Plasmonic Metasensors Based on 2D Hybrid Atomically Thin Perovskite Nanomaterials

In this work, we have designed highly sensitive plasmonic metasensors based on atomically thin perovskite nanomaterials with a detection limit up to 10−10 refractive index units (RIU) for the target sample solutions. More importantly, we have improved phase singularity detection with the Goos–Hänchen (GH) effect. The GH shift is known to be closely related to optical phase signal changes; it is much more sensitive and sharp than the phase signal in the plasmonic condition, while the experimental measurement setup is much more compact than that of the commonly used interferometer scheme to exact the phase signals. Here, we have demonstrated that plasmonic sensitivity can reach a record-high value of 1.2862 × 109 µm/RIU with the optimum configurations for the plasmonic metasensors. The phase singularity-induced GH shift is more than three orders of magnitude larger than those achievable in other metamaterial schemes, including Ag/TiO2 hyperbolic multilayer metamaterials (HMMs), metal–insulator–metal (MIM) multilayer waveguides with plasmon-induced transparency (PIT), and metasurface devices with a large phase gradient. GH sensitivity has been improved by more than 106 times with the atomically thin perovskite metasurfaces (1.2862 × 109 µm/RIU) than those without (918.9167 µm/RIU). The atomically thin perovskite nanomaterials with high absorption rates enable precise tuning of the depth of the plasmonic resonance dip. As such, one can optimize the structure to reach near zero-reflection at the resonance angle and the associated sharp phase singularity, which leads to a strongly enhanced GH lateral shift at the sensor interface. By integrating the 2D perovskite nanolayer into a metasurface structure, a strong localized electric field enhancement can be realized and GH sensitivity was further improved to 1.5458 × 109 µm/RIU. We believe that this enhanced electric field together with the significantly improved GH shift would enable single molecular or even submolecular detection for hard-to-identify chemical and biological markers, including single nucleotide mismatch in the DNA sequence, toxic heavy metal ions, and tumor necrosis factor-α (TNFα).


Introduction
In the past decade, biosensors have provided an effective way for improving quality of life [1][2][3]. Biosensors are usually based on systems that can detect electronic or optical signals in terms of the devices [42]. They are promising materials for the plasmonic field as the sensing substrate to realize zero-reflection for phase singularity. In 2015, Dou et al. [43] demonstrated the synthesis of atomically thin two-dimensional single crystal perovskite nanosheets ((C 4 H 9 NH 3 ) 2 PbBr 4 ) by the solution phase growth method. They tuned the thickness of the perovskite layers from a single layer to 3 layers, 8 layers and 22 layers. The corresponding photoluminescence emission peaks are shifted with the changing band gap for these thin perovskite layers. Later, Bao et al. [44] reported the fabrication of the atomically thin 2D CH 3 NH 3 PbX 3 (X = Cl, Br, or I) perovskite with broadband photoluminescence emission ranging from 660 to 730 nm and a high photoresponsivity of 22 AW −1 under the excitation of 532 nm laser sources.
In this paper, we have designed ultrasensitive plasmonic biosensors with the integration of atomically thin perovskite nanomaterials on metasurfaces reaching a detection limit up to 10 −10 refractive index units (RIU) for the target sample solutions. More importantly, we have improved the phase singularity detection with the Goos-Hänchen (GH) effect. The GH shift is known to be closely related to optical phase signal changes; it is much more sensitive and more sharp than the phase signal in the plasmonic condition, while the experimental measurement setup is much more compact than that of the common used interferometer scheme to exact the phase signals. Here, we have demonstrated plasmonic sensors with an ultra-high value of 1.2862 × 10 9 µm/RIU with the optimum configurations for the plasmonic metasensors. For the first time, GH shift generated through the phase singularity based on the 2D perovskite materials is more than three orders of magnitude compared to other metamaterials schemes, including Ag/TiO 2 hyperbolic multilayer metamaterial (HMM) [45], a metal-insulator-metal (MIM) multilayer waveguide with plasmon-induced transparency (PIT) [46], a metasurface device with a rapid phase gradient [47] and even an electrically controllable graphene nanostructures [48]. The plasmonic GH shift that is reported in this paper is more than six orders of magnitude higher with the atomically thin perovskite metasurfaces (1.2862 × 10 9 µm/RIU) than those without them (918.9167 µm/RIU).

