Interband π Plasmon of Graphene Nanopores: A Potential Sensing

Article pubs.acs.org/JPCC

Interband π Plasmon of Graphene Nanopores: A Potential Sensing Mechanism for DNA Nucleotides Bashir Fotouhi, Vahid Ahmadi,* Mostafa Abasifard, and Ramin Roohi School of Electrical and Computer Engineering, Tarbiat Modares University, Tehran, Iran ABSTRACT: We propose a potential sensing mechanism for DNA nucleotides using the interband π surface plasmon resonance (SPR) of graphene nanopores. The SPR and field-enhancement properties were investigated using the discrete dipole approximation (DDA) and the finite-difference-time-domain (FDTD) methods, respectively. For graphene nanopores smaller than 10 nm in length, increasing the pore diameter red shifts the SPR peak wavelength, and for larger sheets, the SPR peak wavelength is essentially unchanged by variations in the pore diameter. Presentation of a single nucleotide to the pore significantly changes the SPR properties of the graphene nanopore, and each nucleotide has unique SPR properties. Each nucleotide induces a shift of 2−12 nm in the peak wavelength of each SPR mode, and if all of the modes are considered simultaneously, the type of DNA nucleotide present can be clearly determined. Our results show that the small-size-sensitive interband π plasmon in graphene nanopore is probably applicable as a new sensing mechanism for DNA nucleotides.

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materials.37 Simulations16,37 have shown acceptable agreement between modeling and experimental data.8,28 In the field of nanopore DNA sequencing, in most cases, the main purpose of modeling is to bring a new idea or class of DNA-sequencing mechanisms into the field.15,22−24,38 In some cases, molecular dynamics simulations are performed to predict the translocation behavior of a DNA molecule through a nanopore.22,24 In the present work, we studied possible application of the interband π plasmon in graphene nanopores as a new sensing mechanism for DNA nucleotides. Surface plasmon resonance (SPR) and plasmon propagation in graphene have attracted considerable attention because of their important applications in nanophotonics, metamaterials, gap detection, and surfaceenhanced spectroscopy.39,40 The sources of plasmons in graphene are collective intraband excitation of the π* conductance electrons (free-carrier plasmon at 0−3 eV), interband excitations of the π valence electrons (π plasmon at 4−12 eV), and interband excitations of all valence electrons (π + σ plasmon at 14−33 eV).41−46 Intraband plasmons of graphene represent the dominant collective mode in doped or electrostatically biased graphene. Previous studies on plasmons in graphene mainly focused on this mode, which occurs in the terahertz or infrared range of light. At terahertz and infrared frequencies, graphene plasmon resonances can be tuned by electrostatic doping and changes of the ribbon width.41,46−48 Recent studies showed that the plasmon peaks in nanometersize graphene ribbons are tunable with respect to size variations.49 Through the presence of single point defects,

INTRODUCTION Sequencing the human genome is the main foundation of new medical and biological research. Biological1 and solid-state2−4 nanopore-based sequencers have been under development for the past two decades and have been studied experimentally3−6 and theoretically.7−10 The DNA molecule passes through the pore, and the sequence of its nucleotides is identified using ionic or tunneling currents.11−13 However, the success of such measurements depends on attaining single-nucleotide resolution.8 Fast DNA translocation, slow sensing mechanisms, and high membrane thicknessesz are the main challenges.8,14 Graphene, the thinnest material ever measured, which has already been used as a platform in nanopore sensors, might overcome these limitations.8,15 Previous experiments showes that DNA could be driven through a graphene nanopore, and extensive efforts have been devoted to finding fast sensing mechanisms and slowing DNA translocation. Also, new materials such as hexagonal boron nitride (h-BN),16,17 silicene,18 and molybdenum disulfide (MoS2)17 are currently being used in nanopore DNA sequencing. Recent advances suggest that capacitance measurements,8,15,19 Y-shaped carbon nanotubes,20 bilayer graphene nanopores,21 charged graphene nanopores,22 MoS2 membranes,23 surface plasmons,24,25 magnetic or optical tweezers,26−28 and graphene nanopores with self-integrated optical antenna29 could be used in nucleotide detection and translocation speed reduction. Graphene has excellent mechanical flexibility, biocompatibility, high electron mobility, and also unique optical properties.30−36 Molecular dynamics simulations16,17 and density functional theory calculations37 have been widely used to simulate the application of ionic and tunneling currents in DNA sequencing devices based on solid-state, biological, and two-dimensional © 2016 American Chemical OSociety

