关于Veldman等人的一个猜想

本文证明了下列源于Veldman等人的一个猜想;设G是阶为n≥13的1—tough图且对所有独立集x,y,z有d(x) d(y) d(z)≥(3n-14)/2,则G是哈米顿的。     

Generation of Fabry–Pérot oscillations and Dirac state in two-dimensional topological insulators by gate voltage

We investigate electron transport through Hg Te ribbons embedded by strip-shape gate voltage through using a nonequilibrium Green function technique. The numerical calculations show that as the gate voltage is increased, an edgerelated state in the valence band structure of the system shifts upwards, then hangs inside the band gap and merges into the conduction band finally. It is interesting that as the gate voltage is increased continuously, another edge-related state in the valence band also shifts upwards in the small-k region and contacts the previous one to form a Dirac cone in the band structure. Meanwhile in this process, the conductance spectrum displays as multiple resonance peaks characterized by some strong antiresonance valleys in the band gap, then behaves as Fabry–P′erot oscillations and finally develops into a nearly perfect quantum plateau with a value of 2e~2/h. These results give a physical picture to understand the formation process of the Dirac state driven by the gate voltage and provide a route to achieving particular quantum oscillations of the electronic transport in nanodevices.