Methods
To evaluate the sensing performances of the 2D perovskite-enhanced plasmonic configurations, we have chosen an established Kretschmann excitation method as the standard modeling of the sensor head, as shown in Figure 1. One advantage of the sensing interface is the sensing substrate; silver thin film is selected rather than a gold one due to the protection of the hexagonal boron nitride (hBN) layer engineered on it. Single layer hBN is also known as white graphene. It has been well demonstrated that the silver substrate could provide a much narrower width of the resonance curves and also deeper resonance dips [49,50]. Two-dimensional perovskite is sandwiched between the hBN and graphene layers, where its optical property will not be affected due to oxidization and liquid contaminations [51,52]. The single graphene layer [53,54] is on top of the configuration to enhance the adsorption efficiency of the targeted biological molecules through pi-stacking forces. For the experimental measurement, reflectance is collected as the intensity ratio between the reflected light from the sensing surface and the incident light. A He-Ne laser (Thorlab Inc., Newton, NJ, USA) was employed to excite the surface plasmon resonance phenomenon at an appropriate incident angle by rotating the translation stage. On the stage, the sensing substrate is attached to the face of prism by optical matching oil (Cargille Labs, Cedar Grove, NJ, USA). A pin hole is added to eliminate the stray light and a high-precision optical power meter (Newport 2832C) is used to monitor light intensity. For phase interrogation, it is known that TM-polarized light suffers a sharp phase change as long as plasmon resonance is excited. Thus, we detect the interference intensity between Transverse magnetic (TM)-polarized light and transverse electric (TE)-polarized light. The incident light is separated into TM-polarized light and TE-polarized light by a polarized beam splitter (PBS). The TM light beam can excite resonance at the sensing surface by the rotation the translation stage at an appropriate incident angle. The TE light beam is modulated by a galvo-mirror (Thorlabs, GVS001). The optical path difference of TE light causes a change in the phase. The TE light interferes with TM light after a PBS and a polarizer. Here, TM light carries the information of the injected sample attached on the sensing surface. The light intensity detected by a photodetector is collected by a data acquisition (DAQ) card (NI PCI-6115, Austin, TX, USA) with a sampling rate of 100 kHz. The differential phase between TM light and TE light can be extracted through Matlab processing procedures. For Goos-Hänchen (GH) interrogation, when plasmon resonance is excited at the metal/dielectric interface, TM light experiences a large GH shift, while TE light does not. Therefore, differential GH lateral position changes between TM light and TE light can show the information of the sample solutions with a low noise. Similarly, PBS separates the incident light beam into TM and TE light. Chopper ensures that only TE light or TM light can get through at a time. The lateral effect position sensor (Thorlabs, PDP90A) is used to detect the beam position of the reflected light from the plasmonic sensor. As a result, the beam position of alternating TM light and TE light is collected by a data acquisition (DAQ) card. The GH shift between TM light and TE light can be obtained after Matlab processing procedures. We will firstly do the experimental measurement with our theoretical results with glycerin for calibration. If the calibration results have matched well with our simulation, we will do the optical biosensing tests with the target analytes.

