Electronic states of two-dimensional materials and heterostructures

The electronic states of two-dimensional (2D) materials and heterostructures are discussed, comparing theoretical predictions and experimental results for vertical tunneling devices and other structures. For graphene-insulator-graphene (GIG) junctions, predicted current-voltage characteristics display a resonant peak arising from momentum conservation in the junctions,¹ as illustrated in Fig. 1. Recent experiments have confirmed those predictions, including dependence FIG 1. (a)–(c) Band diagrams for a doped GIG junction, at voltages of (a) V <2ΔE/e, (b) V > 2ΔE/e, and (c) V = 2ΔE/e. In (a) and (b), states satisfying k-conservation (i.e. in limit of large electrode area) are shown by the rings located at an energy midway between the Dirac points for the two electrodes. In (c), states at all energies satisfy k-conservation. (d) Qualitative current-voltage (I-V) characteristic. In actual physical devices, the delta-function (arrow) will be broadened into a Gaussianlike characteristic.