Introduction

Quantum dots (QDs) are quasi-zero-dimensional nanomaterials composed of several to dozens of atoms, with sizes in three-dimensional space smaller than or close to the exciton Bohr radius. The movement of electrons within quantum dots is confined in all directions1,2,3. When the size of semiconductor or metallic materials is reduced to the nanoscale, with the typical diameter d<100 nm, the continuous energy bands become discrete energy levels, which can be determined by the size of the material. Therefore, by changing the size of quantum dots, the bandgap width can be adjusted, meeting the need for low-cost and rapid semiconductor bandgap tuning. Currently, research on semiconductor quantum dots mainly focuses on semiconductor quantum dot lasers4,5, solid-state lighting6, solar cells7 and other fields8.

Benefiting from the excellent fluorescence properties and stable, non-toxic characteristics, carbon quantum dots are mainly used in chemical sensors and electrocatalysis9,10,11,12. With the improvement of GQDs preparation technology, the methods are primarily divided into top-down and bottom-up approaches. The top-down approach involves breaking down large molecules into GQDs, with the typical methods including liquid phase exfoliation13,14 and electron beam lithography15. The bottom-up approach involves growing GQDs from smaller polycyclic aromatic hydrocarbons and appropriate molecular precursors. Based on the energy input and preparation characteristics of the system, the methods can be categorized into hydrothermal16, microwave-assisted hydrothermal, soft template17, and metal-catalyzed methods18.

Studies have demonstrated that core-shell structured materials are generally nano-sized, multifunctional composites that integrate two or more functional materials into a spherical geometry, achieved through surface coating technology, such as SiO2 @Au and PS@Au. Currently, the applications of the core-shell structured materials are mainly focused on catalysis19,20, photocatalysis, biomedicine, spectroscopy21, supercapacitors22 and the other fields23, without studying the core-shell structures in the micronscale. GQDs display high electrical conductivity, superior mechanical strength, optical transparency, and terahertz tuning properties24. It has been expected that the unusual core-shell structured colloidal crystals formed by GQDs coating PS microspheres not only improve the optical properties of the colloidal crystals, such as enhanced light absorption scattering efficiency25,26, but also play an important role in high-performance devices27,28,29.

In this study, the nano-sized GQDs, the micron-sized PS spheres, PS@GQDs core-shell structures and the single and the colloidal crystals of PS@GQDs were fabricated under the certain parameter conditions in Table 1 by using the improved ultrasonic dispersion, dispersion polymerization, surface seed-mediated growth and gravity sedimentation, as shown in Fig. 1a. It has been noted that GQDs consist of a single layer of graphene dispersed into the N-Methyl pyrrolidone (NMP). As the typical examples, Fig. 1b shows the TEM and the selected FFT images of GQDs and their clusters. GQDs can form the submicron DBR cluster structures in TEMs, while the observed bright points in the FFT images can be described by the feature Miller indices of the familiar hexagonal polycrystalline system8 (see Figs. S1S3 in details), in the ultrasonic dispersion at high magnification and the subsequent surface seed-mediated growth processes. Additionally, by using the improved gravity sedimentation, the eight colloidal crystal samples have fairly uniform surface morphologies in Fig. 1c. Compared with the isothermal heating evaporation-induced self-assembly30, this method can significantly reduce the evaporation rate and the conventional Schottky-Frenkel defects31.

Table 1 Parameters for the multilayer colloidal crystal samples of PS@GQDs.
Fig. 1
figure 1

(a) Schematic preparation processes, (b) TEM and FFT images of GQD structures, where FFT selection intervals are pointed out by box, (c) Photos of the colloidal crystal samples, synthesized with the parameters in Table 1.

In the conventional approximations, such as the classical Mie-Maxwell-Garnett effective medium theories and the Gorkov-Eliashberg (GE) quantum theory in the Gaussian symplectic ensemble32,33,34,an effective dielectric function (S3) can be derived out by considering the variations in sample geometries, such as the fractal and the percolation, the dielectric and the impurity environments within the incident light field. This has been achieved by further considering the effects of the depolarizing field of GQDs, dipole-dipole interactions, the Fano resonances, and multiscale Gaussian distributions such as the diameters of the nanoscale GQDs and the micron-sized PS@GQDs core-shell structures. Corresponding to the various aforementioned experimental processes, the numerical simulations have been carried out for examining the absorbance of the PS@GQDs multilayer colloidal crystals to describe the hybridization and the spectra classed into three bands in terms of the ultraviolet-vis-near infrared range, this is consistent with the experimental observations and measurements. In the localized plasmon resonances on surfaces and photonic band crossovers, the tunable spectra display the unconventional DBR reflectance absorbance of the colloidal crystals in the UV-Vis-NIR range35,36,37,38.

