200 meV) is opened when the same is sandwiched between hBN layers. A band gap on the order of 71 meV is opened for Bernal stacked ohGAL / hBN and nearly 142 meV opened for hBN / ohGAL /hBN structures for smallest radius and width of nine atomic chains between antidots. Unlike a misaligned graphene on hBN, the misaligned ohGAL/hBN structure shows increased Eg. This study could open up new ways of band gap engineering for graphene based nanostructures. Keywords: Graphene, graphene antidots, hexagonal boron nitride, band structure, band gap engineeringComment: 14 pages, 5 figures, Innovative Systems Design and Engineering,Vol 3, No 12 (2012

Uncertainties in nuclear transition matrix elements for neutrinoless ββ\beta \beta decay II: the heavy Majorana neutrino mass mechanism

Employing four different parametrization of the pairing plus multipolar type of effective two-body interaction and three different parametrizations of Jastrow-type of short range correlations, the uncertainties in the nuclear transition matrix elements $M_{N}^{(0\nu)}$ due to the exchange of heavy Majorana neutrino for the $0^{+}\rightarrow 0^{+}$ transition of neutrinoless double beta decay of $^{94}$Zr, $^{96}$Zr, $^{98}$Mo, $^{100}$Mo, $^{104}$Ru, $^{110}$Pd, $^{128,130}$Te and $^{150}$Nd isotopes in the PHFB model are estimated to be around 25%. Excluding the nuclear transition matrix elements calculated with Miller-Spenser parametrization of Jastrow short range correlations, the uncertainties are found to be 10%-15% smaller

Nuclear deformation and neutrinoless double-β\beta decay of 94,96^{94,96}Zr, 98,100^{98,100}Mo, 104^{104}Ru, 110^{110}Pd, 128,130^{128,130}Te and 150^{150}Nd nuclei in mass mechanism

The $(\beta ^{-}\beta ^{-})_{0\nu}$ decay of $^{94,96}$Zr, $^{98,100}$Mo, $^{104}$Ru, $^{110}$Pd, $^{128,130}$Te and $^{150}$Nd isotopes for the $0^{+}\to 0^{+}$ transition is studied in the Projected Hartree-Fock-Bogoliubov framework. In our earlier work, the reliability of HFB intrinsic wave functions participating in the $\beta ^{-}\beta ^{-}$ decay of the above mentioned nuclei has been established by obtaining an overall agreement between the theoretically calculated spectroscopic properties, namely yrast spectra, reduced $B(E2$:$0^{+}\to 2^{+})$ transition probabilities, quadrupole moments $Q(2^{+})$, gyromagnetic factors $g(2^{+})$ as well as half-lives $T_{1/2}^{2\nu}$ for the $0^{+}\to 0^{+}$ transition and the available experimental data. In the present work, we study the $(\beta ^{-}\beta ^{-})_{0\nu}$ decay for the $0^{+}\to 0^{+}$ transition in the mass mechanism and extract limits on effective mass of light as well as heavy neutrinos from the observed half-lives $T_{1/2}^{0\nu}(0^{+}\to 0^{+})$ using nuclear transition matrix elements calculated with the same set of wave functions. Further, the effect of deformation on the nuclear transition matrix elements required to study the $(\beta ^{-}\beta ^{-})_{0\nu}$ decay in the mass mechanism is investigated. It is noticed that the deformation effect on nuclear transition matrix elements is of approximately same magnitude in $(\beta ^{-}\beta ^{-})_{2\nu}$ and $(\beta ^{-}\beta ^{-})_{0\nu}$ decay.Comment: 15 pages, 1 figur

A note on the Gauss decomposition of the elliptic Cauchy matrix

Explicit formulas for the Gauss decomposition of elliptic Cauchy type matrices are derived in a very simple way. The elliptic Cauchy identity is an immediate corollary.Comment: 5 page

The 0+→0+0^{+}\to 0^{+} positron double-β\beta decay with emission of two neutrinos in the nuclei 96^{96}Ru, 102^{102}Pd, 106^{106}Cd and 108^{108}Cd

Theoretical results for %the $0^{+}\to 0^{+}$ positron double-$\beta$ decay with emission of two neutrinos in the nuclei $^{96}$Ru, $^{102}$Pd, $^{106}$Cd and $^{108}$Cd are presented. The study employs the Hartree-Fock-Bogoliubov model to obtain the wave functions of the parent and daughter nuclei, in conjunction with the summation method to estimate the double beta decay nuclear matrix elements. The reliability of the intrinsic wave functions of $^{96,102}$Ru, $$Mo, $^{102,106,108}$Pd and $^{106,108}$Cd nuclei are tested by comparing the theoretically calculated spectroscopic properties with the available experimental data. Calculated half-lives $T_{1/2}^{2\nu}$ of $^{96}$Ru, $^{102}$Pd, $^{106}$Cd and $^{108}$Cd nuclei for 2$\nu$ $\beta ^{+}\beta ^{+}$, 2$\nu$ $\beta ^{+}EC$ and 2$\nu$ $ECEC$ modes are presented. The effect of deformation on the nuclear transition matrix element $M_{2\nu}$ is also studied.Comment: Submitted to EPJ