Received: March 3, 2016 Revised: May 14, 2016 Published: June 14, 2016 13693

DOI: 10.1021/acs.jpcc.6b02259 J. Phys. Chem. C 2016, 120, 13693−13700

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The Journal of Physical Chemistry C interband π plasmon can be locally enhanced at the atomic scale and yield unprecedented levels of field confinement, demonstrating that such plasmons are sensitive to small sizes and strongly localized.50 Generally, when the plasmon frequency increases, localized modes are generated as a result of the confinement from the graphene edge. The SPR properties of the interband π plasmons of monolayer and multilayer graphene nanodisks show strong small-size and fieldenhancement effects.51 In this study, we investigated the interband π plasmon properties and corresponding field-enhancement of graphene nanosheet using the discrete dipole approximation52 (DDA) and the finite-difference-time-domain53 (FDTD) methods. Then, we looked into the effects of making a nanometerdiameter pore at the center of a monolayer graphene nanosheet with the aim of developing a new sensing methodology for DNA nucleotides. Finally, we investigated the effects of inserting a DNA nucleotide into a nanopore, which significantly changes the SPR properties. We envision that each DNA nucleotide will produce a unique SPR spectrum that can be measured as the nucleotide passes through the pore. Despite technical challenges, this study suggests that the interband π plasmon of graphene, because of small-size effects, provides strong motivation for the development of a new class of sensing materials for DNA nucleotides.

and Eloc are the incident and local electric fields, respectively, at the destination point; parameter k is the wavenumber; Veff is the target volume; and αi and Pi are the polarizability and polarization, respectively, at the destination point. Figure 1 schematically illustrates the proposed structure, a monolayer graphene nanosheet (Figure 1a), a graphene nanopore (Figure 1b), and a graphene nanopore with a DNA nucleotide (Figure 1c). A transverse electric field propagating along the x axis irradiates the system (Figure 1). Using the DDA method, the extinction efficiency of the structure is obtained as a function of the sheet length (a), pore diameter (D), and incident wavelength (λ). Also, we insert a DNA nucleotide into the pore (Figure 1c) and obtain the extinction efficiency, which demonstrates how an interband π plasmon can be used as a possible detection mechanism for DNA nucleotides. In our method, the combination of a graphene nanosheet with a nanopore and a DNA nucleotide, illustrated in Figure 1, is modeled as a three-dimensional lattice of dipoles. We used the optical properties of graphene measured by Nelson et al.60 for each dipole in the lattice of Figure 1a. For the structures shown in Figure 1b,c, the optical properties of the dipoles in the nanopore regions are those of air and a DNA nucleotide (A, T, C, or G), respectively. The optical properties of water are used for the dipoles between the DNA nucleotide and the edge of the graphene nanopore and the surrounding medium. We employed the DDSCAT 7.0 code developed by Draine and Flatau52 to investigate the SPR properties of the proposed structures. Using the FDTD approach,53 we calculated the nearfield enhancement at the top surface of the graphene. However, no complete anisotropic refractive-index data have been reported for graphene in the deep-ultraviolet to blue range of light.51,60 The refractive indexes of Nelson et al.60 and Kravets et al.61 were utilized to model graphene according to the DDA method by Hu et al.51 and Amendola,62 respectively. We used polycrystalline chemical-vapor-deposited monolayer graphene model provided recently by Nelson et al.51,60 The frequencydependent complex refractive index values for adenine (A), thymine (T), guanine (G), and cytosine (C) nucleotides obtained63,64 using Kramers−Kronig analysis65 of absorption spectra were utilized to model the DNA nucleotides by the DDA method.

