## Introduction

Graphene is a promising plasmonic material with superior properties that distinguish it from conventional noble metals1,2, including relatively low optical loss, high spatial confinement, and tunable plasmonic resonances. Graphene-based plasmonic devices have shown potential in broad applications, including optical biosensing3, optical communications4, photodetectors5, and plasmonic metamaterials6. In particular, desired plasmonic resonances are easily excited in lithographically patterned graphene structures4,6,7,8,9,10,11,12,13,14 using a far-field coupling method. However, such structural patterns in graphene are not reconfigurable, thus fixing their resonance wavelengths. Although one can tune the resonance wavelength of graphene through electrical gating7,11,15, it is challenging to achieve broadband tunability across the near- to mid-infrared wavelength ranges. While graphene grating structures have been proposed for on–off switching and plasmonic modulation16,17,18,19, post-fabrication reconfiguration of plasmonic structures has not yet been realized.

It has recently been demonstrated that mechanical crumpling of graphene can be used to create different surface structures while maintaining reversibility20,21,22. However, the potential of crumpled graphene structures for reconfigurable plasmonic materials has not been explored. In this work, we report on the use of mechanically reconfigurable crumpled graphene structures to realize strong plasmonic resonances with broadband tunability. We introduce a resonant electrical inductor–capacitor (LC)-circuit model to describe the characteristics of plasmonic resonances in the crumpled graphene. By varying the geometry of the crumpled graphene structures, we show a tunable spectral range for plasmonic resonances that is fivefold broader than that achieved by conventional electrical gating. Our results show that mechanical reconfiguration of crumpled graphene serves as a new way to manipulate strong plasmonic resonances over a broad spectral range.

## Materials and methods

### Numerical simulations

We performed full-wave simulations using the finite element method (COMSOL Multiphysics, wave optics module) to investigate the plasmonic resonances of crumpled graphene structures. We modeled graphene as a two-dimensional surface current tangential to the crumpled structure: Js = σEt, where Js is the surface current, σ is the optical conductivity of graphene, and Et is the tangential component of the electric field to the graphene surface23,24. We used a mobility value of 10,000 cm2/(V·s), which is achievable for crumpled graphene based on the reported range of mobilities (μ) for flat graphene15 from ~1000 cm2/(V·s) for chemical vapor deposition grown graphene to 230,000 cm2/(V·s) for suspended exfoliated graphene. Moreover, the mobility of wrinkled graphene was shown to be similar to that of flat graphene25,26. For the optical absorption/extinction spectra of uniaxially and biaxially crumpled graphene in Figs. 13, we performed absorption/transmission calculations with periodic boundary conditions imposed on the respective crumpling directions. The optical extinction spectra were obtained by calculating 1−T/T0, where T and T0 are the transmittance values with and without crumpled graphene, respectively. To investigate substrate-induced effects on plasmonic resonances in Fig. 3a, a silicon oxide (SiO2) substrate27 was used as a model material. In Fig. 4a, we obtained the extinction cross-section for a normal-incident electromagnetic field by integrating over the scattered light power and optical loss in graphene. In Fig. 4b, c, we calculated the enhancement of the radiative decay rates by taking the ratio of the radiated light power from a dipole emitter with a crumpled graphene flake to that without the crumpled graphene flake. In Fig. 4, we applied the perfectly matched layer for all boundaries of the calculation domain to reduce reflections from the boundaries.