Optical Parameters of the Sensing Configuration
In this prism-coupling method for plasmonic excitation, we used a high refractive index equilateral SF11 prism. The refractive index of the prism is obtained by the equation below [55]: where the unit for the incident wavelength is micrometer (µm), and this equation is valid for all the wavelengths in visible and near-infrared regions. The parameters for silver thin film substrate and the titanium adhesion layer of the modeling correspond to the experimental measurement ones that are reported by Palik et al. in reference [56]. The thickness of the titanium layer is 2.5 nm, which is a standard thickness for adhesion layers in conventional SPR experiments. The dielectric constant and thickness of monolayer hBN is obtained according to measurement data by Golla et al. [57] and fixed to be 0.34 nm, which is the same as graphene [58,59]. The optical constant of single layer graphene in the visible region is known to follow the equation below [60,61]: The dielectric constants of perovskites that are used for the plasmonic modeling extracted from experimental results are shown in Table 1. Here, the change in the refractive index corresponding to the target molecular binding was assumed to be ∆n bio , ranging from 10 −8 refractive index units (RIU) to 10 −1 RIU [5,62,63]. This range is more than sufficient to reach the detection limit of individual nucleobases' binding of the single-stranded DNA (ss-DNA).

Phase (φ p ) and Goos-Hänchen (GH) Shift (L shift )
It is known that for conventional surface plasmon resonance (SPR) sensors, detection merits are mainly based on the scanning of the change in reflected light intensity (∆R SPR ), or the change in resonance angle (∆θ SPR ) and the change in resonance wavelength (∆λ SPR ). However, these detection methods are not able to achieve the sensitivity for tiny refractive index changes below 10 −5 refractive index units (RIU). Recently, the phase interrogation approach has been exploited to significantly improve the sensitivity of the SPR sensors. Experimental schemes for differential phase measurements based on interferometric and ellipsometric configurations have been demonstrated to extract the phase signal (φ p ) of the reflected light. The phase signal led to a much sharper change to the surrounding media at the resonance interface in comparison to the change in the other parameters of reflected light mentioned above. Here, the Goos-Hänchen (GH) shift (L shift ) emerged as a higher order signal change of the phase, and corresponds to the lateral shift of the reflected beam at the sensing substrate. This lateral shift in the direction along the propagation direction of the surface plasmon waves (SPWs) is similar to the Goos-Hänchen (GH) shift (L shift ) that is usually observed when an abrupt phase change is induced for phenomena such as the Berry phase, Brewster's angle phenomenon and the Aharonov-Bohm effect. However, the quantitative measurements of the Goos-Hänchen (GH) shift (L shift ) for these phenomena are challenging due to the few micrometers magnitude shift in general. Under strong surface plasmon resonance effects, this shift could be optimized and enhanced to 2 orders of magnitude larger.
We have used the Transfer Matrix method (TMM) with Fresnel equations to do systematic investigation on our 2D perovskite-enhanced plasmonic models. The tangential part of the electromagnetic field for the sensing substrate from the 1st layer to the last layer are followed the boundary condition, as below: For the p-polarization light, the Transfer Matrix (TM) for a multilayer model is described as: and here (3) and (4) is the angle of incident with the refractive index of the prism of n 1 . The Fresnel reflection coefficient for p-polarized light is calculated by: Thus, the phase (φ p ) and Goos-Hänchen (GH) shift (L shift ) of this multilayer model are obtained as [46]: and When the surface plasmon resonance is excited, the value of the reflected light intensity is close to zero, and a large phase jump is observed at the SPR angle. The phase retardation at this singular point leads to a large Goos-Hänchen (GH) shift (L shift ). The phase (φ p ) and Goos-Hänchen (GH) shift (L shift ) are very sensitive to the refractive index change ∆n target of the target sample solutions interacting at the sensing interface.
The SPR sensitivity based on Goos-Hänchen (GH) shift is defined as [9]:

Further Design of the 2D Perovskite-Based Plasmonic Metasurfaces
The design of the metasurfaces are studied based on the effective medium theory (EMT) method. It is known to be used for the optimization of plasmonic nanorod arrays and groove structures. Here, we can obtain the dielectric constant for the periodical array structures respectively for the metasurfaces along the transverse (ε ⊥ ) and longitudinal directions (ε ), as below: where N = 1 -W m /P m is the plasmonic concentration for the metallic nanomaterials inside the structures, and W m and P m are widths and periodicity of the metasurface nanostructure. This equation is applicable for both metal array and groove designs [68]. In addition to the TMM approach, we also employed the Lumerical Finite-difference time-domain method (FDTD) solutions to carry out the numerical analyses on the electric field distribution under the resonance conditions.

