Transmission of Dirac Electrons Through Graphene Multilayers with Gaussian Profile
- PDF / 334,881 Bytes
- 7 Pages / 432 x 648 pts Page_size
- 52 Downloads / 181 Views
Transmission of Dirac Electrons Through Graphene Multilayers with Gaussian Profile J. A. Aguilar-Hernández, J. Madrigal-Melchor, J. C. Martínez-Orozco and I. Rodríguez-Vargas Unidad Académica de Física, Universidad Autónoma de Zacatecas, Calzada Solidaridad Esquina con Paseo La Bufa S/N, 98060 Zacatecas, Zac., México ABSTRACT In this work, we use the T-matrix method to study the tunneling of Dirac electrons through graphene multilayers. A graphene sheet is deposited on top of slabs of SiO2-SiC substrates, of which we applied a Gaussian distribution in the size width of the SiC substrate. We calculate the transmittance as a function of energy for different incident angles and different number of layers of the Gaussian distribution. We obtain different stop-band regions. These regions are wider when the width of the barrier is increased. Furthermore, it is possible to tune the width and the position of stop-band with the angle of incidence, the σ value of the Gaussian distribution, and the difference between the maximum-minimum sizes of the barrier. INTRODUCTION Graphene since its discovery in 2004 [1, 2] has generated a great expectation for its properties and potential applications [3-6]. Much of the hype comes from its peculiar band structure, being a zero bandgap semimetal with linear dispersion relation near the K point in the Brillouin zone [7] allowing that the electrons to behave like relativistic particles even when they move much slower than the speed of light, vF = c/300. The results of this odd behavior are unusual effects such as minimum conductivity and Klein tunneling [3, 4]. These effects, from a fundamental perspective, are very interesting and Graphene opens the way to prove them experimentally. However, from a technological perspective they are not at all advisable since they impede the modulation of the electronics properties of the material. One way that allows us to modulate the electronic properties in Graphene, is to deposit a layer of Graphene on a substrate of hBN [8] or SiC [9], so an energy gap will emerge. These substrates allow the Graphene layers to present an energy gap from 0.1 eV to 0.260 eV for SiC and of 53 meV for hBN. In this paper we study the transmission properties of Dirac electrons through a layer of Graphene deposited on a substrate consisting of alternating regions of SiO2 and SiC following a Gaussian profile in the thickness of SiC substrate. We use a Gaussian distribution due to the transmission that has been studied for optical waves in multilayer systems [10, 11] and Schrödinger’s electrons in multilayer structures [12, 13] showing very interesting properties as the formation of perfect stop-bands and pass-bands.
129
THEORY For our study we use the transfer matrix method with the formalism of Pochi Yeh [14], which is used extensively for the study of electromagnetic waves. It is very easy to apply this formalism to the study of wave propagation of any kind [11, 15, 16], so Dirac electrons are no exception. The Gaussian profile of the systems is generated through widt
Data Loading...
