Positive mass theorems for asymptotically AdS spacetimes with arbitrary cosmological constant

We formulate and prove the Lorentzian version of the positive mass theorems with arbitrary negative cosmological constant for asymptotically AdS spacetimes. This work is the continuation of the second author's recent work on the positive mass theorem on asymptotically hyperbolic 3-manifolds.Comment: 17 pages, final version, to appear in International Journal of Mathematic

Resonance-state-induced superconductivity at high Indium contents in In-doped SnTe

We report a reinvestigation of superconducting Sn$_{1-x}$In$_{x}$Te at both low and high In doping levels. Analysis of the superconductivity reveals a fundamental change as a function of \textit{x}: the system evolves from a weakly coupled to a strongly coupled superconductor with increasing indium content. Hall Effect measurements further show that the carrier density does not vary linearly with Indium content; indeed at high Indium content, the samples are overall \textit{n}-type, which is contrary to expectations of the standard picture of In$^{1+}$ replacing Sn$^{2+}$ in this material. Density functional theory calculations probing the electronic state of In in SnTe show that it does not act as a trivial hole dopant, but instead forms a distinct, partly filled In 5\textit{s} - Te 5\textit{p} hybridized state centered around E$_F$, very different from what is seen for other nominal hole dopants such as Na, Ag, and vacant Sn sites. We conclude that superconducting In-doped SnTe therefore cannot be considered as a simple hole doped semiconductor.Comment: 12 pages and 7 figure