Electronic band gap and transport in Fibonacci quasi-periodic graphene superlattice

Abstract

We investigate electronic band gap and transport in Fibonacci quasi-periodic graphene superlattice. It is found that such structure can possess a zero-k gap which exists in all Fibonacci sequences. Different from Bragg gap, zero-k gap associated with Dirac point is less sensitive to the incidence angle and lattice constants. The defect mode appeared inside the zero-k gap has a great effect on transmission, conductance and shot noise, which can be applicable to control the electron transport.Graphene, a monolayer of carbon atoms tightly packed into a honeycomb lattice, has attracted great interest in graphene-based nanoelectronic and optoelectronic devices [1], since it was fabricated by Novoselov and Geim et al. in 2004 [2]. In graphene, the unique band structure with the valance and conduction bands touching at Dirac point (DP) leads to the fact that electrons around the Fermi level can be described as the massless relativistic Dirac electrons, resulting in the linear energy dispersion relation. As a consequence, there are a great number of electronic properties, such as the half-integer quantum Hall effect [3][4][5], the minimum conductivity [3], and Klein tunneling [6]. In particular, Klein tunneling and perfect transmission are crucial for electron transport in various graphene heterostructures [7], i.e. single barrier [8] and n-p-n junctions [9].Motivated by the experimental realization of graphene superlattice (GSL) [10][11][12], electronic bandgap structures and transport properties in GSLs with electrostatic potential and magnetic barrier have been extensively investigated [13][14][15][16][17][18][19][20][21][22], since the conventional semiconductor superlattices are successful in controlling the electronic structures and the extension to graphene may give rise to different features and applications. For instance, DP appears in the GSL [14,15], and it is exactly located at the energy with the zero-k gap [17]. Interestingly, the zero-k gap associated with DP is insensitive to the lattice parameter changes in contrast with the behavior exhibited by Bragg gaps [17]. This gap is analogous to photonic zero-n gap in the photonic crystals containing negativeindex and positive-index materials [20], and originates from a zero total phase [23]. Accordingly, the zero-k gap is robust against the lattice constants, structural disorder [17], and external magnetic field [18], and thus is better to control the electron transport in GSL.In this Letter, we will investigate electronic band gap and transport in Fibonacci quasi-periodic GSLs in the fashion analogous to photonic crystal with metamaterials [23][24][25]. As we know, the quasi-periodic GSL is classified as intermediate between ordered and disordered systems [19,20], which has significant and common features like fractal spectrum and self-similar behavior [21,22]. How- * Corresponding author. Email: xchen@shu.edu.cn ever, what we concentrate on here is the electronic band gap and DP in such quasi-periodic system. We find that zero-k gap happens in all Fibonacci...

Transmission gaps in graphene superlattices with periodic potential patterns

“…[18], these transmission gaps in Dirac electrons tunneling through the periodic barriers can be divided into two types: one of these transmission gaps is the zero-averaged wave-number ( −k zero ) gap associated with the Dirac point [18][19][20][21], where the center of the gap is located at…”

“…The periodic graphene superlattices can be generated by different methods, such as applying periodically gate electrodes [24] or parallel ferromagnetic metal stripes [16] on graphene to generate electrostatic potentials or magnetic barriers. The electronic transport properties and band structures of the graphene-based one-dimensional (1D) superlattices with periodic [17,18], Fibonacci [20], and Thue-Morse sequence [21] have been studied. Furthermore, the transmission gaps in graphene superlattices have also been investigated [23].…”

“…Recently, many studies of graphene superlattices [16][17][18][19][20][21][22][23] have been reported experimentally and theoretically. The periodic graphene superlattices can be generated by different methods, such as applying periodically gate electrodes [24] or parallel ferromagnetic metal stripes [16] on graphene to generate electrostatic potentials or magnetic barriers.…”

Omnidirectional transmission and reflection of pseudospin-1 Dirac fermions in a Lieb superlattice

“…1/h is the quantized conductance in cold-atom systems. For the wider channel, the number of modes can be estimated by assuming the periodic boundary conditions, the allowed modes of k y are spaced by 2π /L y with L y being the width of the Lieb lattice in the y direction [27]. The conductance can be rewritten as…”

“…It has been known that, in graphene superlattices, applied external periodic or quasiperiodic potentials result in not only the strong anisotropy of the energy spectra, but also the extra Dirac points and new zero energy modes [22][23][24][25][26][27][28]. The band structures and transport properties are therefore changed by superlattice potentials efficiently, and some significant applications, for example, electron beam supercollimation and electron wave filter have been achieved [29,30].…”