Results and Discussion
Based on Equation (10), the SPR sensitivity based on Goos-Hänchen (GH) shift for the plasmonic metasurface structures is strongly related to the lateral shift of the p-polarization light (L shift ) for the refractive index change (∆n target ) induced by the target sample solutions at the sensing interface. One of the prominent physical features for surface plasmon resonance (SPR) is that under the resonance condition, the electric field excited at the substrate would be largely enhanced due to the resonant coupling of the light energy. The maximum electric field intensity can be two orders of magnitude higher than the initial field value of the incident light. As a result, the energy level dissipated to the dielectric layer is correspondingly larger than the total internal reflection (TIR) phenomena with only dielectricity and without the use of the metallic thin films. The resonance energy of the evanescent field penetrating to the surrounding media led to a much increased lateral shift from a few micrometers less than 10 µm (<10 µm) for normal TIR to more than 60 µm (>60 µm) for plasmonic resonance. The Goos-Hänchen (GH) shift can be quantitatively calculated from Equation (9) and is proportional to the phase retardation (∆φ p ), occurring at the sensing substrate. In Figure 2, we have plotted the intensity and optical phase change for the reflected light in the p-polarized direction for the continuous silver film engineered with 2D perovskite layers. We can see that the zero reflection under the resonance coupling corresponds to a phase singularity once, where the lower value of the reflected light led to a sharper phase signal change. The phase singularity and the rapid phase change resulted in a large GH shift as shown in Figure 3. The optical phase change is continuous and every circle is within a phase difference of 2π. Thus, the closer to the singular point of resonance through the sensing configuration, the higher the lateral GH shift could be obtained.   As we have discussed in the introduction part, the significant advantage for the phase and GH-SPR detection is that the signal enhancement is higher enough to balance the plasmonic loss induced in the Nanomaterials 2020, 10, 1289 9 of 19 system. Since the 2D perovskite has a higher absorption rate than the silver and gold layers in the visible region (see Figure S1), resonance damping can be tuned to be more precise and more efficient inside the plasmonic sensing structures. With the optimization of the perovskite structures, we can achieve a three orders of magnitude higher GH shift in comparison to that of pure silver thin films (Figure 3b). Firstly, we have systematically studied the plasmonic features with the number of 2D perovskite layers and silver thickness on the GH signal changes of the SPR resonance spectra through Equations (8) and (9). The target analyte molecular interaction that we chose here for detection is mimicking the process of the single stranded DNA (ssDNA) binding to the complementary ones at the interface. The refractive index change induced by the immobilization of the 23-mer ssDNA to form the double-stranded DNA (dsDNA) sequence with picomolar (10 −12 ), picomoles/liter was fixed to be ∆n bio = 1.2 × 10 −6 RIU. Here, we have observed several consistent characteristics for the 2D perovskite-based plasmonic sensing response curves (Figure 2a,b and Figure 3a,b). Firstly, the plasmonic resonance dip angle would redshift to the larger degree with more perovskite layers. This is due to the high value of relative permittivity (i.e., dielectric constant) of the perovskite layers (see Table 1) and is not affected by their imaginary part of these absorption films on the silver substrate. Under the same excitation condition, the positive and large in the value of the real part of the dielectric constant of perovskite would result in a larger surface plasmon wavevector and thus, a lower propagation velocity of the surface plasmon waves. The second optical characteristic for the SPR curve is the widening of the full width at half maximum (FWHM), which is attributed to the imaginary part of the perovskite layers. The large value of their imaginary parts represent a high absorption in the visible region. This enables the flexible tuning of the resonance damping by changing the type of the perovskite and also the precise control of the number of these atomically thin perovskite materials, as shown in Figure 4. Thirdly, the minimal values of the reflected light are changing with the number of the perovskite layers