Results and discussions

First, we describe the surface and the cross-sectional morphologies of the single and a few layer 3M template colloidal crystal samples, self-assembled by the micron-sized PS@GQDs with the multiscale Gaussian fit distributions, as shown in Figs. 2, 3 and their insets. The sample parameters appear in Table 1, such as GQDs contents and the average diameters of PS spheres. In the present work, the feature diameter of GQDs is smaller than 10 nanometers, and the size of the GQD cluster structure ranges from 100 to 1000 nm that exhibit polycrystalline structures, as shown in Fig. 1b, in which the feature bright points were observed in the FFT images. It is clear that as the ultrasound duration increases, the GQD structures transition from a single-crystal (36 hours) to a hexagonal polycrystalline structure (72 hours). Sasikala et al.13 have demonstrated that because of the non-uniform particle size distribution of the GQD cluster structures, thereby an increased full-width at half maximum (FWHM) of the PL behaviors of GQDs (d=5.3nm), ranging from 350 to 600 nm.

Fig. 2
figure 2

Surface SEM images of the colloidal crystal samples synthesized with the parameters in Table 1 (left) and Gaussian fit distributions of PS@GQDs (right), along with FFT images from high-magnification SEM in the insets.

Fig. 3
figure 3

Cross-sectional SEM images with the insets of high-magnification SEMs (left) and low-magnification FFT images (right) of the colloidal crystal samples, synthesized with the experimental parameters, as listed in Table 1.

Brinson et al.35 studied the growth and optical properties of the gold layers on silica and found that the plasmon modes of the system exhibited two bands: one in the range of 400–600 nm and the other in the range of 800–1500 nm agreed quantitatively with Mie scattering theory. They also found that the plasmons associated surfaces with the inner radius Ri and outer R0 of the shell mix and hybridize, resulting in a lower energy, “bright” plasmon that couples strongly to incident light and a higher energy “dark” plasmon that couples weakly to incident light. The hybridization interaction is stronger for thinner shell layers, resulting in a strongly red-shifted resonance for the “bright” plasmon at a wavelength determined by the thickness of the shell and the overall particle radius. This was accompanied by a red shift of the bands. Shi et al.36 elaborated on the characteristic plasmon resonance absorption peaks of PS@Au without studying the micron-scale materials. In the present work, the inner radius Ri of PS sphere approaches to one half of the average diameter of PS@GQDs as listed in Table 1. Therefore, the shell thickness of an individual PS@GQDs is equal to the difference of the radius \(\Delta \text{R}={\text{R}}_{0}-{\text{R}}_{\text{i}}\ge \text{d}\) generally, giving the DBR limit \(\Delta \text{R}=\) d of the thinner GQD shell of PS@GQDs for the colloidal crystal samples.

For the growth of the shell structures as the filling rate fc increases, GQDs formed are of land-like agglomerates, such fractal and percolation geometries, with randomly magic-angle distributions. This is different from the growth of the golden shell structures, with an increase in the volume of the K-H (K2CO3 and HAuCl4 mixed solution) solution35. For comparisons of the single layer template samples S1-S4, assembled by PS @GQDs with the multiscale Gaussian distributions for the same PS diameter about 5.2 µm and different concentrations of GQDs, the colloidal crystals can maintain due to strongly correlated couplings of GQDs. Cao et al.37 and Zondiner et al.38 demonstrated that correlated insulator behavior and the cascade of phase transitions exist through adjusting the Fermi filling state in a few-layer graphene. The SEM images of S5 show the coupling is stronger than that of S6 since the PS diameter in S5 is small, comparable to the cluster structures of GQDs.

Due to the Gaussian distributions for the diameters of PS microsphere, the unconventional colloidal crystals assembled by PS@GQDs exhibit the GQD crystallinity on the surfaces and the gaps in Figs. 2, 3. Compared to the surfaces with the cross-sectional morphologies in SEMs, the arrangements of PS@GQDs show no more colloidal crystal structural ordering. The FFT images of low magnified in Fig. 3 show very broad amorphous halo patterns, but FTT images corresponding the inset SEMs of Fig. 2 display GQD hexagonal polycrystalline and amorphous patterns in crossovers due to the kinetic anisotropism in the fabrications8,37,38. This is consistent with TEM and FFT images of Fig. 1b.