### Optical conductivity of graphene

We calculated the optical conductivity of graphene (σ) for varying Fermi energy (EF) and carrier mobility (μ) values of graphene at a constant temperature of 300 K using a random phase approximation method23,24,28,29. The optical conductivity is expressed by σ(ω) = σintra(ω) + σinter(ω), where σintra(ω) and σinter(ω) are the intraband and interband conductivities, respectively23. They are expressed as below, where ω is the frequency of the incident light, e is the charge of an electron, τ is the Drude relaxation rate, T is the temperature, kB is the Boltzmann constant, and is the reduced Planck constant. EF is the Fermi energy, determined by EF = vf(πn)1/2, where vf is the Fermi velocity of electrons (~106 m/s) and n is the carrier density of graphene. The Drude relaxation rate τ is determined by τ = µEF/evf2, where µ is the carrier mobility of graphene.

$$\sigma _{{\mathrm{intra}}}\left( \omega \right) = \frac{{2e^2\omega _T}}{{\pi \hbar }}\frac{i}{{\omega + i\tau ^{ - 1}}}\log \left[ {2\cosh \left( {\frac{{\omega _{\mathrm{F}}}}{{2\omega _T}}} \right)} \right]$$
(1)
$$\sigma _{{\mathrm{inter}}}\left( \omega \right) = \frac{{e^2}}{{4\hbar }}\left[ {H\left( {\frac{\omega }{2}} \right) + i\frac{{2\omega }}{\pi }{\int}_0^\infty {\frac{{H\left( {\frac{{\omega \prime }}{2}} \right) - H\left( {\frac{\omega }{2}} \right)}}{{\omega ^2 - \omega {\prime}^2}}d\omega \prime } } \right]$$
(2)
$$H(\omega ) = \frac{{\sinh (\omega /\omega _T)}}{{\cosh (\omega _{\mathrm{F}}/\omega _T) + \cosh (\omega /\omega _T)}}$$
(3)

where ωF = EF/ and ωT = kBT/.

## Results and discussion

### Plasmonic resonances of crumpled graphene structures

To study the plasmonic resonances of the crumpled graphene structures, we modeled crumpled graphene as a continuous sinusoidal structure with geometrical parameters, including crumple wavelength (λc) and crumple height (h) (upper inset of Fig. 1a). First, we performed full-wave optical simulations (see Materials and methods) to investigate the far-field spectral response (i.e., optical absorption spectra) of free-standing uniaxially crumpled graphene (Fig. 1a). The incident electric field ($$\overrightarrow E _{\mathrm{ext}}$$) is parallel and perpendicular to the crumpling direction ($$\overrightarrow \lambda _{\mathrm{c}}$$) ($$\overrightarrow E _{\mathrm{ext}}$$||$$\overrightarrow \lambda _{\mathrm{c}}$$ and $$\overrightarrow E _{\mathrm{ext}} \bot \overrightarrow \lambda _{\mathrm{c}}$$, respectively). Our simulation result including the consideration of strain effects on crumpled graphene30,31,32 was very similar to the result obtained without consideration of strain effects (Fig. S1). In the optical absorption spectrum, we observed multiple resonance peaks, including the first- and higher-order (second- and third-order) plasmonic modes (lower insets in Fig. 1a) for $$\overrightarrow E _{\mathrm{ext}}$$||$$\overrightarrow \lambda _{\mathrm{c}}$$, whereas no resonance peak was observed for $$\overrightarrow E _{\mathrm{ext}} \bot \overrightarrow \lambda _{\mathrm{c}}$$. These far-field resonance peaks for $$\overrightarrow E _{\mathrm{ext}}$$||$$\overrightarrow \lambda _{\mathrm{c}}$$ are attributed to resonant graphene plasmons confined in the crumpled graphene structures9,16,33. The most efficient coupling of the incident light to the graphene plasmon is observed in the peak of the maximum optical absorption (Fig. 1a). In subsequent investigations, we focus on this strongest plasmonic resonance.

