Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus

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Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus

Vy Tran, Ryan Soklaski, Yufeng Liang, and Li Yang

Phys. Rev. B 89, 235319 – Published 26 June 2014

An article within the collection: Physical Review B 50^th Anniversary Milestones

Abstract

We report the quasiparticle band gap, excitons, and highly anisotropic optical responses of few-layer black phosphorous (phosphorene). It is shown that these materials exhibit unique many-electron effects; the electronic structures are dispersive essentially along one dimension, leading to particularly enhanced self-energy corrections and excitonic effects. Additionally, within a wide energy range, including infrared light and part of visible light, few-layer black phosphorous absorbs light polarized along the structures' armchair direction and is transparent to light polarized along the zigzag direction, making them potentially viable linear polarizers for applications. Finally, the number of phosphorene layers included in the stack controls the material's band gap, optical absorption spectrum, and anisotropic polarization energy window across a wide range.

Received 17 February 2014
Revised 4 June 2014

DOI:https://doi.org/10.1103/PhysRevB.89.235319

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Physical Review B 50^th Anniversary Milestones

These Milestone studies represent lasting contributions to physics by way of reporting significant discoveries, initiating new areas of research, or substantially enhancing the conceptual tools for making progress in the burgeoning field of condensed matter physics.

Authors & Affiliations

Vy Tran, Ryan Soklaski, Yufeng Liang, and Li Yang

Department of Physics, Washington University in St. Louis, St. Louis, Missouri 63136, USA

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Issue

Vol. 89, Iss. 23 — 15 June 2014

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Images

Figure 1
(a) The ball-stick model of few-layer phosphorous. The $x$ axis is perpendicular to and the $y$ direction parallel with the ridge direction, as indicated. (b) Top view of monolayer phosphorene. (c) The DFT-calculated (dashed lines) and GW-calculated (solid lines) band structures of monolayer phosphorous. The top of the valence band is set to be zero.
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Figure 2
The evolution of band gap calculated by different methods and optical absorption peak according to the stacking layer number of few-layer phosphorene. The power-law fitting curves are presented by dashed lines. The experimental optical peak position is read from Ref. [5].
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Figure 3
(a) VBM and CBM with Hartree potential obtained from trilayer phosphorene by DFT simulations. (b) Energy levels and wave functions of the seventh and eighth eigenvalues under the infinite quantum well with periodic potential barriers. The inset is the fitting result of the energy spacing between $Ψ_{7}$ and $Ψ_{8}$ according to the number of periodic potential barriers.
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Figure 4
Optical absorption spectra of monolayer (a), bilayer (b), trilayer (c), and bulk phosphorene [(d) and (e)] for the incident light polarized along the $x$ (armchair) direction. In particular, (d) is the optical absorbance per layer in bulk phosphorus. The single-particle optical absorption spectra are presented by dashed lines while those spectra with e-h interaction included are presented by solid lines. We employ a 0.1 eV Gaussian smearing in these plots.
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Figure 5
Optical absorption spectra of monolayer (a), bilayer (b), trilayer (c), and bulk phosphorene [(d) and (e)] for the incident light polarized along the $y$ (zigzag) direction. In particular, (d) is the optical absorbance per layer in bulk phosphorus. The single-particle optical absorption are presented by dashed lines while those spectra with e-h interaction included are presented by solid lines.
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Figure 6
(a), (b) Top views of the square of the electron wave functions of the first and second bound excitons in monolayer phosphorene [marked as $E_{1}^{1}$ and $E_{2}^{1}$ in Fig. 4]. (c) Top view of the electron wave function of the first bound exciton in trilayer phosphorene [marked as $E_{1}^{3}$ in Fig. 3]. (d), (e) Side view of the wave functions in (a) and (c), respectively. The hole, represented by a black dot, is fixed at the origin. Lines representing the atomic bonds are superimposed. The scale is in angstroms.
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