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Localized Surface Plasmons in Nanostructured Monolayer Black Phosphorus Zizhuo Liu, and Koray Aydin Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.5b05166 • Publication Date (Web): 06 May 2016 Downloaded from http://pubs.acs.org on May 9, 2016

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Localized Surface Plasmons in Nanostructured Monolayer Black Phosphorus Zizhuo Liu and Koray Aydin∗ Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL 60208, United States E-mail: [email protected]

Abstract Plasmonic materials provide electric-field localization and light confinement at subwavelength scales due to strong light-matter interaction around resonance frequencies. Graphene has been recently studied as an atomically thin plasmonic material for infrared and terahertz wavelengths. Here, we theoretically investigate localized surface plasmon resonances (LSPR) in a monolayer, nanostructured black phosphorus (BP). Using finite-difference time-domain simulations, we demonstrate LSPRs at mid-infrared and far-infrared wavelength regime in BP nanoribbon and nanopatch arrays. Due to strong anisotropic in-plane properties of black phosphorus emerging from its puckered crystal structure, black phosphorus nanostructures provide polarization dependent, anisotropic plasmonic response. Electromagnetic simulations reveal that monolayer black phosphorus nanostructures can strongly confine infrared radiation in an atomically thin material. Black phosphorus can find use as a highly anisotropic plasmonic devices. ∗

To whom correspondence should be addressed

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Keywords Black Phosphorus, Plasmonics, LSPR, 2D Materials, Anisotropy

Introduction Atomically thin two-dimensional (2D) materials have received burgeoning amount of interest in recent years due to exciting physical properties. They exhibit interesting electronic, optical, mechanical and thermal properties due to their mono to few-layer thicknesses. 1–4 2D materials offer a new class of platform to achieve novel electronic and photonic properties in ultra-compact sizes. Although such materials have inherently monolayer to few-layer thicknesses, it has been showed that 2D materials can interact strongly with the incident light. In particular, graphene emerged as a monolayer plasmonic platform. 5–8 Theoretical and experimental studies confirmed that both propagating 9,10 and localized 11–13 surface plasmon modes can be excited in an atomically thin, nanostructured graphene. Until the discovery of the graphene as a plasmonic material, noble metals such as silver and gold have been the material of choice both for fundamental and applied research. However, 2D plasmonic materials provide a unique opportunity by confining plasmons in an extremely thin optical material and also represent a great challenge for light-matter interactions due to their inherent atomically thin thickness. With such highly localized electric fields in 2D plasmonics, it is possible to build and integrate devices in smaller sizes that exhibit novel electronic and optical properties compared with traditional bulk plasmonic materials. By patterning periodic nanostructures in 2D materials, resonances can be observed optically by measuring the extinction spectra. 14,15 Black phosphorus (BP) is a recently emerging 2D layered material that can be exfoliated to few layers and monolayer. 16–23 In a monolayer BP, the phosphorus atoms form a hexagonal lattice with a puckered structure resulting in in-plane anisotropic properties. Black 2


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phosphorus has been recently investigated for potential applications including field effect transistors, 24–27 heterojunction p-n diode, 28 photovoltaic devices, 29 and photodetectors. 30 The Raman scattering spectra and photoluminescence measurements from BP revealed its highly anisotropic properties. 31 A recent theoretical paper by Low et al. reports collective plasmonic excitations in BP. 32 It has been shown that mono to few-layer BP supports anisotropic plasmonic dispersion due to different effective mass along different crystal directions. Here, we propose and numerically demonstrate that localized surface plasmons can be excited in nanostructured monolayer black phosphorus. We present the study of the electromagnetic response of periodically patterned black phosphorus sheet. We consider the parameters varied in a wide range and the different absorption spectrum is compared due to the inherent anisotropy in BP. In particular, we analyze the confinement of the electromagnetic field in both BP nanoribbon and nanopatch arrays. We demonstrate the anisotropic behavior by replacing BP nanoribbons in x direction (armchair direction) and y direction (zigzag direction). The performance of the structures may allow for the realization of new plasmonic devices which will take advantage of the directional dependence of its plasmon properties.

Results and discussion The photonic properties of a monolayer BP can be described by employing a simple semiclassical Drude model. The conductivity 32 is given as: iDj σjj = π(ω + iη¯h )

πe2 n Dj = mj

(1)

where j denotes the direction concerned and Dj is the Drude weight. A similar expression has been utilized for graphene 33 with D =

µe2 h2 ¯

. The electron mass along the x direction and

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y direction 32 can be described by:

mcx =

h ¯2 2γ 2 ∆

mcy =

+ ηc

h ¯2 2νc

(2)

The parameters are determined by fitting the known anisotropic mass. For monolayer BP, 32 we have γ =

4a π

eVm , ∆ = 2 eV, ηc =

h2 ¯ , 0.4m0

νc =

h2 ¯ . 1.4m0

We choose the electron doping

n = 1013 cm−2 as well as η = 10 meV to describe the relaxation rate. a is the scale length of the BP and

π a

is the width of the Brillouin Zone.

