Landau levels of single-layer and bilayer phosphorene

Modarresi

Computational Materials Science

et al. 2016

a b s t r a c tWe investigate the electronic and optical properties of monolayer and stacking dependent bilayer blue phosphorus in the framework of density functional theory (DFT) and tight-binding approximations. We extract the hopping parameters of TB Hamiltonian for monolayer and bilayer blue phosphorus by using the DFT results. The variation of energy band gap with applied external electric field for two different stacks of bilayer blue phosphorus are also shown. We examine the linear response of the systems due to the external electromagnetic radiation in terms of the dielectric functions in the DFT theory. The relatively large electronic band gap and possibility of exfoliation form bulk structure due to weak interlayer coupling, make blue phosphorus an appropriate candidate for future electronic devices.

Section: Introductionmentioning

confidence: 99%

Electronic and optical properties of bilayer blue phosphorus

Modarresi

Computational Materials Science

et al. 2016

“…There is already a growing literature dealing with basic properties of phosphorene, as well as studies of possible technological applications. 7,8,20,21 A series of recent studies have obtained the electronic dispersion using approaches such as first principles calculations 14,16,[22][23][24] , tight-binding model 22,25 , k · p methods 26,27 , and a longwavelength approximation 28 . Following the example of graphene nanoribbons [29][30][31] , one can expect that the electronic spectrum and the transport properties of narrow phosphorene ribbons can be significantly distinct from the case of an infinite sample.…”

Section: Introductionmentioning

confidence: 99%

Boundary conditions for phosphorene nanoribbons in the continuum approach

et al. 2016

We investigate the energy spectrum of single layer black phosphorene nanoribbons (BPN) by means of a low-energy expansion of a recently proposed tight-binding model that describes electron and hole bands close to the Fermi energy level. Using the continuum approach, we propose boundary conditions based on sublattice symmetries for BPN with zigzag and armchair edges and show that our results for the energy spectra exhibit good agreement with those obtained by using the five-parameter tight-binding model. We also explore the behaviour of the energy gap versus the nanoribbon width W . Our findings demonstrate that band gap of armchair BPNs scale as 1/W 2 , while zigzag BPNs exhibit a 1/W tendency. We analyse the different possible combinations of the zigzag edges that result two-fold degenerate and non-degenerate edge states. Furthermore, we obtain expressions for the wave functions and discuss the limit of validity of such analytical model.

“…There is no agreement yet on the field dependence of the Landau levels, as in [11,21] the dependence is linear, while in [22] the dependence is ∼ B 2/3 . In Fig.3 we show the numerically calculated Hofstadter spectrum of a finite (mesoscopic) plaquette, which exhibits a supplementary band in the middle accommodating the edge states [23].…”

Section: The Tight-binding Model and Electron-hole Symmetry Breakmentioning

confidence: 95%

“…This behavior of the transmission coefficients is proved by numerical investigation using Eq. (21), and it is shown in Fig.9a. (Of course, the unitary limit, telling that each miniband behaves as a perfect onedimensional channel, is reached only for disorder-free systems.)…”

Section: Spectral and Transport Properties Of The Quasi-flat Band mentioning

confidence: 99%

Phosphorene confined systems in magnetic field, quantum transport, and superradiance in the quasiflat band

Ostahie

Aldea

2016

Phys. Rev. B

Spectral and transport properties of electrons in confined phosphorene systems are investigated in a five hopping parameter tight-binding model, using analytical and numerical techniques. The main emphasis is on the properties of the topological edge states accommodated by the quasi-flat band that characterizes the phosphorene energy spectrum.We show, in the particular case of phosphorene, how the breaking of the bipartite lattice structure gives rise to the electron-hole asymmetry of the energy spectrum. The properties of the topological edge states in the zig-zag nanoribbons are analyzed under different aspects: degeneracy, localization, extension in the Brillouin zone, dispersion of the quasi-flat band in magnetic field.The finite-size phosphorene plaquette exhibits a Hofstadter-type spectrum made up of two unequal butterflies separated by a gap, where a quasi-flat band composed of zig-zag edge states is located.The transport properties are investigated by simulating a four-lead Hall device (importantly, all leads are attached on the same zig-zag side), and using the Landauer-Büttiker formalism. We find out that the chiral edge states due to the magnetic field yield quantum Hall plateaus, but the topological edge states in the gap do not support the quantum Hall effect and prove a dissipative behavior. By calculating the complex eigenenergies of the non-Hermitian effective Hamiltonian that describes the open system (plaquette+leads), we prove the superradiance effect in the energy range of the quasi-flat band, with consequences for the density of states and electron transmission properties.