Electrically Tunable Energy Bandgap in Dual-Gated Ultra-Thin Black Phosphorus Field Effect Transistors

The energy bandgap is an intrinsic character of semiconductors, which largely determines their properties. The ability to continuously and reversibly tune the bandgap of a single device during real time operation is of great importance not only to device physics but also to technological applications. Here we demonstrate a widely tunable bandgap of few-layer black phosphorus (BP) by the application of vertical electric field in dual-gated BP field-effect transistors. A total bandgap reduction of 124 meV is observed when the electrical displacement field is increased from 0.10V/nm to 0.83V/nm. Our results suggest appealing potential for few-layer BP as a tunable bandgap material in infrared optoelectronics, thermoelectric power generation and thermal imaging.Comment: 5 pages, 4 figure

Supereulerian graphs and the Petersen graph, II

In this note, we verify two conjectures of Catlin in [J. Graph Theory 13 (1989) 465 - 483] for graphs with at most 11 vertices. These are used to prove the following theorem which improves prior results in [10] and [13]: Let G be a 3-edge-connected simple graph with order n. If n is large and if for every edge 11.v E E(G), d(u) + d(v) 2 % - 2, then either G has a spanning eulerian subgraph or G can be contracted to the Petersen graph