Screening and plasmons in pure and disordered single- and bilayer black phosphorus

Jin, Fengping; Roldán, Rafael; Katsnelson, M. I.; Yuan, Shengjun

doi:10.1103/physrevb.92.115440

Cited by 49 publications

(65 citation statements)

References 70 publications

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“…From DFT calculations of the band structure in BP [38], we can anticipate that inclusion of more bands should also produce broadening of the plasmon resonance at elevated electron temperature. The difference between the two orientations of BP due to crystal anisotropy is clear, with two different plasmon bands that share in common the dispersion dependence ω ∝ √ q characteristic of 2D systems, in agreement with previous calculations [45]. We conclude that thermally activated plasmon modes resemble those enabled by doping, but we emphasize the transient character of the former, which can be sustained during times scales of 100's fs, because relaxation of electronic heat to phonon modes takes place.…”

Section: Fig 3 Chemical Potential μsupporting

confidence: 77%

Nonlocal plasmonic response of doped and optically pumped graphene, MoS2 , and black phosphorus

2017

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Plasmons in two-dimensional (2D) materials have emerged as a new source of physical phenomena and optoelectronic applications due in part to the relatively small number of charge carriers on which they are supported. Unlike conventional plasmonic materials, they possess a large Fermi wavelength, which can be comparable with the plasmon wavelength, thus leading to unusually strong nonlocal effects. Here, we study the optical response of a selection of 2D crystal layers (graphene, MoS 2 , and black phosphorus) with inclusion of nonlocal and thermal effects. We extensively analyze their plasmon dispersion relations and focus on the Purcell factor for the decay of an optical emitter in close proximity to the material as a way to probe nonlocal and thermal effects, with emphasis placed on the interplay between temperature and doping. The results are based on tight-binding modeling of the electronic structure combined with the random-phase approximation response function in which the temperature enters through the Fermi-Dirac electronic occupation distribution. Our study provides a route map for the exploration and exploitation of the ultrafast optical response of 2D materials.

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Section: Fig 3 Chemical Potential μsupporting

confidence: 77%

Nonlocal plasmonic response of doped and optically pumped graphene, MoS2 , and black phosphorus

2017

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“…Therefore, BP films are treated as a model system to host the anisotropic and hyperbolic 2D plasmons . Great theoretical and experimental efforts have been devoted to investigating the plasmons in this natural anisotropic material. Below, we discuss the theoretical studies on the plasmon dynamics of BP films and the experimental progress in detecting BP plasmons, as well as the potential applications of plasmons in anisotropic 2D materials.…”

Section: Plasmons In Anisotropic 2d Materialsmentioning

confidence: 99%

“…Due to the highly anisotropic in‐plane dynamics, a number of theoretical works were performed to study the plasmons in BP . Low et al studied collective electron excitations in monolayer and multilayer BP within the random phase approximation (RPA) using an effective low‐energy Hamiltonian .…”

Section: Plasmons In Anisotropic 2d Materialsmentioning

confidence: 99%

“…In the past few years, tremendous attention has been given to graphene plasmons, with a remarkable manifestation of high tunability and low loss . Recently, a number of theoretical efforts have been devoted to studying the plasmonic properties of BP, where anisotropic plasmon dispersions occur due to its band anisotropy . Fascinatingly, the hyperbolic plasmon polaritons, whose iso‐frequency contour is a hyperbola, are predicted to naturally exist in BP films, which originate from the coupling between the intraband and interband optical conductivity .…”

Section: Introductionmentioning

confidence: 99%

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The Optical Properties and Plasmonics of Anisotropic 2D Materials

Wang

Zhang

Huang

et al. 2019

Advanced Optical Materials

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In the fast growing 2D materials family, anisotropic 2D materials, with their intrinsic in‐plane anisotropy, exhibit a great potential in optoelectronics. One such typical material is black phosphorus (BP), with a layer‐dependent and highly tunable bandgap. Such intrinsic anisotropy adds a new degree of freedom to the excitation, detection, and control of light. Particularly, hyperbolic plasmons with hyperbolic q‐space dispersion are predicted to exist in BP films, where highly directional propagating polaritons with divergent densities of states are hosted. Combined with a tunable electronic structure, such natural hyperbolic surfaces may enable a series of exotic applications in nanophotonics. Herein, the anisotropic optical properties and plasmons (especially hyperbolic plasmons) of BP are discussed. In addition, other possible 2D material candidates (especially anisotropic layered semimetals) for hyperbolic plasmons are examined. This review may stimulate further research interest in anisotropic 2D materials and fully unleash their potential in flatland photonics.

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“…[21][22][23][24][25] In particular, it is possible to drive a semiconductor to semimetal transition, with the appearance of Dirac like dispersion. [16][17][18]26 In this paper we study the electronic spectrum of biased BP in the presence of a strong magnetic field. For this we use a tight-binding model which properly accounts for the band structure in a wide energy window of the spectrum.…”

Section: Introductionmentioning

confidence: 99%

Quantum Hall effect and semiconductor-to-semimetal transition in biased black phosphorus

Yuan¹,

Veen²,

Katsnelson³

et al. 2016

Phys. Rev. B

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We study the quantum Hall effect of 2D electron gas in black phosphorus in the presence of perpendicular electric and magnetic fields. In the absence of a bias voltage, the external magnetic field leads to a quantization of the energy spectrum into equidistant Landau levels, with different cyclotron frequencies for the electron and hole bands. The applied voltage reduces the band gap, and eventually a semiconductor to semimetal transition takes place. This nontrivial phase is characterized by the emergence of a pair of Dirac points in the spectrum. As a consequence, the Landau levels are not equidistant anymore, but follow the εn ∝ √ nB characteristic of Dirac crystals as graphene. By using the Kubo-Bastin formula in the context of the kernel polynomial method, we compute the Hall conductivity of the system. We obtain a σxy ∝ 2n quantization of the Hall conductivity in the gapped phase (standard quantum Hall effect regime), and a σxy ∝ 4(n + 1/2) quantization in the semimetalic phase, characteristic of Dirac systems with non-trivial topology.

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Screening and plasmons in pure and disordered single- and bilayer black phosphorus

Cited by 49 publications

References 70 publications

Nonlocal plasmonic response of doped and optically pumped graphene, MoS2 , and black phosphorus

Nonlocal plasmonic response of doped and optically pumped graphene, MoS2 , and black phosphorus

The Optical Properties and Plasmonics of Anisotropic 2D Materials

Quantum Hall effect and semiconductor-to-semimetal transition in biased black phosphorus

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