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THEORETICAL CALCULATIONS The DDA method was used to calculate far-field electromagnetic radiation scattering, absorption, and extinction for targets of arbitrary shapes with complex refractive indexes and sizes on the order of or smaller than the incident wavelength.51,52 Recently, DDA was used to analyze the surface plasmon properties of materials of different shapes,54,55 and the method showed acceptable agreement between modeling and experiment.56−59 In the DDA method, an arbitrary-shaped target is divided into a cubic lattice of N dipoles. The interdipole separation is sufficiently small compared to the target length and the ambient wavelength. A study by Draine and Flatau52 confirmed that the DDA method is applicable if | m|kd ≪ 1, where m is the complex refractive index, k is the wavenumber, and d is the above-mentioned interdipole separation. Graphene is modeled by a cubic lattice of N = 3 × M × M dipoles. As already mentioned, M should be defined large enough to satisfy the condition |m|kd ≪ 1. Approximately, 6 × 105 dipoles were used in the calculations. For each dipole, its position (ri) and polarizability (αi) are needed. In this method, the extinction (Qext), absorption (Qads), and scattering efficiencies are defined by Cext =

Cabs =

Q ext = Veff =

RESULTS AND DISCUSSION SPR Properties of Graphene Nanosheets. The far-field extinction efficiencies of a graphene nanosheet with a fixed thickness of t = 0.34 nm and different length values from 3 to

N

4πk |E0|2

* j . Pi) ∑ Im(E loc,

4πk |E0|2

∑

(1)

i=1

i=1 N

Cext πaeff

■

2

,

4 πaeff 3 3

{Im[P. (α i

Q abs =

i

−1

)*P*i ] −

2 3 2 k |Pi| 3

}

(2)

Cabs πaeff 2

(3) Figure 1. Schematic representations of the proposed structures: (a) graphene nanosheet with length a, (b) graphene nanopore with length a and pore diameter D, and (c) DNA nucleotide inserted in a nanopore. A plane wave impinges on the structures with the electric field component parallel to the y axis and propagating along the x axis.

(4)

where aeff is the radius of the effective volume; Cext and Cabs are the extinction and absorption cross sections, respectively; E0 13694

DOI: 10.1021/acs.jpcc.6b02259 J. Phys. Chem. C 2016, 120, 13693−13700

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The Journal of Physical Chemistry C 250 nm are shown in Figure 2. If the angle between the direction of the x axis and the polarization direction is set to 0° or 90° (Figure 1), one can obtain longitudinal and transverse modes, respectively. Our study was performed for the transverse mode, because of the fact that, in monolayer graphene, the transverse mode dominates and the longitudinal mode can be neglected.51 As illustrated in Figure 2, the extinction efficiency spectrum has one dominant mode (M1), and the corresponding peak wavelength is red-shifted from 251 to 285 nm as the nanosheet length is changed from 3 to 250 nm. Figure 3 presents the peak wavelength, λmax, of the transverse-mode extinction efficiency as a function of the length of the monolayer graphene nanosheet. For nanosheet lengths greater than 40 nm, the extinction efficiency peak approaches a saturation value, and for lengths larger than 100 nm, it is almost constant. Such a peak occurs in the UV light range (200−300 nm) and is related to the interband π plasmon of graphene.51 The plasmon produces near-field-enhancement effects; the electric field-enhancement factor (EFEF) is defined as |E|2/|E0|2, where E is the electric field at the destination point and E0 is the incident electric field. Figure 4 shows the maximum EFEF at the hot spot of the graphene nanosheet as a function of the sheet length from 3 to 250 nm. The maximum EFEF value is 19.68 (au), which corresponds to a graphene nanosheet with a = 5 nm. Also, Figure 5 presents the EFEF at the hot spot of the graphene nanosheet as a function of the incident wavelength for some nanosheet length values between 10 and 250 nm. In doped graphene, the free-carrier plasmon belongs to the collective excitation of electrons within the partially occupied π* conduction band. Despite the free-carrier plasmon, highenergy interband π and π + σ plasmons exist in both pristine and doped graphenes.41 The extinction efficiency spectra of the graphene nanosheet has a peak in the UV range of light, which is attributed to a mixture of collective and single excitation of electrons from the π valence band to the π* conduction band.51 The plasmon peak is strongly dependent on the size and shape of the target.47,51,66−70 The plasmon peak of monolayer graphene nanodisks, 51 multilayer graphene nanodisks,51

Figure 3. Peak wavelength of the extinction efficiency for a graphene nanosheet as a function of sheet length from a = 3 nm to a = 250 nm. For small sheets, the peak wavelength is red-shifted with increasing sheet size, and for larger sheets (a > 80 nm), it is saturated; the saturation wavelength is about 285 nm.

