Scaling laws of band gaps of phosphorene nanoribbons: A tight-binding calculation

Sisakht, Esmaeil Taghizadeh; Zare, Mohammad; Fazileh, Farhad

doi:10.1103/physrevb.91.085409

Cited by 117 publications

(75 citation statements)

References 41 publications

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“…In such systems, electrons effectively behave as light massive Dirac fermions along the armchair direction and as heavy fermions along the zigzag direction, consistent with ab initio results [14,[20][21][22] and experimental ARPES measurements of the band structure [23]. The manifestations of anisotropy are tightly connected to the lattice symmetry.…”

Section: Introductionsupporting

confidence: 64%

Optical third harmonic generation in black phosphorus

Hipolito

Pedersen

2018

Phys. Rev. B

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We present a calculation of third harmonic generation (THG) for two-band systems using the length gauge that avoids unphysical divergences otherwise present in the evaluation of the third-order current density response. The calculation is applied to bulk and monolayer black phosphorus (bP) using a nonorthogonal tight-binding model. Results show that the low-energy response is dominated by mixed inter-intraband processes and estimates of the magnitude of THG susceptibility are comparable to recent experimental reports for bulk bP samples.

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Section: Introductionsupporting

confidence: 64%

Optical third harmonic generation in black phosphorus

Hipolito

Pedersen

2018

Phys. Rev. B

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“…The latter involves two main parameters of unlike signs corresponding to two nearest-neighbor hopping integrals, and a number of less-relevant long-range parameters needed to accurately reproduce the quasiparticle VB and CB edges of monolayer and bilayer BP. The model has been successfully applied in a number of studies including those related to phosphorene nanoribbons [21,22], electric [21,23] and magnetic fields [16,24], different kinds of disorder [24], and realistic modeling of field-effect electronic devices [25]. However, the applicability of that model is limited to single-and bilayer BP, whereas thicker (experimentally available) samples cannot be considered.…”

Section: Introductionmentioning

confidence: 99%

Toward a realistic description of multilayer black phosphorus: FromGWapproximation to large-scale tight-binding simulations

Руденко¹,

Yuan²,

Katsnelson³

2015

Phys. Rev. B

214

147

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We provide a tight-binding model parametrization for black phosphorus (BP) with an arbitrary number of layers. The model is derived from partially self-consistent GW0 approach, where the screened Coulomb interaction W0 is calculated within the random phase approximation on the basis of density functional theory. We thoroughly validate the model by performing a series of benchmark calculations, and determine the limits of its applicability. The application of the model to the calculations of electronic and optical properties of multilayer BP demonstrates good quantitative agreement with ab initio results in a wide energy range. We also show that the proposed model can be easily extended for the case of external fields, yielding the results consistent with those obtained from first principles. The model is expected to be suitable for a variety of realistic problems related to the electronic properties of multilayer BP including different kinds of disorder, external fields, and many-body effects.

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“…A relevant electronic property for purposes of optical applications and quantum confinement effect is related to the scaling behaviour of the band gap with ribbon width, as previously investigated in the literature for 2D materials, for instance: graphene nanoribbons 1,2,29-31,41,42 , boron nitride nanoribbons 43,44 , silicene nanoribbons [45][46][47][48] and phosphorene nanoribbons 23,32,33 . Recent studies via first principles calculations have indicated that the band gaps of BPNs possess different scaling laws depending on the edge type and thus suggesting its usage as a convenient tool for identifying acBPNs and zzBPNs samples with similar geometric widths, since the previous results have shown that the band gap is larger in zzBPNs than in acBPNs for the same ribbon width.…”

Section: Scaling Laws Of Band Gaps For Phosphorene Nanoribbonsmentioning

confidence: 99%

“…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. Recent studies of BPNs have been based on a tight-binding approach [32][33][34] and via first-principles simulations 23,24,35 that, while giving reasonably precise results for small structures, can become computationally expensive for larger structures. In addition, pure computational approaches are not appropriate to give physical insights into the basic mechanisms behind the results, which is of fundamental importance for a pure theoretical understanding.…”

Section: Introductionmentioning

confidence: 99%

Boundary conditions for phosphorene nanoribbons in the continuum approach

et al. 2016

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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.

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Scaling laws of band gaps of phosphorene nanoribbons: A tight-binding calculation

Cited by 117 publications

References 41 publications

Optical third harmonic generation in black phosphorus

Optical third harmonic generation in black phosphorus

Toward a realistic description of multilayer black phosphorus: FromGWapproximation to large-scale tight-binding simulations

Boundary conditions for phosphorene nanoribbons in the continuum approach

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