Biperiodic superlattices and transparent states in graphene

Abstract

The transmission and transport properties of biperiodic graphene superlattices are studied theoretically. Special attention is paid to the so-called transparent states of biperiodic superlattices. A Dirac-like Hamiltonian is used to describe the charge carriers in graphene. The transfer matrix method and the Landauer–Büttiker formalism are implemented to obtain the transmittance and conductance, respectively. Similar results to those reported for Schrödinger electrons are obtained. However, in the case of Dirac electrons the splitted bands and the transparent states associated to the biperiodicity depend strongly on the angle of incidence as well as the character of the charge carriers. In fact, the dynamic of the splitted bands and transparent states is inverted for holes. The origin of transparent states is unveiled by obtaining an analytic expression for the transmittance. It is found that resonant transmission through single and double barriers gives rise to transparent states. Regarding the transport properties, it is possible to identify the fundamental changes caused by the biperiodicity. In particular, it is found a splitting, shifting, and diminishment of the conductance peaks with respect to the case of regular periodicity. This opens the door to corroborate experimentally the fundamental characteristics of biperiodic gated graphene superlattices through transport measurements.

Extended states in random dimer gated graphene superlattices

“…We study the role of the dimer well as a resonant cavity randomly embedded in the host GGSLs. To do so, we focus on the resonant conditions imposed by the transmittance for a dimer well [33,36]…”

“…where M 1b 12 is the (1,2) matrix element of M bB , which is proportional to sin(q x d B ), and Tr(M bB M wB ) represents the trace of the unit-cell associated to the B seed. For more details on the analytic form and derivation of these terms see [36]. From equation (18), we can realize that sin(q x d B ) and Tr(M bB M wB ) constitute the resonant tunneling condition.…”

Filtering electrons by mode coupling in finite semiconductor superlattices

“…Similar coupling and improvement can also be obtained in arbitrary superlattice (not limited at Kronig-Penney superlattice) with symmetric unit cell, while the width choice of each segment should support perfect resonances. Besides the one-dimensional nanowire superlattice, the two- or three-dimensional semiconductor superlattice can also be studied by employing our approach, such as the in-plane superlattice or out-plane superlattice of two-dimensional materials 37 , 38 . Therein, the incidence angle and parameter components along the superlattice are critical to the further interpretation.…”