We further investigated plasmonic resonances in crumpled graphene for various λc and h. First, we observed the optical absorption and extinction spectra for different aspect ratios of crumple height to wavelength (h/λc) at a constant λc of 250 nm (Fig. 1b and Fig. S2). The plasmonic resonance wavelength (λres) redshifted from ~4.5 to ~11.3 µm with increasing h/λc from 0.25 to 2.0. The optical absorption and extinction (σabs and σext) also increased with higher h/λc from 0.25 to 1.0 but showed no significant change from h/λc = 1.0 to 2.0 (Fig. S2a, c, e). Next, we varied λc from 50 nm to 1 μm with a fixed aspect ratio (h/λc = 1) and observed redshifts for λres from ~3.2 to ~13.8 µm and an increase in σabs and σext from ~0.12 to ~0.41 and from ~0.14 to ~0.50, respectively (Fig. S2b, d, f). Moreover, near-field distributions for graphene plasmons varied with different h/λc values (Fig. 1c). An enhanced near-field intensity near the apex and valley regions was manifested with increasing h/λc. We observed a maximum near-field intensity enhancement of ~402 in the apex and valley regions of crumpled graphene structures at h/λc= 1. Taken together, these results demonstrated the tunability of both far- and near-field plasmonic resonances by the reconfiguration of crumpled graphene structures.

### Analytical description of the plasmonic resonance in crumpled graphene structures

To describe the plasmonic resonance in crumpled graphene structures, we introduced a resonant LC-circuit model based on the electric field and current distributions (Fig. 2a). An effective inductance Leff and effective capacitance Ceff are used to account for the characteristics of the current and charge induced by the graphene plasmons, respectively34,35. By using the crumpled structure parameters, including λc and h, as well as the electronic properties of graphene, we derived Leff and Ceff as follows:

$$L_{\mathrm{eff}} = \frac{{\pi \hbar ^2}}{{e^2E_{\mathrm{F}}}}\lambda _{\mathrm{c}}{\mathrm{,}}\,C_{\mathrm{eff}} = \frac{{\varepsilon _0}}{{2\alpha }}\ln \left[ {1 + \left( {1 + e^{ - \alpha }} \right)} \right]$$
(4)

where is the reduced Planck constant, e is the elementary charge, ε0 is the permittivity in vacuum, and α = π − 2tan‒1(2h/λc) is the curvature factor for the crumpled structures. By using Leff and Ceff, we derived the plasmonic resonance wavelength (λres) of the crumpled graphene expressed as λres = 2πc(LeffCeff)1/2 (see SI for detailed derivation).

To validate our LC-circuit model, we compared the value for λres predicted by the LC-circuit model with that predicted by numerical simulations. With varying λc from 50 nm to 1 μm and h/λc from 0.5 to 2, the λres obtained by the full-wave simulations (dots) agreed with that of our LC-circuit model (solid curves) (Fig. 2b). In contrast, conventional analytical models account for only crumple wavelengths of a periodically modulated graphene sheet16,17,18,19 and cannot predict changes in λres in response to varying h/λc (dashed curve in Fig. 2b). The Ceff changes with varying h/λc (i.e., change of α), leading to a shift in λres. This implies that controlling the charge interactions on confronting graphene surfaces by varying h/λc enables the tunability of λres across the near- to mid-infrared wavelength ranges. The mechanically reconfigurable crumpled graphene structures are thus an excellent platform for broadband tunability of plasmonic resonances.

To compare the wavelength tunability of the plasmonic resonances by mechanically reconfigurable crumpled graphene structures to that achievable by conventional electrical gating, we studied the electrical tunability of the plasmonic resonances in uniaxially crumpled graphene by varying the electronic properties of graphene such as the Fermi energy EF and carrier mobility µ (Fig. 2c). In our simulation, λres blueshifted from ~7.6 to ~3.9 µm with increasing EF from 0.24 to 0.84 eV (Fig. 2c), showing the relation λres EF‒1/2 as predicted by our LC-circuit model (a solid curve in Fig. 2c). Additionally, the σabs increased with higher μ (inset of Fig. 2c). Most notably, the tunable range of the plasmonic resonance wavelengths (∆λres) for varying EF was ~3.7 µm, while ∆λres for varying λc was ~20.1 µm (∆λres = λres,maxλres,min in Fig. 2b). These results show broad spectral tunability from the mid- to near-infrared by the mechanical reconfiguration of crumpled graphene structures, which allows for a new tuning knob combined with conventional electrostatic gating.