Furthermore, for the fabrications of two and three-layer templates in S7 and S8, as the thickness increases from 60 to 180 µm, the individual spheres and local structures are similar. Still, the thickness of the colloidal crystal increases from 165 to 344 µm in the improved gravity sedimentation. This may be because the adsorption force of the crystal can exceed the support thickness of the template, showing a significant positive correlation between the template and colloidal crystal thickness. The smoothness of the colloidal crystal slightly decreases while the stacking pattern remains. The surface morphologies indicate that GQDs and the submicron clusters are distributed within the colloidal crystal. The nanoscale GQDs are primarily coated on surfaces of PS sphere, while the submicron clusters are distributed in agglomerate interstice geometries such as fractals and percolation. The polycrystalline structures reveal the multiscale Gaussian distributions32,33,34.

We turn to discuss Raman spectra in Figs. 2, 3. It has been demonstrated that GQDs (d<100nm) can be achieved through the subcritical hydro/solvothermal processing of graphene materials. Due to the magic-angle effects of a few layers of graphene, such as strongly correlated couplings37,38, herein, a few layers of graphene powders are dispersed into the N-Methylpyrrolidone (NMP). The high-purity, superfine GQDs liquid was fabricated in ultrasonic dispersion in Fig. 1b. Corresponding to the first six-kind crystal samples in the first and second rows for comparison of the left and right images, it is evident that when the GQDs content is 52%, changes in GQD size and colloidal crystal thickness have no significant impact on Raman intensity. In Fig. 4, the presence of the characteristic G peak of graphene still confirms the existence of PS@GQDs microspheres. Meanwhile, the Raman characteristic peaks can maintain at 626 cm−1, 1008 cm−1, 1608 cm−1, and 3060cm−1 in accordance with those of the polystyrene powder. The third row shows that, in the first column, Raman peak intensity increases significantly with the growth of the crystal thickness. The second column still demonstrates that thickness has no significant impact on Raman peak positions without altering the band structures.

Fig. 4
figure 4

Raman intensity with the characteristic G peak of graphene in the insets (left) and the usual baseline-corrected spectra (right) of GQD multilayer colloidal crystal samples, synthesized with the experimental parameters listed in Table 1. Here, the curve color of two-kind Raman intensities is the same for an individual sample in Table 1.

In the previous researches10,11,12,13, the main Raman characteristic peaks of polystyrene are typically found at 620, 1000, 1600, and 3000 cm−1. These peaks correspond to C-H bending vibration, C-C stretching vibration, benzene ring breathing vibration, and C-H stretching vibration39, respectively. Graphene characteristic peaks include the D peak (1350 cm−1), which is usually due to edge effects or lattice defects and is weak or absent in perfect monolayer graphene40. The G peak, around 1580 cm−1, is caused by the E2g vibration mode of carbon atoms in the plane and is a characteristic peak of graphene. The 2D peak, around 2700 cm−1, is a second harmonic peak. Unlike the G peak, the shape and position of the 2D peak can be used. It is evident that the red-shift reveals strong hybridization for the ultrathin shell of GQDs, with a few layers of graphene on Fano resonance, giving the correlated insulator PS@GQDs at the phase transitions37,38.

Strikingly, in the first row, as the typical example, the characteristic peaks of polystyrene are clearly present at 626, 1008, 1608, and 3060 cm−1. The peaks show a slight red shift. Additionally, the characteristic G peak of graphene appears. As the concentration of GQDs increases, the Raman peaks slightly enhance, but the peak positions can maintain. This is because the increased concentration of GQDs also raises the possibility of GQDs stacking disorder, forming magic-angle graphene, which enhances Raman scattering intensity but does not alter the band structure of PS@GQDs32,35. The UV−Vis spectroscopy is the most fundamental method for characterizing colloidal dispersions. This analysis can provide information about the structure of the quantum dots. GQDs show a broad absorption peak in the ultraviolet−visible range. The UV−Vis spectrum of GQDs includes two absorption peaks. The peak at 250−280 nm was related to the π→π* band of sp2 carbons in the aromatic structure of GQDs13. However, Azimi et al.14 found the peak in the 310−370 nm wavelength region.

Hereafter, we study the unconventional DBR reflectance for the colloidal crystal samples. Figure 5 shows the reflectance curve, UV-IR peaks and FWHM under the certain parameter conditions. The results indicate that peak positions for S1 are located at 379, 1431 and 1533 nm. The sub-peak positions for S5 appear at 396, 1319 and 1427 nm. The sub-peak positions for S5 occur at 380, 1427 and 1531 nm. Therefore, the overall reflectance spectra could be classed into three bands 379–396 nm, 379–1319nm and 1319–1533 nm, characterized by the unconventional DBR of the colloidal crystals of PS@GQD at the transitions, giving the continuity of the correlated coupling of plasmon.