and the thickness of silver thin film in Figures 5, 6, 7 and 8d. The light absorbed by the pure silver substrate is not enough to generate a zero-reflection. This zero-reflection is the key point for achieving optical phase singularity and then, the much more prominent lateral GH shift at the sensing interface (see Figure 8d). More importantly, the thickness of the 2D perovskite is in the range of a few nanometer scale and thus, the width of the resonance curves would not be significantly increased. The detection resolution of the device is not compromised in comparison to the enhanced detection sensitivity. In addition, the GH shift only occurred for the p-polarization light (transverse magnetic waves), which is parallel to plane of incident light as the electrons on the metallic surface were collectively oscillating in this direction and generated plasmon resonance. The s-polarization light (transverse electric waves) remains unaffected, and thus, could be used as a reference control signal during the experimental measurements to avoid the environmental noises, as shown in Figure 6a,b. Through this approach, the signal to noise ratio for the GH setup can be significantly improved with only one signal channel detection. In Figures 2b and 8d, the minimum reflectivity for the bi-layer of FAPbI 3 perovskite engineered on the 45 nm thick silver substrate is 2.1674 × 10 −8 , where the values are 7.2356 × 10 −2 and 8.1485 × 10 −3 for the 45 nm and even 50 nm pure silver thin films. A much sharper phase signal change in a Heaviside manner was induced at the deeper resonance dip. Based on this dramatic phase jump, an enhanced GH shift is generated correspondingly at these resonance angles, as illustrated in Figure 4b. The largest GH shifts for MAPbI 3 , MAPbBr 3 and MAPbI 3−x Cl x perovskite-enhanced plasmonic configuration are respectively with 49 nm Ag/monolayer perovskite for 633 nm excitation wavelength (red curve in Figure 5a), 47 nm Ag/bi-layer perovskite for 532 nm excitation wavelength (blue curve in Figure 5b), and 48 nm Ag/monolayer perovskite for 604 nm excitation wavelength (red curve in Figure 5c). The detailed values for the obtained minimum reflectivities under the five different excitation wavelengths and also the GH shifts for each type of perovskite structures are listed in Tables 2 and 3. For the optimum configurations based on all the calculation results, the highest sensitivity of 1.2862 × 10 9 µm/RIU at a resonance dip angle of 54.3543 • was 49 nm Ag/bi-layer perovskite for 604 nm excitation wavelength (blue curve in Figure 5d). enhanced plasmonic configuration are respectively with 49 nm Ag/monolayer perovskite for 633 nm excitation wavelength (red curve in Figure 5a), 47 nm Ag/bi-layer perovskite for 532 nm excitation wavelength (blue curve in Figure 5b), and 48 nm Ag/monolayer perovskite for 604 nm excitation wavelength (red curve in Figure 5c). The detailed values for the obtained minimum reflectivities under the five different excitation wavelengths and also the GH shifts for each type of perovskite structures are listed in Tables 2 and 3. For the optimum configurations based on all the calculation results, the highest sensitivity of 1.2862 × 10 9 μm/RIU at a resonance dip angle of 54.3543° was 49 nm Ag/bi-layer perovskite for 604 nm excitation wavelength (blue curve in Figure 5d).      It is worth noting that in comparison to the conventional angular scanning and even phase interrogation approach, the GH detection method based on 2D perovskite layer showed a very prominent signal change for the same refractive index change of the target sample solutions. One can compare the maximum phase signal change (∆ϕp = 92.2749°) and the resonance dip angle shift (∆θSPR  Figure 7b and Table 3 for ∆nbio = 1.2 × 10 -6 RIU. The resonance dip angle shift increases with the increased perovskite thickness and is not affected by the resonance depth during the sensing process. However, the slightly improved angular SPR sensitivity is significantly compromised by the much more wide plasmonic resonance curves. Figure 8c showed that even the full width tenth maximums (FWTMs) for the 4 layer and 5 layer of perovskite thin films largely increased from 0.8655° for the bi-layer to 1.8302° and 2.7320°, respectively. These broadened curve widths would deteriorate the detection resolution of the sensing device due to the inaccuracy of fixing the incident angle to be exactly at the position of the resonance dip (see the orange curves in Figure 1b). Even for the silver thickness of 55 nm and 5 layer of 2D perovskite in