The dielectric function 34 for a thin film reads(with 2D conductivity):

ǫjj = ǫr +

iσjj ǫ0 ωa

(3)

For a monolayer BP, the relative permittivity 35 is given as ǫr = 5.76. In the finite-difference time-domain (FDTD) simulations, BP film thickness (a) is chosen to be 1 nm. This audacious assumption will speed up the simulation time and resemble the real results as long as the simulation mesh is fine enough in the BP film. In our simulation setup, we choose the mesh to be 0.25 nm. The rightness of using finite thickness to simulate 2D film and more details about the simulation are discussed in the Supporting Information. In our designs, periodic monolayer BP nanoribbons are placed on a transparent insulator and an optically thick gold mirror. The metallic mirror is used to reflect light and suppress the transmission. Compared with free standing BP nanoribbons, the dielectric layer between the BP and gold mirror forms a Fabry-Perot cavity, therefore increases the interaction of light with monolayer BP. Dielectric thickness can be chosen to maximize the absorption using Fabry-Perot interference (see Supporting Information). In our simulations, the dielectric thickness is chosen to be 5 µm. We performed full-field electromagnetic simulations with the wavelengths between 20 - 80 µm. For the optical constants in the simulation, we used a constant, non-dispersive refractive index of n = 1.7 for the dielectric spacer and perfect electric conductor model for the metallic mirror. 4


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Figure 1: (a) Schematics of periodically patterned BP nanoribbons. (b) Anisotropic absorption spectrum can be observed in BP ribbon arrays along x and y direction. The arrows in the inset indicate the polarization of the electric field. (c) Calculated electric field amplitude, Ez for one BP nanoribbon unit cell(along x direction). (d) Calculated total electric field intensity (|E|2 ) for one BP nanoribbon unit cell(along x direction). Electromagnetic field is localized around the edges of the nanoribbon.

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Localized plasmon resonances can be excited with an incident light when electric field is perpendicular to the nanoribbons (Fig. 1a). Since metallic mirror suppresses the transmission, absorptivity (A) can be calculated with a simple formula A = 1 - R, where R is the reflectivity from the simulated structure. Since BP exhibits anisotropic optical and electronic properties along x and y directions, we anticipate polarization-dependent localized plasmon resonance behavior for monolayer BP nanoribbons along the armchair and zigzag directions. In order to investigate the effect of anisotropic optical properties on the plasmonic behavior of the BP, we performed electromagnetic (EM) simulations for two different nanoribbon structures as shown in Fig. 1b. The structural parameters for both x (armchair) and y (zigzag) directions are chosen to be the same. Having the period p = 250 nm and the monolayer BP ribbon width w = 150 nm, the absorption spectrum is plotted in Fig. 1b. For both cases, an absorption peak has been observed for s polarized light. Due to the mass anisotropy, the smaller mass along x indicates higher resonance frequency therefore shorter wavelength. Compared with the zigzag direction (red line), the absorption peak in armchair direction is higher and the resonance linewidth is narrower. This result suggests that the black phosphorus is optically more lossy for the zigzag direction at the corresponding resonance wavelength. As mentioned before, since graphene has also been described with the similar Drude model but with different Drude weight, the plasmons in BP naonribbons also behave differently in scales compared with graphene nanoribbons (see Supporting Information). The side-view electric field profile of the vertical component (Ez ) shown in Fig. 1c is plotted with the case of the nanoribbon arrays along x direction at the resonance wavelength (31.5 µm). Positive and negative dipoles can be easily seen indicating a localized plasmon resonance behavior. The edges of the BP nanoribbon distort the in-plane component of the electric field. And for the edge surface plasmon modes, the electric field enhancement is mostly pronounced around the edges, which resemble the edge modes in graphene ribbon structures. 36 Fig. 1d and the supporting video confirm that the total electric field intensity is localized around the two

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edges of the BP nanoribbon.

Figure 2: (a,b) Schematics and perspective side view of the BP ribbon arrays along x and y direction separately. (c,d) Absorption map of two directions with fixed period 250 nm and various widths. (e,f) Absorption spectra for various widths of two directions. We have also performed additional simulations for different nanoribbon widths as well as different periodicities in order to understand the effect of the nanoribbon array parameters on the observed plasmon resonance behavior. In Fig. 2, we summarize our results for monolayer BP nanoribbon arrays with various widths. In these simulations, the periodicity of the arrays is kept at 250 nm, as shown from the side-view in Fig. 2a and Fig. 2b for ribbons along both x and y directions. The width is changed from 0 nm (no BP) to 250 nm (continuous BP). 7