Fig. 5
figure 5

The full reflectance in the top row of the colloidal crystals synthesized with the parameters in Table 1. Here, high- and low-energy, UV-IR peaks are pointed out by color big arrows. The curve color is the same for an individual sample as Raman intensity in Fig. 4. The color dotted lines in the middle row are the result of the deconvolution of the peaks. In the bottom row, FWHMs are plotted as the function of GQD rate, the diameter of PS@GQDs and the 3 M template layer, with the curve colors are the same as the arrow colors in the same column.

In the ultraviolet range, the high-energy peaks can be resolved into four peaks at 338, 357, 382, and 417 nm and half-peak widths of approximately 4.5, 22.8, 38.7, and 63.9 nm. Furthermore, in the near-infrared, two twin peaks are located at 1431 and 1533 nm, approximately 100 nm apart. Combined with the morphological changes of S1–S4 in Figs. 3, 4, this indicates that variations in the nanoscale GQDs content cause slight changes in PS@GQDs, leading to irregular slight changes in the gaps between microspheres, consistent with the analysis of S1–S5 in Fig. 3. These peaks exhibit characteristic peak pattern recognition, and their positions can maintain with the increase of GQDs concentration. The DBR anomalies can be explained as the decrease in the periodicity of the crystal structure with the introduction of GQDs.

It is observable that the reflection peak gradually blue-shifts from 396 nm (S5) to 388 nm (S6) as the particle size increases. However, the infrared spectrum is completely different, with the reflection peak gradually red-shifting from 1319 nm (S5) and 1427 nm (S5) to 1354 nm (S5) and 1430 nm (S5), respectively. Additionally, a secondary peak appears at 1530 nm. The specific Gaussian fitting is shown in the second row (middle), where the ultraviolet peaks are centered at 390, 414, 371, 382, and 445 nm, with half-peak widths of 11.7, 35.3, 45.0, 6.1, and 22.6 nm, respectively. The near-infrared peaks are centered at 1236, 1176, 1309, 1343, and 1434 nm, with half-peak widths of 98.5, 46.1, 59.9, 37.3, and 73.3 nm, respectively. The reflective peak steadily red-shifts from 380 to 412 nm and then to 415 nm as the thickness of the colloidal crystal increases. For a colloidal crystal sample with a thickness of 165 nm, two reflection peaks appear at 1427 and 1531 nm. For a sample thickness of 191 nm, the peaks appear at 1437 and 1539 nm. For a sample thickness of 206 nm, the peaks appear at 1430 and 1530 nm. As the thickness of the colloidal crystal increases, both the first and second peaks initially red-shift and then blue-shift, with a peak difference about 100 nm. The peaks are centered at 382, 355, and 419 nm, with half-peak widths of 12.8, 4.5, and 8.3 nm. With the increase of the colloidal crystal thickness, the half-peak width of the ultraviolet peaks initially narrows and then widens. Additionally, the interference effects are weaker in the infrared range.

Finally, we analyze the DBR absorbance. Figure 6 shows that the sub-peaks appear at 466 and 1300 nm for S1, and 474 nm, 1325 nm for S5 as well as 476, 1219, and 1302 nm for S4, respectively. Similarly, the overall absorbance can be classed into three bands as 466–474 nm, 474–1219 nm, and 1219–1325 nm, respectively. The UV absorption peaks of the seven samples (S1–S7) are around 300 and 470 nm. In the monolayer graphene, the characteristic peak is located at 262 nm, with minimal absorption above 300 nm, indicating good optical transparency41. However, GQDs exhibit a further blue shift as their size decreases42. It is well known that polystyrene has characteristic absorption peaks43 at 290 nm and 1000–1200 nm. The UV absorption peaks for the samples show a slight red shift compared to their constituent PS and GQDs. This shift is due to the coating of GQDs, which alters the dielectric constant and the potential modification of the PS surface. Additionally, the coupling of GQDs of different sizes on the PS surface forms small continuous absorption peaks, with absorption oscillation characteristics below 1200 nm, consistent with that of Fig. 5.

Fig. 6
figure 6

The full absorbance in the top row of the colloidal crystals, synthesized with the experimental parameters in Table 1. Here, high- and low-energy, UV-IR peaks are pointed out by color big arrows. The curve color is the same for an individual sample as Raman intensity in Fig. 4. The color dotted lines in the middle row are the result of the deconvolution of the UV-IR peaks in splitting. In analogy with Fig. 5, FWHMs are plotted in the bottom row. The curve colors are the same as the arrow colors in the top row. The numerical simulations to absorbance for plasmon excitations under the appropriate parameter conditions (a) \({f}_{c}\)=0.43(black), 0.45(red), 0.47(navy), 0.49(cyan), 0.51(purple),0.53(orange), Λ = 0.6, 0.7, 0.8, 0.9,1.0, 1.1 at the fixed d = 6 nm and \({R}_{i}/{R}_{0}\simeq 0.69\), (b) \({f}_{c}\)=0.38(black), 0.40(red), 0.42(navy), 0.44(cyan), 0.46(purple), 0.48(orange), \({R}_{i}/{R}_{0}=\) 0.47, 0.54, 0.60, 0.66, 0.73, 0.79, d = 3.9, 4.2, 4.5, 4.8, 5.1, 5.4 at the fixed temperature Λ = 0.8 , corresponding to different excitations and the same, respectively.