### Substrate and crumple structural effects on plasmonic resonances

Next, we investigated substrate-induced effects on the plasmonic resonances in uniaxially crumpled graphene structures. Figure 3a shows the optical absorption spectrum of free-standing crumpled graphene in comparison to that of crumpled graphene on an undulating substrate (for a comparison to crumpled graphene on a flat substrate, see Materials and methods and Fig. S3a). The λres of the crumpled graphene on the undulating substrate was redshifted compared to that of the free-standing crumpled graphene (5.065 µm vs. 4.457 µm). The redshift of λres is attributed to confinement of resonant plasmons exclusively in the apex of the crumpled graphene on the undulating substrate (the upper left inset of Fig. 3a). It is notable that the field intensity distribution profiles in the apex and valley regions are different because of the broken symmetry of the plasmonic resonance modes between the apex and valley due to the undulating subtrate9,36. The σext and quality factor (Q-factor) were enhanced approximately twofold for the undulating substrate compared to the free-standing crumpled graphene (14.0 vs. 7.6% and 63.8 vs. 26.1) (Fig. S3b). However, the crumpled graphene supported on a flat substrate exhibited plasmonic resonances similar to the free-standing graphene (λres = 4.488 µm vs. 4.457 µm, Q-factors = 26.2 vs. 26.1, and σext,max = 6.9 vs. 7.6%) (Fig. S3a, b). These results show that the refractive index of the substrate enables control of the charge interactions on confronting graphene surfaces. Therefore, rational choice and design of substrates enables further modulation of plasmonic resonances in mechanically reconfigurable crumpled graphene structures.

To further explore the shape-induced plasmonic resonance of crumpled graphene, we investigated plasmonic resonances in biaxially crumpled graphene (Fig. 3b). We studied a biaxially crumpled graphene structure with the same crumpled wavelengths in both crumpling directions (λc,x = λc,y) (the bottom inset of Fig. 3b). The biaxial crumpling of graphene enabled a twofold stronger coupling of the incident light to plasmonic resonance modes (i.e., higher σext ~1 vs. ~0.5) (Fig. S4b) and an enhancement of the near-field intensity by a factor of 1.52 ( = (60/40)2) compared to uniaxially crumpled graphene (the upper left insets of Fig. 3b vs. the inset of Fig. S4a). Moreover, the biaxially crumpled graphene showed strong near-field enhancements on the slope (the upper left inset of Fig. 3b), whereas the uniaxially crumpled graphene exhibited strong near-field enhancements in the apex and valley regions (the inset of Fig. S4a). With varying h/λc from 0.5 to 2 for a constant λc, the biaxially crumpled graphene yielded one third the tunable wavelength range of the plasmonic resonance (∆λres ~ 1.7 µm) for the uniaxially crumpled graphene (∆λres ~ 6.1 µm) (Fig. S4a). Notably, biaxially crumpled graphene exhibited optical absorption reaching up to ~0.46 (Fig. 3b) and Q-factors on the order of those in uniaxially crumpled graphene (Fig. S4c). The absorption spectra for biaxially crumpled graphene showed the same plasmonic resonance peak wavelengths at different mobilities, including at 1000, 4000 and 10,000 cm2/(V·s) (Fig. S5a). The Q-factors increased with an increase in carrier mobility (Fig. S5a; the inset of Fig. 3b vs. Fig. S5b). The biaxially crumpled graphene shows a smaller range for wavelength tunability than the uniaxial case but shows enhanced far-field coupling of the incident light for inducing plasmonic resonances, which can be useful for ultrasensitive plasmonic detection.