Figure 4. Maximum EFEF as a function of graphene nanosheet length at the hot spot of the graphene nanosheet. The hot spot is at the top surface of the graphene nanosheet, and the maximum EFEF is 19.68 (au), which occurs for a = 5 nm. For graphene sheets larger than 5 nm (a > 5 nm), increasing the sheet length decreases the EFEF, but for values larger than a > 50 nm, the EFEF is almost unchanged.

spherical and cylindrical metals are red-shifted with increasing diameter.69 As a result of quantum-size effects, when the cluster size gets larger/smaller, the band-gap energy generally decreases/increases. When length of the monolayer graphene nanosheet increases, the interband π plasmon and electron transition energies come closer together, due to strong plasmon damping, and the SPR wavelength approaches a saturation value,51 which particularly occurs for lengths greater than 40 nm (Figure 3). Unlike the free-carrier plasmon/electron, the interband π plasmon/electron cannot move across a long distance, so this plasmon is strongly localized, sensitive to small sizes, and insensitive to large sizes.50 SPR Properties of Graphene Nanopores. Making a pore in the graphene nanosheet introduces two extra modes (M2, M3) in the extinction efficiency. M1 is confined to the outer edge of the graphene nanosheet, M2 is confined between the edges of the pore and the graphene nanosheet, and M3 is confined to the edge of the pore (Figure 6). When the pore diameter increases, M1 and M2 are blue-shifted because of the

Figure 2. Extinction efficiency of a graphene nanosheet as a function of sheet length. There is only one dominant mode, which is red-shifted with increasing sheet length. Increasing the sheet length mainly red shifts the peak wavelength because of the lowering the band-gap energy as a consequence of quantum finite-size effects. For large enough sheets (a > 80 nm), the plasmon and single-particle excitation energies come closer to each other, leading to saturation of the peak wavelength. 13695

DOI: 10.1021/acs.jpcc.6b02259 J. Phys. Chem. C 2016, 120, 13693−13700

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Figure 5. EFEF at the hot spot of the graphene nanosheet as a function of the incident wavelength for some nanosheet length values. Increasing the sheet length decreases the EFEF.

Figure 7. Effect of the pore diameter on the SPR peak wavelength for different graphene sheet sizes. For small enough sheets (a < 10 nm), the peak wavelength is red-shifted with an increase in the porediameter-to-sheet-length ratio to D/a < 0.8. However, in all of the sheets, for D/a ≥ 0.8, increasing the pore diameter blue shifts the peak wavelength. For very large sheets, small pore diameters have no effect on the peak wavelength, but increasing the pore diameter to larger values blue shifts the SPR peak wavelength.

M1 and M3, and M1 and M3 counteract, so the total peak wavelength is unchanged (Figure 7). However, if D ≈ a, then the M1 and M2 peak wavelengths dominate, and the total peak wavelength is blue-shifted. For example, for D ≈ a = 60 nm, the total peak wavelength is about 270 nm. As shown in Figure 7, for all of the sheets, if the pore diameter is large enough (D/a > 0.8), then the SPR peak wavelength is blue-shifted. As shown in Figure 7, it is notable that sensitivity to the pore diameter is greater for small sheets in both regions (i.e., for D/a > 0.8 and D/a < 0.8). Generally, the behaviors of the SPR peak wavelengths are similar for both small and large sheets. The only difference is that small pores red shift the SPR peak wavelength of small sheets but do not have any effect on the SPR peak wavelength for larger sheets. This is because of the fact that the interband π plasmon of graphene is strongly affected by small dimensions and sizes.51 Thus, in larger graphene sheets, to achieve this small dimension, larger values of D/a are needed. We considered the EFEF of the graphene nanopore under an external transverse electric field propagating in the x direction (direction of the graphene thickness; Figure 1). The EFEFs for the hot spot of a graphene sheet with a = 10 nm are presented as a function of the excitation wavelength for pore diameters between 2 and 8 nm in Figure 8. Generally, when the pore diameter increases, the peak value of the EFEF is lowered, and the peak is broadened. SPR in Graphene Nanopores as a Sensing Mechanism for DNA Nucleotides. In the field of rapid DNA sequencing, previous works showed that ionic and tunneling currents,3−8 Raman spectroscopy,24 and capacitance calculations19 confirmed nanopore DNA sequencing is feasible.15 However, rapid DNA sequencing has some limitations such as fast DNA translocation, membrane thickness, membrane fluctuations, and low-speed detection currents. In this section, we introduce the possible application of the surface π plasmon resonance in graphene as a potentially promising sensing mechanism for DNA nucleotides. The idea is that each nucleotide has unique optical properties and presenting a given nucleotide to the

