Normal and skewed phosphorene nanoribbons in combined magnetic and electric fields

Arsoski, V.; Grujić, Marko M.; Čukarić, N.; Tadić, M.; Peeters, F. M.

doi:10.1103/physrevb.96.125434

Cited by 10 publications

(5 citation statements)

References 29 publications

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“…Ey = 30 mV/Å) along the width. In figure 5 we observe the band structure, the conductance and the DOS in the presence of Ey which are in agreement with [12,31]. It is observed that the transverse electric field causes upward and downward shift of energy for valence and conduction sub bands, respectively.…”

Section: Resultssupporting

confidence: 77%

Optical transitions and localized edge states in skewed zigzag phosphorene nanoribbons

Shekarforoush¹,

Khoeini²,

Shiri³

2018

mat express

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Using the Tight Binding (TB) parameters extracted from Density Functional Theory (DFT) and Recursive Green's Function method (RGF), it is shown that skewed-zigzag black phosphorous (phosphorene) nanoribbons obtain large and tuneable bandgap in response to vertical and transverse electric fields. Depending on the direction of the applied field the mid-gap states could possess the localized or metallic nature i.e. non-zero mid-gap density of states. Adjustability of the bandgap and optical dipole transition matrix elements are explained based on the symmetry of involved band edge states. This promises new electronic and optical devices based on phosphorene nanoribbons.

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Section: Resultssupporting

confidence: 77%

Optical transitions and localized edge states in skewed zigzag phosphorene nanoribbons

Shekarforoush¹,

Khoeini²,

Shiri³

2018

mat express

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“…Furthermore, the difference in physical properties has potential applications. For instance, the control of external electric and magnetic fields on the electronic structure [47] and the coupling and manipulation of the edge states in multilayer PNRs [48]. However, the existed studies have only involved PNRs with above mentioned few particular edge geometries.…”

Section: Introductionmentioning

confidence: 99%

Crystallographic Characterization of Black Phosphorene and its Application in Nanostructures

et al. 2019

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The central question in the field of two-dimensional (2D) materials is how a material behaves when it is patterned at nanometer scale with different edge geometries. Due to the anisotropy inherent in the puckered structure, black phosphorene nanostructures may have more varieties of edge geometries. Here, we present a comprehensive 2D planar crystallographic characterization of phosphorene uniformly by a chiral vector (angle), from which a new type of edge atomic configuration, the slope edge geometry is discovered. The phosphorene nanoribbons (PNRs) with slope edges, like previously noticed zigzag and skewed-armchair PNRs, also own interesting twofold-degenerate edge states. These three marginal directions, together with the skewed-zigzag and armchair directions without edge states, divide a phosphorene into four regions among which the electronic property is different from each other. Further, for a PNR cutting along any possible direction, by taking into account the z-direction in structure, whether or not it owns edge states depends on the existence of periodic zigzag-like morphology along the edges. For application, moreover, we propose a PNR-based z-shaped homogenous junction with scale ∼100 nm, where the central scattering region between two PNR electrodes is a phosphorene quantum dot (PQD) of PNR segment with various edge morphologies. Interestingly, the calculated conductance by Kwant code based on tight-binding combing with scattering-matrix for the junction relies sensitively on the central PQD edge states. In specification, for the junctions of PQD with edge states the conductance exhibit a terrace with resonant oscillations near Fermi energy, otherwise the electron transport is blocked due to the absence of edge states. Remarkably, the number of oscillating peaks exactly matches to the number of sawtooth along an edge of PQD, since the discrete energy levels of the zigzag-like edge provide the transporting channels for electrons. The results here may be extended to the group-VA 2D materials for observing the electronic property of nanostructures in experiments, and provide a reference for the preparation of better nano-devices. *

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“…It is the case for thin layers of materials with anisotropic band structures, among which black phosphorene is a remarkable example, showing a large band gap and interesting optical, electrical, mechanical, and thermal properties [24]. Similar to other 2D materials with a hexagonal lattice, phosphorene nanoribbons can be fabricated with various skewed and regular zigzag or armchair edges, all of which differ in their electronic structures and transport properties [25]. Nanoribbons with regular zigzag edges host flat-band edge states near the center of the band gap, and therefore, have metallic properties.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, nanoribbons with regular armchair edges have no in-gap states and are insulating without an external field. Regardless of the edge type, nanoribbon electronic and transport properties can be tuned by applying an electric field [25].…”

Section: Introductionmentioning

confidence: 99%

Exotic quantum states in multilayer phosphorene nanoribbons in electric and magnetic fields

Arsoski

Tadić

2023

Phys. Scr.

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Using the tight-binding method, we modeled the energy spectra of multilayer phosphorene nanoribbons in a perpendicular electric field and in-plane magnetic field. Phosphorene nanosheets have a highly anisotropic honeycomb-like lattice. Their band gap is wider than that of their bulk counterparts, and armchair and zigzag edges of either skewed or regular type terminate the nanowire edges. Zigzagand various skewed edges support states whose wave functions decay exponentially from an edge. These states are virtually dispersionless and split the band gap. In principle, regular armchair edges do not host edge states. Thus, the energy spectrum in thiscase has a wide band gap. Here, we consider nanoribbons composed of multilayer phosphorene with regular armchair edges. A wide direct energy band gap exists when external fields are absent, but its width decreases when a perpendicular electric field is applied. The Dirac-like cones cross-section emerges at the zone center for a particular field value, named the lowest critical field. Although spin-orbit coupling was not included in the model, there is a small gap at the anticrossing site. The local density of states shows that the conduction- and valence-band states near the anticrossing are localized on the top and bottom surfaces of the nanoribbon. A thorough analysis of the interlayer coupling integrals indicates that for sufficiently thin phosphorene slabs, the electron and hole states at the opposite sides of the slab couple mutually strongly, despite the tendency of an external electric field to separate them. A further increasein the electric field induces an inversion between the conduction and valence band states in the zone center, which is inherent to topological insulators. However, sharp anticrossings at the zone center emerged for certain higher field values, named highercritical fields. Furthermore, when an in-plane magnetic field is applied, the conduction and valence band states shift, causing the dispersion to twist around the center of the k-space. Therefore, the band gap is indirect and closes for a sufficiently large magneticfield. A similar effect is observed in quantum spin Hall insulators, in which an inplane magnetic field induces a semiconductor-to-semimetal transition. We conclude that the band inversion and topological-like features induced by external fields can beattributed to the strong interlayer coupling inherent to multilayered materials with anisotropic honeycomb lattices.

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Normal and skewed phosphorene nanoribbons in combined magnetic and electric fields

Cited by 10 publications

References 29 publications

Optical transitions and localized edge states in skewed zigzag phosphorene nanoribbons

Optical transitions and localized edge states in skewed zigzag phosphorene nanoribbons

Crystallographic Characterization of Black Phosphorene and its Application in Nanostructures

Exotic quantum states in multilayer phosphorene nanoribbons in electric and magnetic fields

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