### Plasmonic resonances of finite-area crumpled graphene flakes

Since our studies up to this point have only dealt with infinite sheets of graphene, we explored finite-area biaxially crumpled graphene flakes patterned into hundreds of nanometer-size squares. Such crumpled graphene flakes may find use in bio-imaging and sensing. Figure 4a shows the extinction cross-section spectra for a free-standing biaxially crumpled graphene flake with three periods of crumples in both the x and y directions. Plasmonic resonance peaks were observed for various values of h/λc. The near-field distributions at the plasmonic resonance peaks show that resonant plasmons were strongly confined to the center of the crumpled graphene flake (the insets of Fig. 4a). The biaxially crumpled graphene flake exhibited near-field intensity enhancements of ~1 × 104, compared to ~1.5 × 103 for patterned graphene nanostructures, such as nanodisk dimers37. We note that the extinction cross-section spectra with μ = 10,000 cm2/(V·s) showed the same plasmonic resonance peak wavelengths as those with lower mobilities, including at 1000 and 4000 cm2/(V·s) (Fig. S6a). Crumpled graphene flakes may provide several benefits, including enhanced coupling with an external light and strong near-field enhancements.

Finally, to investigate the light–matter interactions38,39 of crumpled graphene flakes, we introduce a dipole emitter placed 40 nm above the center of a free-standing biaxially crumpled graphene flake. The orientation of the dipole moment for the emitter is parallel to the x crumpling direction (the inset of Fig. 4b). To characterize the decay rate enhancement by crumpled graphene flakes, we obtained radiative decay rates (Γrad) and total decay rates (Γ), which were normalized by those of the emitter in free space without the crumpled graphene flake (Γ0). Figure 4b shows the radiative decay rate spectra for various values of h/λc. We observed significant enhancements in the radiative decay rates, up to three orders of magnitude, at the plasmonic resonance peaks (Fig. 4b) as well as maximum Purcell factors (Γ/Γ0) of ~1.6 × 105 (Fig. S7). Our maximum Purcell factor was similar to that previously reported for graphene disks40. The radiative decay rates at λres increased by an order of magnitude from 0.6 × 103 to 5.6 × 103 with increasing h/λc from 0.5 to 1. These results show that the reconfiguration of crumpled graphene flakes enables tunability for the decay rate enhancements. We note that the radiative decay rate spectra with μ = 10,000 cm2/(V·s) showed the same plasmonic resonance peak wavelengths as those with a lower mobility of 1000 cm2/(V·s) (Fig. S6b). We also observed a change in the radiative decay rate (Fig. 4c) and total decay rate (Fig. S8) for various vertical distances from the emitter to the crumpled graphene flake between 0 and 120 nm at the plasmonic resonances. The radiative decay rates showed enhancements of three orders of magnitude over a wide range of vertical distance between 20 and 110 nm. This suggests that crumpled graphene flakes can be used to perform robust molecular sensing against the locational uncertainty of molecules. The plasmonic resonances at mid-infrared wavelengths of ~6 µm together with the large Purcell factors as well as the tunability of the plasmonic resonances show potential for ultrasensitive plasmonic detection of molecules41.

## Conclusions

In summary, we have demonstrated, for the first time, mechanically reconfigurable crumpled graphene exhibiting broadband tunability of strong plasmonic resonances from the mid- to near-infrared. The reconfigured crumpled graphene structures, with varying crumple wavelengths and heights, enabled the manipulation of plasmonic resonances over a tunable wavelength range five times broader than that afforded by conventional electrical tuning of graphene. We have also demonstrated efficient excitement of graphene plasmons in crumpled graphene structures by far-field coupling of light as well as strong confinement of the excited plasmons in crumpled graphene. The strong plasmonic resonances enabled optical absorption enhancements of up to ~0.46 as well as high near-field enhancements on the order of 1 × 104 for biaxially crumpled graphene flakes. Furthermore, we showed strong light–matter interactions for the crumpled graphene flakes, which enabled large decay rate enhancements to yield a maximum Purcell factor of ~1.6 × 105. We believe that our crumpled graphene structures, with strong and broadly tunable plasmonic resonances in the near- to mid-infrared, can find broad applications1,42,43, including photonic and optoelectronic devices, ultrasensitive chemical and biological sensing, photovoltaic devices, and spectroscopy.