Figure 6. Regions where the first (M1), second (M2), and third (M3) modes of the graphene nanopore SPR dominate. M1 is confined to the outer edge of the graphene nanosheet, M2 is confined between the edges of the pore and the graphene nanosheet, and M3 is confined to the edge of the pore. Each mode is mainly affected by the shape, size, and material of the corresponding region.

decrease of the cluster size and, consequently, the increase of the band-gap energy. In contrast, for M3, increasing the pore diameter red shifts the corresponding peak wavelength. As a result, for small enough sheets (a < 10 nm), M2 is smaller than the M1 peak value, and the peaks are also far enough apart. However, M3 is red-shifted, and the M1 and M3 peak wavelengths are also close to each other. Thus, the amount of M3 wavelength shift dominates, and the peak wavelength is red-shifted (Figure 7). However, for some cases, namely, a > 10 nm and a < 60 nm, increasing the pore diameter slightly blue shifts the peak wavelength (e.g., a = 40 nm; Figure 7). In this case, M2 is neglected again, and M1 dominates the wavelength shift. In graphene nanosheets, interband π plasmons are strongly localized and sensitive/insensitive to small/large sizes of the structure.50,51 Thus, for larger sheets, small pore diameters have no effect on the M1 and M2 peak wavelengths. Also, M3 can be neglected because the corresponding extinction efficiency is small compared to that of M1. For larger pore diameters and large sheets, M2 can be neglected compared to 13696

DOI: 10.1021/acs.jpcc.6b02259 J. Phys. Chem. C 2016, 120, 13693−13700

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Figure 9. Effects of inserted A, T, C, and G nucleotides on the SPR modes. The graphene sheet length and pore diameter are assumed to be a = 3 nm and D = 1.5 nm, respectively. In some cases (e.g., nucleotide G), the shift of the M1,3 peak wavelength is small (ΔλSPR = −2 nm), but the shift of the M2 peak wavelength is larger (ΔλSPR = 10 nm), and if M2 and M1,3 are considered simultaneously, discrimination among the DNA nucleotide types is possible.

Figure 8. EFEF of the hot spot for a graphene nanosheet with a = 10 nm as a function of incident wavelength and pore diameter. Generally, when the pore diameter increases, the peak value of the EFEF is lowered, and the peak is broadened.

graphene nanopore has its individual effects on the surface π plasmon resonance. The optical properties of DNA nucleotides are different mainly in the UV range (200−300 nm) of light,63 and the interband π plasmon resonance of graphene appears in this UV rangethe very type of plasmon that is highly localized and sensitive to small sizes. Hence, we demonstrate that the interband π plasmon resonance of graphene reveals useful information about the DNA nucleotide presented to the pore and that distinguishing between the types (A, T, C, and G) of nucleotide presented is possible. Also, we should note that the optical properties of DNA nucleotides are similar in the infrared range (intraband plasmon) and unknown for the wavelengths corresponding to the π + σ plasmon (around 100 nm). Indeed, the wavelengths of the infrared plasmons in graphene are not small enough to be used in single-molecule detections. This is why we use interband π plasmon in our suggested method. Previous research illustrated both theoretically24 and experimentally29 that a plasmon field effectively reduces the DNA translocation speed, which is one of the main challenges of nanopore sequencing. However, developing an experimental method to read SPR spectra sufficiently rapidly is very challenging and has not yet been realized. In Figure 9, the extinction efficiencies of a graphene nanopore in the presence of A, T, C, and G nucleotides are shown for a graphene sheet with a = 3 nm and with a 1.5-nm pore in the center of the sheet. As shown in Figure 9, the M2 extinction efficiency value is smaller than that of the combination mode of M1 and M3 (M1,3). Table 1 presents the calculated SPR peak-wavelength shifts relative to the conditions under which no DNA nucleotide is presented to the pore. The wavelength shifts were calculated for M1,3 and M2 as a function of the presented DNA nucleotide type. Distinguishing between the presented DNA nucleotide types is potentially possible if all of the modes are considered simultaneously. For example, when the presented nucleotide type is A, the peak-wavelength shift for M2 is ΔλSPR = 3 nm, and it is difficult to detect the type of DNA nucleotide using only M2. However, for M1,3, the shift value is ΔλSPR = −12 nm; thus, by using the peak-wavelength shifts of all modes, it is possible to identify the DNA nucleotide type that is presented to the pore. As reported in Table 1, the average peak-wavelength shift for M1,3 is 6.5 nm, and that for