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Absorption spectra as a function of wavelength and varying widths for nanoribbon arrays along x and y directions are plotted in Fig. 2c and Fig. 2d, respectively. It is clear that the absorption peak position, therefore the resonance wavelength increases to longer wavelengths with increasing nanoribbon width, which follow the scaling behavior of localized plasmons. The wider BP nanoribbons support the electromagnetic oscillations at longer wavelengths. The shift trends are similar for both armchair and zigzag directions, but the absorption peak is much larger for armchair direction (x). In Fig. 2e and Fig. 2f, we plot the absorption spectra for different nanoribbon widths along x and y directions separately. It can be seen that with increasing width, the resonance peaks become broader due to the increasing optical losses at longer wavelengths. One interesting property we note is that there is an absorption maximum of 0.47 for 190 nm width nanoribbon with a periodicity of 250 nm. Additional simulations are performed for different periodicities changing from p = 150 nm to 500 nm for fixed nanoribbon width of w = 150 nm. Results are summarized in Fig. 3. For small periodicities (periodicity is closer to the nanoribbon width), there is a strong coupling between neighboring nanoribbons resulting in a change for the resonance wavelength positions. The absorption increases for reduced periodicities mainly due to the smaller gap between the nanoribbons and stronger inter-ribbon coupling. However, for larger periodicities, where the interaction between neighboring BP nanoribbons are weak, the position of the absorption peak shifts to shorter wavelengths. And the total absorption decreases due to the smaller volume of the BP in certain areas. For the large period case, the resonance almost stays at the same wavelength as expected for a localized plasmon resonance, and the plasmon wave vector follows the trend q ∼

π 37 . w

Previous results in graphene ribbons have shown the

existence of phase shift of the plasmons upon reflection, 13,38 which might also occur in BP nanoribbons. More discussions could be found in the the Supporting Information. Inspired by the anisotropic plasmonic response of the BP nanoribbon arrays along x and y direction, we can construct BP nanopatch arrays (square shaped isolated BP nanostructures) as shown in Fig. 4a. For consistency and ease of comparison with earlier discussions, we

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Figure 3: (a,b) Absorption map of two directions with fixed width 150 nm and various periods. (c,d) Absorption spectra for various periods of two directions.

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choose the nanopatch array parameters as p = 250 nm and w = 150 nm in both x and y directions. When light is polarized along the x direction (0◦ ), we observe a high absorption resonance peak at shorter wavelength. For y-polarization, i.e., the polarization angle is 90◦ , the resonance shifts to longer wavelengths as expected due to higher effective mass along the zigzag (y) direction. Compared with Fig. 1b, the resonance wavelengths are kept at the same position as expected. But the absorption intensity is reduced which can be explained due to the discontinuity of the ribbons in the case of nanopatch arrays resulting in lower BP volume. Interestingly, for polarization angle of 45◦ , localized plasmon resonances for armchair and zigzag directions can be excited simultaneously. Absorption intensity reduces at respective plasmon resonance wavelengths due to reduced light intensity at corresponding x and y directions. In order to understand the resonance behavior for monolayer BP nanopatch arrays, we calculated the amplitude and electric field intensity using EM simulations. Fig. 4c plots the amplitude of the Ez for x-polarization (0◦ ) right above the BP film and clearly illustrates the electric dipole behavior expected in structures exhibiting localized plasmon resonances. Total electric field intensity profile shown in Fig. 4d implies that the electric field is mostly localized at the left and right edges corresponding to the polarization of the light. The electric field intensity is highest around four corners of the square due to the sharpness in shape. In conclusion, we propose and numerically demonstrate localized surface plasmons modes in monolayer BP using nanoribbon and nanopatch arrays. Anisotropic behavior in the absorption spectra are predicted when exciting BP plasmons along two different directions (armchair and zigzag). Various structure parameters are examined to analyze the material properties and the localized nature. Furthermore, we find that the electric field is mostly localized around the edges of the structure. It is possible to design a symmetric metasurface with BP and fulfill the polarization conversion due to the anisotropic absorption. And BP could also be used to build a polarization sensor at IR wavelengths even with symmetrical

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Figure 4: (a) Schematics of periodically patterned BP nanopatches. (b) Anisotropic absorption spectrum can be observed when applying light with different angles. (c) Calculated electric field amplitude, Ez for one BP nanopatch unit cell(along x direction). (d) Calculated total electric field intensity (|E|2 ) for one BP nanopatch unit cell(along x direction).

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structures. Although it is still a big challenge for current research to obtain large monolayer BP film with either exfoliation method or chemical vapor deposition method, our proposed structures provide the guidelines for future experimental research on new 2D anisotropic plasmonics with BP and directional dependent plasmonic devices.

Acknowledgement This material is based upon work supported by the Materials Research Science and Engineering Center (NSF-MRSEC) (DMR-1121262) of Northwestern University. We also acknowledge partial support from the Institute for Sustainability and Energy at Northwestern (ISEN) through ISEN Booster Award.

Notes The authors declare no competing financial interests.

Supporting Information Available Details of the simulation method and data, discussions about dielectric thickness as well as additional figures and video for the electrical field can be found in supporting material. This material is available free of charge via the Internet at http://pubs.acs.org/.

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