Graphene quantum dots have near-infrared peaks in the 1000–1500 nm range. The low-energy IR absorption peaks of S1–S7 are between 1219 and 1325 nm, showing a red shift compared to polystyrene microspheres and falling within the range of graphene and its quantum dots. This indicates that the near-infrared absorption peaks of PS@GQDs are predominantly influenced by GQDs, originating from quantum confinements and surface states at the structure transitions41. Additionally, S1-S7 exhibit banded absorption peaks around 500-1200 nm, with unconventional DBR absorption characteristics.

The characteristic absorption peak at 466 nm (S1) indicates that the colloidal crystal has some blue light filtering properties. As the concentration of GQDs increases, this peak slightly red-shifts to 468 nm (S4), remaining relatively stable overall. This stability can be related to the structure formed by GQDs and aminated PS surfaces35,36. In the near-infrared range, with increasing GQDs volume, the colloidal crystal exhibits characteristic absorption peaks at 1300 nm (S1), 1381 nm (S2), 1290 nm (S3), and 1381 nm (S4), indicating that the peak first red-shifts, then blue-shifts, and red-shifts again14,35.

The Gaussian fitting of the UV range reveals peak centers at 435, 465, and 503 nm, with half-peak widths of 23.3, 40.4, and 48.1 nm, respectively. The near-infrared fitting centers appear at 1296, 1215, and 1386 nm, with FWHMs 104.4, 41.9, and 104.6 nm, respectively. With increasing GQDs, the half-peak width of the UV peaks changes minimally while the near-infrared peaks increase. This indicates that the UV refraction consistency changes less, related to the energy bands of GQDs and PS. The UV bandgaps of PS often involve higher energy level electron transitions, which are relatively specific and fixed. In contrast, the bandgaps of GQDs, which are fewer in quantity compared to PS, change with size13. The dominant PS absorption peaks in the PS@GQDs system result in relatively fixed UV absorption peaks. Therefore, the UV absorption peaks change minimally, while the near-infrared peaks show significant changes due to the GQD stacking.

To visually study the effect of PS@GQDs microspheres on the absorption peaks, we selected PS@GQDs with diameters of 1.6 µm (S6), 5.2 µm (S5), and 6.7 µm (S7). When the core-shell diameters are 1.6, 5.2, and 6.7 µm, the UV absorption peaks of the three samples remain stable at 474 nm. In the near-vis-near infrared range, the absorption peaks occur at 1325, 1290, and 1341 nm, respectively, showing a trend of initial blue shift followed by a red shift.

Further UV peaks can be divided into six peaks centered at 441, 411, 482, 525, 582, and 533 nm, with the half-peak widths (FWHM) of 22.4, 21.6, 25.0, 11.7, 23.0, and 33.1 nm. The near-infrared peaks can be divided into two peaks centered at 1306 and 1361 nm, with half-peak widths of 80.2 and 107.1 nm, respectively. When the PS spherical diameter is 1.6 µm, the UV range exhibits multiple continuous, discrete peaks, resulting in larger half-peak widths36. As the particle size increases to 5.2 µm, only a peak appears in the UV range, causing a sharp decrease. With a further increase in particle size, the half-peak width increases again, indicating that as the particle size of PS@GQDs increases, the confinement effect decreases. The UV fitting peak center is at 464 nm, with a half-peak width of 61.3 nm. The near-infrared fitting peak centers are at 1277, 1216, 1307, 1356, and 1410 nm, with half-peak widths of 38.4, 37.6, 52.6, 56.7, and 55.6 nm. Generally, the UV spectrum indicates that GQDs contribute to the ultraviolet, while GQDs structures are mainly responsible for generating near-infrared. Strong coupling between PS spheres and GQDs structure could reduce the DBR periodicity.

On the other hand, by considering FWHMs, the TE/TM mode hybridization, the thermal deformations of the samples in the cluster and the agglomerates as well as the Schottky-Frenkel defects in plasmonic excitations, the absorbance formula indicates that the anomalous DBR absorbance is the function of the ratio \(\frac{{R}_{0}}{{R}_{\text{i}}}\), the wavelength \(\uplambda\) and the diameter d of GQDs , the filling rate \({f}_{c}\) and the thermal mass parameter \(\Lambda =\frac{{m}^{*}}{m}\), closely relating to the experimental UV-IR curves. The numerical simulations to the unconventional DBR absorbance can be thereby carried out under the appropriate parameter conditions.