Figure 8b, the resonance dip angle only shifted with a small value of 2.6143° for the sample solutions induced with 1.2 × 10 -1 RIU change. For the ∆nbio = 1.2 × 10 -6 RIU, the highest angular and phase signal changes with 2D FAPbI3 perovskite are respectively 0.00001° and 4.6954°. These signal changes are much lower than the device resolution for some of the rotation stages and phase detectors. Aa a result, the conventional angular scanning and phase interrogation methods are not competent for the detecting of the tiny refractive index change up to 10 -6 RIU in comparison to the large GH shift of ~1600 μm with 2D FAPbI3 perovskite-enhanced plasmonic device. For the 2D MAPbI3−xClx perovskite structures, the highest GH sensitivity is 4.0518 × 10 8 μm/RIU, with optimum configuration of 48 nm silver thickness and single layer perovskite (see Table 3). We have also listed the minimum reflectivity and the GH shift for all types of perovskite plasmonic sensors in Tables 2 and 3. One can observe that the largest GH signal change corresponds to lowest minimum reflectivity, where the zero-reflection would trigger the phase singularity and thus, a significant GH shift.    Figure 7. In addition to the 1543.50 μm for FAPbI3 perovskite, there are 12.0978 μm for MAPbI3, and 29.2289 μm for MAPbBr3 and 486.2172 μm for MAPbI3−xClx perovskite. These signal changes are much higher than pure graphene-enhanced SPR sensors (single layer graphene engineered on 50 nm silver substrate) with a lateral shift of 0.0028 μm. The capability to detect the small refractive index change promised the sensing of low-concentration chemical and biological molecules up to 1 fM (10 -15 mol/L) and even 1 aM (10 -18 mol/L). One can choose the type of perovskite configurations based on the molecular weight and also the concentration range. To achieve wide dynamic detection range, we can use the tunable laser to change the excitation wavelength for continuous sensing of both small and large   It is worth noting that in comparison to the conventional angular scanning and even phase interrogation approach, the GH detection method based on 2D perovskite layer showed a very prominent signal change for the same refractive index change of the target sample solutions. One can compare the maximum phase signal change (∆φ p = 92.2749 • ) and the resonance dip angle shift (∆θ SPR = 1.7484 • ) from Figure 8a,b induced by the same amount of the target analytes in a large value of 1.2 × 10 −3 RIU and 1.2 × 10 −1 RIU with the GH shift change (∆L shift = 1543.5 µm) in Figure 7b and Table 3 for ∆n bio = 1.2 × 10 −6 RIU. The resonance dip angle shift increases with the increased perovskite thickness and is not affected by the resonance depth during the sensing process. However, the slightly improved angular SPR sensitivity is significantly compromised by the much more wide plasmonic resonance curves. Figure 8c showed that even the full width tenth maximums (FWTMs) for the 4 layer and 5 layer of perovskite thin films largely increased from 0.8655 • for the bi-layer to 1.8302 • and 2.7320 • , respectively. These broadened curve widths would deteriorate the detection resolution of the sensing device due to the inaccuracy of fixing the incident angle to be exactly at the position of the resonance dip (see the orange curves in Figure 1b). Even for the silver thickness of 55 nm and 5 layer of 2D perovskite in Figure 8b, the resonance dip angle only shifted with a small value of 2.6143 • for the sample solutions induced with 1.2 × 10 −1 RIU change. For the ∆n bio = 1.2 × 10 −6 RIU, the highest angular and phase signal changes with 2D FAPbI 3 perovskite are respectively 0.00001 • and 4.6954 • . These signal changes are much lower than the device resolution for some of the rotation stages and phase detectors. Aa a result, the conventional angular scanning and phase interrogation methods are not competent for the detecting of the tiny refractive index change up to 10 −6 RIU in comparison to the large GH shift of~1600 µm with 2D FAPbI 3 perovskite-enhanced plasmonic device. For the 2D MAPbI 3−x Cl x perovskite structures, the highest GH sensitivity is 4.0518 × 10 8 µm/RIU, with optimum configuration of 48 nm silver thickness and single layer perovskite (see Table 3). We have also listed the minimum reflectivity and the GH shift for all types of perovskite plasmonic sensors in Tables 2 and 3. One can observe that the largest GH signal change corresponds to lowest minimum reflectivity, where the zero-reflection would trigger the phase singularity and thus, a significant GH shift.
