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Tunable intraband optical conductivity and polarization-dependent epsilon-near-zero behavior in black phosphorus

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Science Advances  08 Jan 2021:
Vol. 7, no. 2, eabd4623
DOI: 10.1126/sciadv.abd4623
  • Fig. 1 Device schematic and electro-optic characterization.

    (A) Anisotropic puckered crystal structure of BP (P atoms are in sp3 hybridization). (B) Device schematic and measurement scheme for hBN-encapsulated BP devices. (C) Optical microscope image of the device discussed in the main text. (D) Normalized reflection spectrum from the BP device shown in (C). (E) Color map of source-drain current variation as a function of both gate voltage and source-drain bias. (F) Gate voltage modulated source-drain current at one representative source-drain voltage (100 mV). (G) Variation of source-drain current with source-drain voltage showing linear conduction with systematic increase as gate voltage increases on the positive side; the slight dip is due to the fact that the minimal conductance point (MCP) is not at 0 V. (H and I) Interband optical modulation along the armchair (AC) and zigzag (ZZ) axis, respectively, showing the anisotropy in the electro-optic effects. (J) Schematic of changes in the AC axis optical conductivity (real part) upon doping.

  • Fig. 2 Intraband response dominated reflection modulation.

    (A and C) Measured (colored lines) and simulated/fit (black lines) intraband response mediated reflection modulation along the AC and ZZ axes. The fits have been performed between 750 and 2000 cm−1 to eliminate any band edge effect influence on the optical conductivity so that the Drude model suffices. (B and D) Fits shown separately, without offset showing a narrowing and strengthening of the Fano-like response near the hBN and SiO2 phonons with increasing charge density in BP. (E and F) Modeled false-color plot of modulation in reflection spectra (zoomed in between 800 and 1600 cm−1) as a function of doping density for the AC and ZZ directions assuming the following parameters: BP meff = 0.14 m0 (AC), 0.71 m0 (ZZ), and Si meff = 0.26 m0 (electrons) and 0.386 m0 (holes).

  • Fig. 3 Modeled dielectric function and tunable hyperbolicity.

    (A and C) Extracted real and imaginary part (denoted as ϵ1 and ϵ2) of the dielectric function for BP 2DEG along the AC axis for different doping densities. The orange shaded region shows the ENZ behavior. The region where the real part of the permittivity along the AC axis goes negative while remaining positive for the ZZ direction is the hyperbolic region and extends to frequencies beyond our measurement window. (B and D) The same for the ZZ axis. (E) False-color plot of the modeled real part of the dielectric permittivity along the AC direction assuming BP meff = 0.14 m0 showing the tunability of ENZ. (F) Calculated isofrequency contours for in-plane plasmonic dispersion (TM-polarized surface modes) showing the tunability of hyperbolicity.

  • Fig. 4 Extracted Drude weight and effective mass for BP.

    (A) Drude weight evolution obtained from fitting reflection data for AC and ZZ axes, plotted with expected Drude weight. (B) Extracted effective mass from the Drude weight fits plotted versus voltage/charge density assuming a parallel plate capacitor model and 100% gating efficiency.

Supplementary Materials

  • Supplementary Materials

    Tunable intraband optical conductivity and polarization-dependent epsilon-near-zero behavior in black phosphorus

    Souvik Biswas, William S. Whitney, Meir Y. Grajower, Kenji Watanabe, Takashi Taniguchi, Hans A. Bechtel, George R. Rossman, Harry A. Atwater

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