Figure 6a shows the six-kind individual excitations of plasmon with different thermal mass parameters at the fixed GQD size d = 6 nm under the experimental parameter conditions listed in Table 1. It is found that as the filling rate and the thermal mass parameter increase, the UV peak decreases due to the decrease of quantum effect from black line to orange, respectively. Especially, the Vis-NIR spectra display the waveguide cutoff effects in the crossovers at the transitions. Figure 6b shows the individual excitation at the fixed mass parameter Λ = 0.8 for different GQD sizes. It is interesting that as the parameters such as \({f}_{c}\), \(\frac{{R}_{0}}{{R}_{\text{i}}}\) and d (< 6 nm)13,41, increase, the spectral oscillations are strong, majorly originated from localized enhanced GQD size effects on surfaces across plasmon resonances in the crossovers. It is observable that the peak red-shifts and FWHMs for plasmon excitations in the UV–Vis-NIR range are accordance with the experimental observations and the measurements in Figs. 5, 6 qualitatively.

It has been noted that the plasmon coherence superpositions and the phase separations for the unusual excitations in the ultraviolet-vis-near infrared regime at the structural transitions rely on the sample geometries in sizes and link to the two-point symplectic correlations. For instance, the UV peak at 250−280 nm was observed13,41, the peaks found in the 310−370 nm wavelength region could be related to π →π* transitions, originating from C=O bonds. As the mentioned above, the absorption intensity was adopted to calculate the concentrations of these nanoparticles in the solution14. The crossovers of the localized plasmon resonances on surfaces and photonic bands emerge near the percolation threshold about f_c=0.5 at the structural transitions, with the unconventional DBR reflectance absorbance.

Conclusion

In this study, the nano-sized GQDs, the micron-sized PS@GQDs and the multilayer colloidal crystals of PS@GQDs have been successfully synthesized in owing to the improved ultrasonic dispersion method and surface seed-mediated growth and self-assembling techniques, respectively. In the SEM/TEM images, Raman spectra and the ultraviolet-near infrared characterizations, it has been found that the tunable colloidal crystals exhibit the unconventional DBR scattering absorption that can be classed into the three bands, ranging from the ultraviolet-vis-near infrared, which is unlike the conventional DBR spectroscopy. The experimental measurements indicate that the modification of the PS surface significantly red-shifted in the ultraviolet-near infrared bands (300-1200 nm). The interference fringes of GQDs of various sizes with PS microspheres formed Bragg reflectors, creating plasmon resonant amplitudes below 1200 nm. Raman spectral studies show that the PS@GQDs multilayer colloidal crystals displayed Raman peaks of polystyrene with a slight red shift.

On the other hand, in the framework of the Mie-Maxwell-Garnett effective medium theories and the Gorkov-Eliashberg (GE) quantum theory, an effective dielectric function and the DBR absorption that rely on the multiscale geometries in sizes and the dielectric environments have been derived out, for the micron-sized PS @GQDs. The numerical simulations have been carried out. The unconventional DBR absorption phenomena can be understood as the novel form of the topological excitations at the structural transitions with the Gaussian symplectic symmetry in plasmon resonances and photon band crossovers near the percolation threshold. This is consistent with the experimental observations and the measurements.

Experiment

Fabrication of graphene quantum dots

To prepare GQDs dispersion using ultrasonic dispersion, take 0.0275 g of 1–3 layers hexagonal graphene powder, with a single-layer rate of 80%, product model CAS: 7782-42-5. Place the graphene powder into a 10 mL disposable plastic test tube and add 10 mL of N-methyl-2-pyrrolidone (NMP) to the graphene powder test tube. Repeat the above steps. Place the test tubes containing the graphene NMP solution into an ultrasonic machine with a power of 350 W (low power), maintaining a constant water temperature of 50–60℃. Ultrasonicate for 5 hours to disperse the graphene paper powder in NMP solution. Separate the undissolved precipitate from the GQDs/NMP solution, then continue ultrasonication for 90 hours. After ultrasonication, take out the saturated NMP solution of graphene paper for further use.