GH shift changes for optimized 2D perovskite plasmonic structures are shown in Figure 7. In addition to the 1543.50 µm for FAPbI 3 perovskite, there are 12.0978 µm for MAPbI 3 , and 29.2289 µm for MAPbBr 3 and 486.2172 µm for MAPbI 3−x Cl x perovskite. These signal changes are much higher than pure graphene-enhanced SPR sensors (single layer graphene engineered on 50 nm silver substrate) with a lateral shift of 0.0028 µm. The capability to detect the small refractive index change promised the sensing of low-concentration chemical and biological molecules up to 1 fM (10 −15 mol/L) and even 1 aM (10 −18 mol/L). One can choose the type of perovskite configurations based on the molecular weight and also the concentration range. To achieve wide dynamic detection range, we can use the tunable laser to change the excitation wavelength for continuous sensing of both small and large target analytes with different concentrations. In Figure 9, a linear and large GH shift ∆L shift = 17.3576 µm is shown, corresponding to the refractive index induced by the target biomolecules ∆n target = 1.2 ×10 −8 RIU. The GH signal~18 µm was enhanced by six orders of magnitude compared to those of pure silver ones (1.1027 × 10 −5 µm). Thus then, sensitivity with the atomically thin perovskite metasurfaces is 1.2862 × 10 9 µm/RIU, which is more than 10 6 times than 918.9167 µm/RIU for silver sensing substrate with the same thickness. To realize the ultimate goal of single molecular and even submolecular detection, we have also used the effective medium theory (EMT) from Equations (11) and (12), the Lumerical Finite-difference time-domain method (FDTD) for integrating the 2D perovskite into a plasmonic metasurface structure and obtained a much enhanced GH-SPR sensitivity and also localized electric field enhancement. By optimizing the width from 10 to 60 nm of the silver groove structure for a fixed period of 150 nm, the resonance curve could be further damped and more close to the zero-reflection. The depth of the groove is fixed at 3 nm, which is optimized by the FDTD calculation from 0 to 5 nm (see Figure S2). The zoom-in curves at the resonance dips centered around 55.6 • were plotted in Figure 10b and the complete reflection curves are shown in Figure S3. With a fixed groove width, the SPR resonance curves would become broadened with increasing groove depth. However, if the groove depth is not large enough, the electric field enhancement is not prominent and also, the molecules length is usually more than 2 nm. Thus, there is a balance between electric field enhancement and the widened resonance curves. As mentioned above, the broad curve would affect the detection resolution, since the incident angle should be fixed at the resonance dip angle before the GH-SPR detection for the target analytes. A 20% larger GH shift of 1854.91 µm was obtained as shown in Figure 10c, corresponding to a higher sensitivity of 1.5458 × 10 9 µm/RIU. Moreover, the strong electric field between the edge of the groove would further enhance the detection of the binding interaction of the biological molecules (Figure 10a). The electric field is enhanced by 100-fold at the edge corner compared to the intensity values of both the incident light waves and the evanescent field excited on the base substrate. 55.6° were plotted in Figure 10b and the complete reflection curves are shown in Figure S3. With a fixed groove width, the SPR resonance curves would become broadened with increasing groove depth. However, if the groove depth is not large enough, the electric field enhancement is not prominent and also, the molecules length is usually more than 2 nm. Thus, there is a balance between electric field enhancement and the widened resonance curves. As mentioned above, the broad curve would affect the detection resolution, since the incident angle should be fixed at the resonance dip angle before the GH-SPR detection for the target analytes. A 20% larger GH shift of 1854.91 μm was obtained as shown in Figure 10c, corresponding to a higher sensitivity of 1.5458 × 10 9 μm/RIU. Moreover, the strong electric field between the edge of the groove would further enhance the detection of the binding interaction of the biological molecules (Figure 10a). The electric field is enhanced by 100-fold at the edge corner compared to the intensity values of both the incident light waves and the evanescent field excited on the base substrate.

