A stable "flat″ form of two-dimensional crystals: could graphene, silicene, germanene be minigap semiconductors?
Summary of "A stable "flat″ form of two-dimensional crystals: could graphene, silicene, germanene be minigap semiconductors?"
The discovery of a flat two-dimensional crystal known as graphene has contradicted Landau-Peierls-Mermin-Wagner arguments that there is no stable flat form of such crystals. Here, we show that the "flat" shape of graphene arises due to a microscopic buckling at the smallest possible interatomic scale. We show that the graphene, silicene, and other two-dimensional crystals are stable due to transverse short-range displacements of appropriate atoms. The distortions are small and form various patterns, which we describe in a framework of Ising model with competing interactions. We show that when temperature decreases, two transitions, disorder into order and order into disorder, arise. The ordered state has a form of stripes where carbon atoms are shifted regularly with respect to the plane. The flat graphene, silicene, or germanene planes look like a microscopic "washboard" with the wavelength of about couple of interatomic spacing of appropriate sublattices, which for graphene is about 1.8-3.6 Å. At lower temperatures, the ordered state transforms into a glass. Because of up-down asymmetry in buckled graphene, silicene and other two-dimensional crystals deposited on substrate, a minibandgap may arise. We derive a criterion for the minigap formation and show how it is related to the buckling and to the graphene-substrate interaction. Because of the bandgap, there may arise new phenomena and in particular a rectification of ac current induced by microwave or infrared radiation. We show that the amplitude of direct current arising at wave mixing of two harmonics of microwave electromagnetic radiation is huge. Moreover, we predict the existence of miniexcitons and a new type of fermionic minipolaritons whose behavior can be controlled by the microwave and terahertz radiation.
Department of Physics, Loughborough University , Leicestershire, LE11 3TU, United Kingdom.
This article was published in the following journal.
Name: Nano letters
Medical and Biotech [MESH] Definitions
Echocardiography amplified by the addition of depth to the conventional two-dimensional ECHOCARDIOGRAPHY visualizing only the length and width of the heart. Three-dimensional ultrasound imaging was first described in 1961 but its application to echocardiography did not take place until 1974. (Mayo Clin Proc 1993;68:221-40)
The process of generating three-dimensional images by electronic, photographic, or other methods. For example, three-dimensional images can be generated by assembling multiple tomographic images with the aid of a computer, while photographic 3-D images (HOLOGRAPHY) can be made by exposing film to the interference pattern created when two laser light sources shine on an object.
Four-dimensional Computed Tomography
Three-dimensional computed tomographic imaging with the added dimension of time, to follow motion during imaging.
Two-dimensional Difference Gel Electrophoresis
Methods of comparing two or more samples on the same two-dimensional gel electrophoresis gel.
Dynamic three-dimensional echocardiography using the added dimension of time to impart the cinematic perception of motion. (Mayo Clin Proc 1993;68:221-40)
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