Fabrication of colloidal crystals

Prepare PS@GQDs microsphere colloidal crystals using the improved gravity sedimentation as follows: Take 5 mL of the prepared PS emulsion and place it in an Erlenmeyer flask. Add deionized water to the flask and put it on a magnetic stirrer. Add 0.665 mL of polyethyleneimine (PEI) with a concentration of 0.01 g/mL. The surface area of the modified polystyrene microspheres with 1 mL of PEI is 1.14×106 cm2. Stir for more than 1 hour. Remove the upper liquid layer, retain the lower emulsion, and perform centrifugation and washing operations with deionized water several times. Adjust the centrifugation speed and time to achieve separation. Remove any residues from the reaction process, and disperse the centrifuged emulsion in anhydrous ethanol in a test tube. This results in a modified polystyrene microsphere emulsion with a concentration of 0.0795 g/mL. Place all the obtained modified PS microsphere emulsions in an Erlenmeyer flask. Add anhydrous ethanol to the flask and place it on a magnetic stirrer. Add 1.5 mL of GQDs/NMP solution ultrasonicated for 95 hours. Stir for more than 1 hour. Control the volume ratio of GQDs/NMP solution to PS microsphere emulsion at 30:1.

Remove the upper liquid layer and perform centrifugation and washing operations with anhydrous ethanol several times. Remove any residues from the reaction process, and disperse the centrifuged emulsion in 10 mL test tubes with anhydrous ethanol. This results in PS@GQDs microsphere emulsion. Apply a 0.06 mm thick layer of the sample on a 3 cm × 3 cm ITO conductive glass, ensuring no bubbles on the glass surface to prevent subsequent leakage. Use a 1 cm × 1 cm square as a template groove in the center of the glass, cutting the groove perpendicular to the glass direction. Rinse the prepared template with tap water for 30 seconds. Finally, with anhydrous ethanol for 5 seconds, ensuring each liquid immerses the groove. Add 20 µL of PS@GQDs microsphere emulsion to one corner of the colloidal crystal template groove, ensuring the liquid does not flow out of the groove. Cover the petri dish and allow it to evaporate naturally. When the liquid level drops but has incompletely evaporated, continue adding PS@GQDs emulsion, ensuring the liquid does not flow out of the groove.

Characterizations

The surface and side thickness, including particle size and morphology, of colloidal crystal samples deposited on ITO conductive glass were studied using a scanning electron microscope (SEM, FEI, Netherlands, low vacuum mode resolution:

1.5 nm (10 kV, Helix detector), 1.8 nm (3 kV, Helix detector), magnification: 40x to 400,000x, acceleration voltage: 50V–30kV). Before SEM imaging, the colloidal crystal samples were sputter-coated with platinum for 12 minutes. The samples were analyzed at an acceleration voltage of 10 to 20 kV. The absorption spectra and 0-degree reflection spectra of colloidal crystal samples deposited on ITO conductive glass were studied using a UV-Vis-NIR spectrophotometer (SolidSpec-3700 UV, Shimadzu, Japan, wavelength range: 190–3300 nm, wavelength accuracy: UV/Vis ±0.1 nm, NIR ±0.5 nm, wavelength repeatability: UV/Vis ±0.02 nm, NIR ±0.03 nm, photometric accuracy: ±0.003 Abs (1 Abs), ±0.002 Abs (0.5 Abs), photometric repeatability: ±0.0005 Abs, resolution: ≤ 0.1 nm (UV/Vis); ≤ 0.2 nm (NIR), baseline drift: <0.0002 Abs/h (2 hours after power on), minimum wavelength step: 0.01 nm) with an integrating sphere and variable angle as optical accessories. The Raman spectra of colloidal crystal samples on ITO conductive glass were studied using a laser confocal Raman spectrometer (LabRAM HR800 Raman-1, Horiba JobinYvon, 532 nm light source).

Theory

According to the familiar optical theorem32, even with a lossy dielectric, the absorbance takes the form

$${\sigma }_{\text{abs}}=\frac{k}{{k}_{0}}\frac{\text{Im}\overline{\epsilon }}{|\overline{\epsilon }+2{|}^{2}}$$

Here, \(k\) is the number of wave, \({k}_{0}\) is the topological number of wave and \(\overline{\epsilon }\) is the dielectric function for an effective core shell structure. In the conventional approximations, such as the Mie-Maxwell–Garnett theories and the Gorkov-Eliashberg (GE) quantum theory, an average Mie’s dielectric permeability \(\overline{\epsilon }\) for the micron-sized PS@GQDs can be expressed as

$$\frac{\overline{\epsilon }}{{\epsilon }_{\text{e}}}=\frac{3{\epsilon }_{\text{i}}}{2{\epsilon }_{\text{m}}+{\epsilon }_{\text{i}}}-6\frac{{\epsilon }_{\text{m}}-{\epsilon }_{\text{i}}}{2{\epsilon }_{\text{m}}+{\epsilon }_{\text{i}}}\text{ln}\frac{{R}_{0}}{{R}_{\text{i}}}+\left[{\left(\frac{{R}_{0}}{{R}_{\text{i}}}\right)}^{3}-1\right]$$