Table 1. Shifts of the SPR Peak Wavelengths Relative to the Conditions under Which No DNA Nucleotide Is Presented: Effects of the Type of Inserted DNA Nucleotide on the M1,3 and M2 Peak-Wavelength Shiftsa,b peak-wavelength shift ΔλSPR (nm) DNA nucleotide type

M1,3

M2

A T C G

−12 −3 −9 −2

+3 −2 −4 +10

a

In this case, the graphene nanosheet is 3 nm, and the pore diameter is 1.5 nm. bIf M2 and M1,3 are considered simultaneously, discrimination among the DNA nucleotide types is possible.

M2 is almost 4.75 nm. Therefore, mode M1,3 is more sensitive to the presented nucleotide. Obviously, the peak wavelength corresponding to the localized interband π plasmon of the graphene nanopore is sensitive to the presentation of DNA nucleotides, and also each nucleotide results in a unique extinction efficiency spectrum (Figure 9 and Table 1). Finally, the localized EFEFs calculated for the different types of nucleotides show that this factor is almost insensitive to the type of the nucleotide presented. To find the optimal pore diameter and sheet size for a possible application in DNA sequencing, we define the average sensitivity to DNA nucleotides as Savg

1 = 4

k = M1,3

∑∑ ∑ j

i

M2

|λmax, k , j − λmax, k , i| λmax, k , j

i , j = A, T, C, G; k = M1,3 , M 2

, (5)

where λmax is the peak wavelength of the SPR, i and j are the types of DNA nucleotides, and k is the mode number of the SPR spectrum. To find the optimal conditions, we should note here that a single-stranded DNA molecule cannot pass through a sub-1.5-nm pore,22 so the pore diameter must be larger than 1.5 nm. Finally, we should note that, according to our results, because of the constant size of DNA smolecule, sensitivity to the presented DNA nucleotide is optimal for a nanosheet with 13697

DOI: 10.1021/acs.jpcc.6b02259 J. Phys. Chem. C 2016, 120, 13693−13700

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The Journal of Physical Chemistry C

translocation speed. The main source of membrane fluctuations is strong ion collisions. In our suggested method, ions are neglected, which results in a major reduction in the membrane fluctuations. The main challenge of our suggested method is unknown practical parameters. Because this is the first time that the SPR of graphene nanopores has been considered for use as a new sensing mechanism for DNA nucleotides, we must note that practical parameters and challenges such as plasmon excitation and detection and the effects of noise, contamination, and defects are still unknown. However, electron energy loss spectroscopy has been used for interband plasmon excitation in monolayer and bilayer graphene.50 This method could be a candidate for the experimental investigation of the presented mechanism. Also, using a combination of surface plasmons with ionic or tunneling currents or Raman spectroscopy24 might overcome practical challenges. Metals such as Ag, Al, and Rh have SPR peaks in the proposed UV range,71 and these metals could also be used as tips or nanoantennas for plasmon excitation and detection.48

