Bosonic Super Liouville System: Lax Pair and Solution

We study the bosonic super Liouville system which is a statistical transmutation of super Liouville system. Lax pair for the bosonic super Liouville system is constructed using prolongation method, ensuring the Lax integrability, and the solution to the equations of motion is also considered via Leznov-Saveliev analysis.Comment: LaTeX, no figures, 11 page

Gate-Voltage Control of Chemical Potential and Weak Anti-localization in Bismuth Selenide

We report that Bi$_2$Se$_3$ thin films can be epitaxially grown on SrTiO$_{3}$ substrates, which allow for very large tunablity in carrier density with a back-gate. The observed low field magnetoconductivity due to weak anti-localization (WAL) has a very weak gate-voltage dependence unless the electron density is reduced to very low values. Such a transition in WAL is correlated with unusual changes in longitudinal and Hall resistivities. Our results suggest much suppressed bulk conductivity at large negative gate-voltages and a possible role of surface states in the WAL phenomena. This work may pave a way for realizing three-dimensional topological insulators at ambient conditions.Comment: 5 pages, 4 figures