and

$${\epsilon }_{\text{e}}=\frac{3{\epsilon }_{\text{a}}{\epsilon }_{\text{m}}}{2{\epsilon }_{\text{a}}+{\epsilon }_{\text{m}}}{\left\{\frac{3{\epsilon }_{\text{m}}}{2{\epsilon }_{\text{m}}+{\epsilon }_{\text{i}}}\frac{2{\epsilon }_{\text{a}}+{\epsilon }_{\text{i}}}{2{\epsilon }_{\text{a}}+{\epsilon }_{\text{m}}}+\left[{\left(\frac{{R}_{0}}{{R}_{\text{i}}}\right)}^{3}-1\right]\right\}}^{-1}$$

Here, \(\overline{\epsilon }\) is the function of the ratio \(\frac{{R}_{0}}{{R}_{\text{i}}}\) between the internal radius \({R}_{\text{i}}\) and the outside \({R}_{0}\) of the core–shell structures, relying on the dielectric environments \({\epsilon }_{\text{a}}\simeq 1\) such as in air or water and the PS insulator \({\epsilon }_{\text{i}}\simeq {\epsilon }_{\text{s}}=2.5\). Furthermore, the GQD shell dielectric permeability ϵm approaches to the Maxwell–Garnett formula33,\({\epsilon }_{\text{m}}={\epsilon }_{\text{s}}\frac{1-{f}_{\text{c}}+3{f}_{\text{c}}{\epsilon }_{\text{c}}/\left({\epsilon }_{\text{c}}+2{\epsilon }_{\text{s}}\right)}{1-{f}_{\text{c}}+3{f}_{\text{c}}{\epsilon }_{\text{s}}/\left({\epsilon }_{\text{c}}+2{\epsilon }_{\text{s}}\right)}\). Due to the dipole–dipole interactions, the impurities and the structures, such as fractal and the percolation geometries, are characterized by the insulator \({\epsilon }_{i}\) and the filling rate \({f}_{c}\) of the cluster of GQDs with the diameter, d. By considering the effects of the depolarizing field and the Fano resonance, the permeability of GQD cluster,\({\epsilon }_{\text{c}}=\frac{2{\epsilon }_{\text{a}}-1+\frac{8\pi }{3}{\chi }_{\text{e}}}{1-\frac{4\pi }{3}{\chi }_{\text{e}}}\). The electronic susceptibility \({\chi }_{\text{e}}\) links to the GE susceptibility \({\chi }_{\text{GE}}\) through the relation,\({\chi }_{\text{e}}=\frac{{\chi }_{\text{GE}}}{1+\frac{4\pi }{3}{\chi }_{\text{GE}}}\). The GE susceptibility34 is given by \({\chi }_{\text{GE}}=\frac{1}{20\pi }\frac{{e}^{2}}{\Delta d}+\frac{139\Lambda A}{1200{\pi }^{2}{k}_{\text{f}}{a}_{\text{B}}}\), where \(e\) is the charge of electron and \(\Lambda =\frac{{m}^{*}}{m}\) is the thermal mass parameter of electron, including Schottky-Frenkel excitations31. The level spacing \(\Delta =\frac{12\pi {a}_{\text{B}}{e}^{2}}{g\Lambda {k}_{\text{f}}{d}^{3}}\) is the inverse of the density of states (DOS) per spin near the tunable Fermi level of GQDs and \(g=1+\frac{3{\pi }^{2}}{2{k}_{\text{f}}d}+\frac{2}{{\left({k}_{\text{f}}d\right)}^{2}}\) is a modified DOS factor. In such situations, strong spin-orbital couplings of GQDs and the TE/TM mode hybridization of PS@GQDs cluster structures link to the frequency-dependent two-point correlation function in the Gaussian symplectic ensemble. It has been noted that in a lossless dielectric, the optical theorem yields the total cross-section, equal to the total scattering cross, \({\sigma }_{\text{abs}}\)=\({\sigma }_{sc}\). The DBR anomalies of PS@GQDs can arise in plasmon resonances and photonic band crossovers at the topological transitions37,38, near the percolation threshold of GQD cluster, fc = 0.5. In the limit of Ri = R0, the dielectric permeability \(\overline{\epsilon }\) is independent of \(\frac{{R}_{0}}{{R}_{\text{i}}}\). In this case, the DBR can be adjusted. This gives the thin shell limits of \(\Delta \text{R}\)=d and \(\frac{\text{d}}{{R}_{\text{i}}}\ll 1\), consistent with the experimental observations and the measurements.