# Tunable Fano Resonances in an Ultra-Small Gap
## 2 Experimental Structure and Model Parameters  
A schematic of the NCoM structure is depicted in Figure 1a. It consists of a single silver nanocube and a silver film. An aluminum oxide (Al\({}_{2}\)O\({}_{3}\)) spacer layer lies between the nanocube and the silver film. Figure 1b is a cross section of a NCoM structure prepared on a silicon substrate, and Figure 1c is a transmission electron microscope (TEM) image of silver nanocubes that reveals their cubic shape. The radius of the rounded corner is defined as \(r\), and the face-to-face width of each nanocube is defined as \(d\). The NCoM structure was fabricated in a bottom-up process. Firstly, an 80-nm-thick silver film was coated on a silicon substrate via electron beam evaporation. Then, the Al\({}_{2}\)O\({}_{3}\) spacer film was deposited on the silver film via atomic layer deposition at 100 \({}^{\circ}\)C. Finally, a silver nanocube solution was dropped onto the Al\({}_{2}\)O\({}_{3}\) film, which was rinsed with deionized water after 1 min to remove excess nanocubes. The NCoM sample was then blown dry with nitrogen gas. The silver nanocubes were uniformly monodispersed on the Al\({}_{2}\)O\({}_{3}\)/silver film.  
The experiments were performed at the single-particle level with a dark-field scattering microscope (Olympus, BX 53). The scattering spectrum is obtained by irradiation with a halogen lamp without any polarizer added. A dark-field objective (Olympus, 100\(\times\), NA = 0.9, MPLFLN) was used to illuminate the samples and collect the scattered light, which was sent to a CCD(charge coupled device) (Qimaging, QICAM B series) or a spectrometer (Andor, SR303i). All the experiments were performed at room temperature. Figure 1d is a dark-field image of the NCoM structure, which is likely a Laguerre Gaussian 01 donut [37]. Since the average distance between the individual nanocubes was greater than 3 \(\upmu\)m, interactions among them were negligible.  
Numerical calculations were performed with a commercial finite difference time domain (FDTD) Solutions 8.19.1584, which was developed by Lumerical Solutions. All the sharp corners (edges) of the nanocubes are slightly smoothed by the spherical (cylindrical) surface, consistent with experimental observations. The silver nanocube and its surrounding space are divided into 0.5 nm meshes. The incident light illuminates the metal surface vertically, and the polarization of the electric field is along the x-axis. The refractive index of silver is referred from the commonly used data from [PERSON] and [PERSON] [42]. As the surface of each nanocube is covered by surfactant molecules (Polyvinylpyrrolidone, PVP), the nanocubes are located 1 nm above the Al\({}_{2}\)O\({}_{3}\) film for the simulation. The specific structural model parameters are listed in Table 1.  
Figure 1: (a) 3D diagram of the NCoM structure, where silver nanocubes are randomly distributed on the Al2O3 film; (b) Cross-section diagram of the NCoM structure prepared on a silicon substrate, consisting of silver nanocubes on a silver substrate, separated by the Al2O3 film; (c) Transmission electron microscope (TEM) image of the silver nanocube. The insert is a cross section of a single silver nanocube: r is the radius of the rounded corner size, and d is the face-to-face width of the silver nanocube; (d) Dark-field optical image of the silver nanocubes.