Conclusions
An ultrasensitive plasmonic biosensor has been designed in this paper by engineering the atomically thin 2D perovskite nanostructures on the silver metasurfaces. A record-high GH-SPR sensitivity of 1.2862 × 10 9 μm/RIU was achieved, which is six orders of magnitude higher than the performance with the conventional continuous silver thin film (918.9167 μm/RIU). The atomically

Conclusions
An ultrasensitive plasmonic biosensor has been designed in this paper by engineering the atomically thin 2D perovskite nanostructures on the silver metasurfaces. A record-high GH-SPR sensitivity of 1.2862 × 10 9 µm/RIU was achieved, which is six orders of magnitude higher than the performance with the conventional continuous silver thin film (918.9167 µm/RIU). The atomically thin perovskite nanomaterials with high absorption rates enable the precise tuning of the depth in the plasmonic resonance dip. We have also provided our comparison plasmonic results for experimental and simulation data for different layers of atomically thin nanomaterials in Figures S4-S6. These results also supported that the optimum configuration can lead to the more enhanced plasmonic sensing signal both for the glycerol calibration tests and for the protein molecular detections. Thus, one can optimize the structure to reach the near zero-reflection at the resonance angle and a sharp phase singularity could be induced, leading to a much more enhanced GH lateral shift at the sensing interface. The 2D perovskite layers were sandwiched between a single layer hexagonal boron nitride (hBN) and graphene to avoid their degradation by water and humidity. The top layer of graphene was used to capture the target biomolecules due to the pi-stacking interaction between the hexagonal carbon ring structures. This advantage could also enhance the adsorption efficiency of the analytes. By integrating the 2D perovskite nanolayer into the metasurface array structure, the GH sensitivity was further improved to 1.5458 × 10 9 µm/RIU. More importantly, a strong localized electric field enhancement was excited between the groove edge. We believe that this enhanced electric field together with the enhanced GH shift would enable the single molecular or even submolecular detection for hard-to-identify chemical and biological markers, including single nucleotide mismatch in the DNA sequence, toxic heavy metal ions and tumor necrosis factor-α (TNFα).

Supplementary Materials:
The following are available online at http://www.mdpi.com/2079-4991/10/7/1289/s1, Figure S1: Experimental measurement results showing the broad absorption spectra of CH 3 NH 3 PbI 3 (MAPbI 3 ) perovskites, Figure S2: SPR curve widths tuned by the groove depth of 2D Perovskite-based metasurface structure, Figure S3: SPR curves with Reflectivity tuned by the groove width of the metasurface structure with 2D perovskite layers, corresponding to the zoom-in Figure 10b, Figure S4: Experimental and simulation results based on three-layer graphene/gold metasurfaces. Theoretical curves of (a) reflectance with respect to various incident angles in the air, (c) differential phase and (e) differential GH shift between p-polarized light and s-polarized light of glycerol solutions with different concentrations. Experimental curves of (b) reflectance, (d) differential phase and (f) differential GH shift. The resonance angle is 44.10 • in good agreement with the theoretical one. The phase and GH shift shows high sensitivity as 22,842 deg/RIU and 7,500 µm/RIU respectively, Figure S5: (a) and (b) Experimental and simulation data, respectively, of GH shift in a device based on a bilayer WS 2 , Figure S6: The averaged GH shift of BSA molecules with molar concentration from 1aM to 1mM based on bilayer WS 2 /gold metasurfaces. The insert curve gives the binding trace of BSA molecules during a short time.