a = 3 nm and a D = 1.5 nm pore. Figure 10 shows the average sensitivities to the DNA nucleotides for graphene nanosheets with a = 3, 4, 5, and 6 nm. The minimum pore diameter for possible DNA translocation is D = 1.5 nm, so the pore diameter was changed from 1.5 nm to larger values. We should note here that, for a = 3 nm, the pore diameter was changed from 1.5 to 2.5 nm, and for a = 6 nm, the diamtere was changed from 2 to 5 nm. This is because, for larger sheets, when the diameter of the pore is small (e.g., a = 6 nm and D = 1.5 nm), the second mode M2 is too small to be detected. Generally, when the pore diameter is increased, the average sensitivity decreases. Also, increasing the sheet size gradually reduces the average sensitivity to the DNA nucleotides presented to the nanopore. Therefore, the best sensitivity occurs for a = 3 nm and D = 1.5 nm. Generally, using the SPR properties of graphene nanopores instead of ionic or tunneling currents has some advantages and disadvantage. For example, the main challenges of nanopore DNA sequencing are the high DNA translocation speed, lowspeed sensing mechanism (such as ionic and electronic currents), and membrane fluctuations due to strong ion collisions.8,22 The plasmonic wave is faster than ionic and electronic currents, so our sensing mechanism is faster than methods based on such currents. Indeed, previous studies showed that the plasmonic field reduces the DNA translocation speed through nanopores.24,25,29 Our proposed method is a rapid sensing mechanism that simultaneously reduces the DNA

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CONCLUSIONS In summary, we have studied the extinction efficiency and nearfield-enhancement properties of the interband π plasmon of monolayer graphene nanosheets and graphene nanopores. Using the DDA method, we showed that, for graphene nanosheets smaller than 40 nm, extinction-efficiency peak wavelength red shifts with increasing sheet length and remains constant for values above 100 nm. Making a pore in the nanosheet generates two additional modes in the extinction efficiency. Because of quantum-size effects and the confinement regions of the modes, increasing the pore diameter results in blue shifts of modes M1 and M2 and a red shift of mode M3. Based on the size of the sheet and the diameter of the pore, the dominant mode is changed, which is why, for small sheets, the SPR peak wavelength is red-shifted with increasing pore diameter. Also, SPR for some sheet lengths (e.g., a = 40 nm) is blue-shifted, and for large enough sheets (larger than 60 nm), it is not changed. Because of damping of the interband π plasmon by interband transitions, this type of plasmon is very localized and small-size-sensitive. Therefore, we used the interband π plasmon of a monolayer graphene nanopore as a promising sensing mechanism for DNA nucleotides. The DNA nucleotide presented to the graphene nanopore causes a 2−12-nm shift in the peak wavelength for each extinction-efficiency mode. If all of the modes are considered simultaneously, the type of DNA nucleotide presented can be identified. Our results indicate that this method is sensitive to the presentation of nucleotides and also that each nucleotide has unique SPR properties. Despite its technical challenges, use of the interband π plasmon resonance of monolayer graphene nanopores is a potential sensing mechanism for single-stranded DNA nucleotides.

Figure 10. Average sensitivities to DNA nucleotides for graphene nanosheets with a = (a) 3, (b) 4, (c) 5, and (d) 6 nm. The minimum pore diameter for possible DNA translocation is D = 1.5 nm, so the pore diameter is changed from 1.5 nm to larger values. We should note here that, for a = 3 nm, the pore diameter is changed from 1.5 to 2.5 nm and, for a = 6 nm, the pore diameter is changed from 2 to 5 nm. This is because of the fact that, for larger sheets, for small pore diameters (e.g., a = 6 nm and D = 1.5 nm), the second mode M2 is too small to be detected. Generally, when the pore diameter is increased, the average sensitivity decreases. Also, increasing the sheet size gradually reduces the average sensitivity to the DNA nucleotides presented to the nanopore. Therefore, the best sensitivity occurs for a = 3 nm and D = 1.5 nm.

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AUTHOR INFORMATION

Corresponding Author

*Tel./Fax: +98 21 82883368. E-mail: [email protected]. Author Contributions

The manuscript was written and approved by all authors. Notes

The authors declare no competing financial interest. 13698

DOI: 10.1021/acs.jpcc.6b02259 J. Phys. Chem. C 2016, 120, 13693−13700

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ACKNOWLEDGMENTS The authors thank N. Amiri and V. Faramarzi for valuable discussions. The computing facilities were provided by Tarbiat Modares University. The authors also acknowledge the Iran Nanotechnology Initiative Council (INIC) for partial support of this project.

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