Melham's Conjecture on Odd Power Sums of Fibonacci Numbers

Ozeki and Prodinger showed that the odd power sum of the first several consecutive Fibonacci numbers of even order is equal to a polynomial evaluated at certain Fibonacci number of odd order. We prove that this polynomial and its derivative both vanish at $1$, and will be an integer polynomial after multiplying it by a product of the first consecutive Lucas numbers of odd order. This presents an affirmative answer to a conjecture of Melham.Comment: 15page

Bias-induced insulator-metal transition in organic electronics

We investigate the bias-induced insulator-metal transition in organic electronics devices, on the basis of the Su-Schrieffer-Heeger model combined with the non-equilibrium Green's function formalism. The insulator-metal transition is explained with the energy levels crossover that eliminates the Peierls phase and delocalizes the electron states near the threshold voltage. This may account for the experimental observations on the devices that exhibit intrinsic bistable conductance switching with large on-off ratio.Comment: 6 pages, 3 figures. To appear in Applied Physics Letter

Quantum tunneling through planar p-n junctions in HgTe quantum wells

We demonstrate that a p-n junction created electrically in HgTe quantum wells with inverted band-structure exhibits interesting intraband and interband tunneling processes. We find a perfect intraband transmission for electrons injected perpendicularly to the interface of the p-n junction. The opacity and transparency of electrons through the p-n junction can be tuned by changing the incidence angle, the Fermi energy and the strength of the Rashba spin-orbit interaction. The occurrence of a conductance plateau due to the formation of topological edge states in a quasi-one-dimensional p-n junction can be switched on and off by tuning the gate voltage. The spin orientation can be substantially rotated when the samples exhibit a moderately strong Rashba spin-orbit interaction.Comment: 4 pages, 4 figure

Strong correlation and massive spectral-weight redistribution induced spin density wave in a-Fe1.06Te

The electronic structure of a-Fe1.06Te is studied with angle-resolved photoemission spectroscopy. We show that there is substantial spectral weight around Gamma and X, and lineshapes are intrinsically incoherent in the paramagnetic state. The magnetic transition is characterized by a massive spectral-weight transfer over an energy range as large as the band width, which even exhibits a hysteresis loop that marks the strong first order transition. Coherent quasiparticles emerge in the magnetically ordered state due to decreased spin fluctuations, which account for the change of transport properties from insulating behavior to metallic behavior. Our observation demonstrates that Fe1.06Te distinguishes itself from other iron-based systems with more local characters and much stronger interactions among different degrees of freedom, and how a spin density wave is formed in the presence of strong correlation.Comment: 5 pages, 4 figure