We consider initial value/boundary value problems for fractional diffusion-wave equation:where L is a symmetric uniformly elliptic operator with t-independent smooth coefficients. First we establish the unique existence of the weak solution and the asymptotic behavior as the time t goes to ∞ and the proofs are based on the eigenfunction expansions. Second for α ∈ (0, 1), we apply the eigenfunction expansions and prove (i) stability in the backward problem in time, (ii) the uniqueness in determining an initial value and (iii) the uniqueness of solution by the decay rate as t → ∞, (iv) stability in an inverse source problem of determining t-dependent factor in the source by observation at one point over (0, T ).

Graphene-based materials are promising candidates for nanoelectronic devices because very high carrier mobilities can be achieved without the use of sophisticated material preparation techniques. However, the carrier mobilities reported for single-layer and bilayer graphene are still less than those reported for graphite crystals at low temperatures, and the optimum number of graphene layers for any given application is currently unclear, because the charge transport properties of samples containing three or more graphene layers have not yet been investigated systematically. Here, we study charge transport through trilayer graphene as a function of carrier density, temperature, and perpendicular electric field. We find that trilayer graphene is a semimetal with a resistivity that decreases with increasing electric field, a behaviour that is markedly different from that of single-layer and bilayer graphene. We show that the phenomenon originates from an overlap between the conduction and valence bands that can be controlled by an electric field, a property that had never previously been observed in any other semimetal. We also determine the effective mass of the charge carriers, and show that it accounts for a large part of the variation in the carrier mobility as the number of layers in the sample is varied.

We report ambipolar charge transport in α-molybdenum ditelluride (MoTe2 ) flakes, whereby the temperature dependence of the electrical characteristics was systematically analyzed. The ambipolarity of the charge transport originated from the formation of Schottky barriers at the metal/MoTe2 contacts. The Schottky barrier heights as well as the current on/off ratio could be modified by modulating the electrostatic fields of the back-gate voltage (Vbg) and drain-source voltage (Vds). Using these ambipolar MoTe2 transistors we fabricated complementary inverters and amplifiers, demonstrating their feasibility for future digital and analog circuit applications.

The field of 'Valleytronics' has recently been attracting growing interest as a promising concept for the next generation electronics, because non-dissipative pure valley currents with no accompanying net charge flow can be manipulated for computational use, akin to pure spin currents 1 . Valley is a quantum number defined in an electronic system whose energy bands contain energetically degenerate but non-equivalent local minima (conduction band) or maxima (valence band) due to a certain crystal structure. Specifically, spatial inversion symmetry broken two-dimensional honeycomb lattice systems exhibiting Berry curvature is a subset of possible systems that enable optical 2-5